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K TO 12 GRADE 5 LEARNER’S MATERIAL IN MATHEMATICS (Q1-Q4)

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Lesson 1: Visualizing Numbers up to 10 000 000 with emphasis on
numbers 100 001 – 10 000 000
A group of doctors donated a ...
Use number discs to show the following numbers.
1. 10 345 789
2. 389 456
3. 4 234 789
4. 123 098
5. 4 456 678
Read the fol...
Lesson 2 : Reading and Writing Numbers up to 10 000 000 in Symbols
and in Words
EXPLORE AND DISCOVER!
The Department of Ag...
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K TO 12 GRADE 5 LEARNER’S MATERIAL IN MATHEMATICS (Q1-Q4)

  1. 1. Lesson 1: Visualizing Numbers up to 10 000 000 with emphasis on numbers 100 001 – 10 000 000 A group of doctors donated a total of 234 534 kilograms of rice to the earthquake victims. Can you imagine how big the number 234 534 is? One way you can imagine is to think of discs to represent the number shown below. Two 100 000 Three 10 000 Four 1 000 Five 100 Three 10 Four 1 200 000 30 000 4 000 500 30 4 234 534 What number is represented by these number discs? Write your answer in your notebook. 100 000 100 000 10 000 10 000 10 000 1 000 1 000 1 000 1 000 100 100 100 100 100 10 10 10 1 1 1 1 100 000 100 000 10 000 10 000 100 000 1 000 1 000 1 000 1 000 100 100 100 1 000 10 000 10 10 100 1 1 10 10 Get Moving! Explore and Discover!
  2. 2. Use number discs to show the following numbers. 1. 10 345 789 2. 389 456 3. 4 234 789 4. 123 098 5. 4 456 678 Read the following items. Then, write your answer to each item in your notebook. 1. There were 345 895 children and adults who watched the football game. Draw number discs to show the given number. 2. How will you show the number 2 345 789 using number discs? 3. There were 1 234 897 tree seedlings distributed to the barangays by the Department of Environment and Natural Resources. Draw number discs to show the given number. 4. Mrs. Angeles bought some appliances worth Php 156 907. Represent this amount using number disc. 5. Which number is 100 000 smaller than 234 456? a. 134 456 b. 334 456 c. 34 456 d. 434 456 Keep Moving! Apply Your Skills!
  3. 3. Lesson 2 : Reading and Writing Numbers up to 10 000 000 in Symbols and in Words EXPLORE AND DISCOVER! The Department of Agriculture distributed 1 456 897 eggplant seedlings in some farmers in Region IVA. How do you read and write the number 1 456 897 in words and in symbol? The number 1 456 897 is read as “ one million four hundred fifty-six thousand eight hundred ninety-seven”. In symbol it is 1 456 897. GET MOVING! A. Write the following numbers in words. 1. 10 345 897 2. 7 456 902 3. 234 713 4. 678 345 5. 1 097 234 B. Rewrite the numbers correctly by putting a space in the correct places in column A. In column B, write the numbers in words. Number Column A Column B 1234678 6578234 10234123 123987 23908
  4. 4. KEEP MOVING! Write the numbers in symbols. 1. Three million seven hundred eighty-six thousand four hundred 10 2. Five hundred ten thousand twenty- six 3. Ten million two hundred seven thousand one hundred seven 4. Six million eighty-three 5. Four million seven hundred twenty thousand three hundred eight APPLY YOUR SKILLS! A. 1. What is largest 7- digit number having different digits? Write it in symbols and in words ___________________________________ 2. What is the number next to 234 456? Write it in symbol and in words ___________________________________ 3. What is the smallest 6-digit number having different digits? Write it in symbol and in words ___________________________________ 4. What is the number before 1 567 678? Write it in symbol and in words ___________________________________ 5.What is the number between 890 789 and 890 791? Write it in symbol and in words ____________________________________
  5. 5. 1 Lesson 3 : Rounding Numbers to the Nearest Hundred Thousands and Millions EXPLORE AND DISCOVER! The circumference of the earth is 40 053 840 meters. About how many million meters is the circumference of the earth? You can find the answer by rounding 40 053 840 to the nearest millions. Study these examples. Number Rounded to Millions Hundred thousands 3 456 789 3 000 000 3 500 000 14 578 907 15 000 000 14 600 000 2 389 897 2 000 000 2 400 000 1 345 890 1 000 000 1 300 000 7 567 079 8 000 000 7 600 000 GET MOVING! A. Round each number to the place value of the underlined digit. 1. 12 234 556 ______________________ 2. 3 456 871 ______________________ 3. 5 098 678 ______________________ 4. 9 789 123 ______________________ 5. 6 234 189 ______________________ B. Complete the table. Number Round to the nearest Millions Hundred thousands 4 496 709 13 508 807 5 889 897 6 045 890 7 527 099
  6. 6. 2 KEEP MOVING! A. Encircle the numbers that can be rounded to the given number. 1. 8 900 000 8 923 567 8 984 456 8 908 671 8 938 123 8 971 109 2. 7 000 000 6 821 507 7 284 471 7 578 653 6 968 123 7 771 178 3. 4 500 000 4 493 517 4 381 426 4 508 671 4 561 126 4 478 120 4. 3 200 000 3 194 100 3 283 401 3 221 611 3 138 170 3 201 156 5. 6 000 000 5 622 160 6 904 431 5 998 601 6 868 173 6 001 101 B. Round to the highest place value. 1. 345 789 ______________________________ 2. 1 563 890 ______________________________ 3. 3 213 456 ______________________________ 4. 9 912 123 ______________________________ 5. 312 465 ______________________________
  7. 7. 3 APPLY YOUR SKILLS! A. Complete the table. Greatest Number Rounded Number Least Number 3 000 000 2 400 000 10 200 000 6 300 000 1 000 000 B. Read the problem and complete the table below. Mrs. Angeles bought the following cars for her 5 children. Honda Civic – Php 1 289 980 Limousine - Php 5 561 003 Ferrari - Php 8 123 315 Jaguar - Php 4 123 980 BMW - Php 3 901 312 Copy the price of each item. Then, round each to the nearest hundred thousand and millions. Item Price Hundred Thousands Millions Honda Civic Php 1 289 980 Limousine Php 5 561 003 Ferrari Php 8 123 315 Jaguar Php 4 123 980 BMW Php 3 901 312
  8. 8. Lesson 4: Using Divisibility rules for 2, 5 and 10 to find common factors Explore and Discover! Jaira has 70 collected stamps. Can she shared that equally to 2 friends? 5 Friends? 10 friends? To solve the problem, you need to know if 2 5 and 10 are factors of 70 or if 70 is divisible by 2 5 and 10. To see if the number is divisible by 2, 5 or 10 ,test by checking the ones digit DIVISIBILITY TEST 70 By 2: Is the ones digit 0,2,4,6 or 8? YES By 5: Is the ones digit 0 or 5? YES By 10: Is the ones digit 0? YES Get Moving! A. Put a check under each column to identify whether each number is divisible by 3, 6 or 9. 2 5 10 54180 912 2700 5605 568 3765 233 80
  9. 9. B. Determine whether the first number listed is divisible by the second number. Write Yes or No on the blank. Yes or No 1. 45 ; 2 ____________ 2. 5080 ; 5 ____________ 3. 90 ; 5 ____________ 4. 1180 ; 10 ____________ 5. 6998 2 ____________ Keep Moving! Underline the answer that makes each sentence correct. 1. Twenty is (divisible/not divisible) by ten. 2. Three hundred is (divisible/not divisible) by five. 3. Nine hundred ninety is (divisible/not divisible) by two. 4. One hundred six is (divisible/not divisible) by five. 5. Ten thousand four hundred two is (divisible/not divisible) by two. Apply Your Skills! Use divisibility rules to help you solve the following problems. 1. Frances has a collection of 672 stamps. She wants to place the stamps in 2 envelopes .Can she place the same number of stamps in each envelope? 2. The number of books in Karla’s collection is divisible by 2,5 and 10. She has more than 11 books and fewer than 25 books. How many books does Karla have?
  10. 10. Lesson 5: Using Divisibility rules for 3, 6 or 9 to find common factors Explore and Discover! Nena’s garden has 414 bougainvillea plants. She wants to arrange them in either rows of 3, 6 or 9. Which are the possible arrangements of the plants? To solve the problem, you need to know if 3 6 or 9 are factors of 414 or if 414 is divisible by 3, 6 or 9. Recall the rules:  Divisible by 3: sum of digits of the number is divisible by 3 414= 4+1+4=9, 9 is divisible by 3,therefore 414 is divisible by 3  Divisible by 6: number is divisible by both 2 and 3 414 is divisible by 2 and 3, therefore 414 is divisible by 6  Divisible by 9: sum of the digits of the number is divisible by 9 414= 4+1+4=9, 9 is divisible by 9, therefore 414 is divisible by 9 Get Moving! A. Put a check under each column to identify whether each number is divisible by 3, 6 or 9. 3 6 9 528 1242 3456 624 852 2547 324 120 B. Write the letter of the correct answer on your notebook. 1. Which of the following is divisible by 3? a.11 b.36 c.23 2. Which of the following is divisible by 9? a. 108 b.100 c.124 3. Which of the following is divisible by 6? a. 71 b.134 c.234 4. 3 is a factor of a.272 b.153 c.92 5. 6 is a factor of a.84 b.75 c.53
  11. 11. Keep Moving! A . Tell whether each number is divisible by 6 or not. 1.906 2.1322 3.4714 4.5166 5.84510 B. Tell whether each number is divisible by 9 or not. 1.89019 2.4617 3.48753 4.1404 5.75834 Apply Your Skills! Answer the following questions and write the answers on your notebook. 1. Are all numbers divisible by 9 also divisible by 3? 2. How many numbers between 50 to 100 are divisible by 3? 3. Marjorie wants to arrange her 186 books in three rows. Would it be possible?
  12. 12. Lesson 5: Using Divisibility rules for 4, 8, 12 and 11 to find common factors Explore and Discover! The school auditorium has 372 chairs. Mrs.Cruz, the principal wants to align them in either rows of 4,8,12 or 11. Which are the possible alignments of the chairs? To solve the problem, you need to know if 4, 8,12 or 11 are factors of 372 or if 372 is divisible by 4, 8, 12 or 11. Recall the rules:  Divisible by 4: if the last two digits form a number that is divisible by 4.Also, numbers ending in two zeros are divisible by 4 372→ 72 ÷ 4 = 18, therefore 372 is divisible by 4,chairs can be aligned by 4  Divisible by 8: if the number formed by the last 3 digits is divisible by 8.Also, a number ending in three zeros are also divisible by 8 372 ÷4 = 93,therefore 372 is divisible by 8,chairs can be aligned by 8  Divisible by 12: if the sum of the digits of the number is divisible by 2 and 3 372= 3+7+2=12, 12 is divisible by 2 and 3, therefore 372 is divisible by 12  Divisible by 11:if the sum of the digits in the odd places and the sum of the digits in the even places are equal or their difference is a multiple of 11. 372→(3+2)-7= -2,therefore 372 is not divisible by 11,chairs CANNOT be aligned by 11 Get Moving! A. Encircle 4,8,11 and 12 if these are factors by these numbers. 1. 1572 - 4 8 11 12 2. 88 - 4 8 11 12 3. 160 - 4 8 11 12 4. 642 - 4 8 11 12 5. 2400 - 4 8 11 12 B. Write on the blank before each number whether it is divisible by 4,8,11 or 12. _____1. 500 _____2. 3000
  13. 13. _____3. 121 _____4. 492 _____5. 648 Keep Moving! Supply the missing number to make the number divisible by the number opposite it. 1.273_ - 4 2.216_ - 8 3.91_ - 12 4.26_ - 11 5.38_ - 12 Apply Your Skills! Answer the following questions and write the answers on your notebook. 1. Can 88 stamps be shared equally by 4 friends? 8 friends? 11 friends? 12 friends? 2. Annie wants to distribute his 276 marbles to 12 children. Will each child receive the same number of marbles?
  14. 14. Lesson 7: Solving Routine and Non – Routine Problems Involving Factors, Multiples and i Divisibility Rules for 2,3,4,5,6,7,8,9,10,11 and 12 Explore and Discover! Read the problems below. Can you solve the problem? Here are the steps in analyzing and solving word problems. Study the solution below. Problem 1: Michael has to split 60 students in his class into different groups with equal number of students each .Not all students can be in one group and each group has to have more than one student. In how many ways can he form these groups? Mila baked cookies for her 3 sons and 2 daughters. If she baked 45 cookies only. How many cookies did her 3 sons have and 2 daughters have?  Understand Know what is asked: In how many ways can he form these groups? Know the given facts: 60 students, different groups with equal number of students each  Plan Determine the way/s to be used: factoring, finding the multiples and divisibility rules  Solve Show your solution: A. Find the factors of 60. 60= 4X15= 2X2X3X5 B. Get the numbers(once) on the given factors. Then find the multiples of each number till you reach 60.  Multiples of 2 = 2, 4, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60  Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60  Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60 Members 2 3 4 5 6 10 12 15 20 30 Groups 30 20 15 12 10 6 5 4 3 2 Ways 10 ways C. Identify the number that can divide 24 equally. Answer: There are 10 ways to form a group.
  15. 15. Problem 2: Which of the problems do you think is easier to solve? Why? Can you try solving this problem? Do this with your partner. 1. A farmer in Calauan gathered 96 pineapples. If he would want to distribute those 96 pineapples in baskets, how many ways can he distribute when each basket has the same number of pineapples? Get Moving! Solve the following problems: 1. Josephine planted 600 onions equally in 20 rows. How many onions were planted in each row? Understand:____________________________________________________________ Plan:__________________________________________________________________ Solve:_________________________________________________________________ Check and Look back:____________________________________________________ 2. The product of numbers is 138.If one factor is 2, hat is the other factor? Understand:____________________________________________________________ Plan:__________________________________________________________________ Solve:_________________________________________________________________ Check and Look back:____________________________________________________  Understand Know what is asked: How many cookies did her 2 sons have? How many cookies did they have individually? Know the given facts: 3 sons and 12 daughters ,30 cookies  Plan Determine the way/s to be used: Finding Multiples  Solve Find the multiples of 2 and 1 till you get the sum of 30. 3 sons 3 6 9 12 15 18 2 daughters 2 4 6 8 10 12 sum 5 10 15 20 25 30 Answer: There are 18 cookies for her 3 sons and 12 cookies for her 3 daughters. Show your solution:  Check and Look back Review and recheck your answer:
  16. 16. 3. How many 5,00 are there in 50,000? Understand:____________________________________________________________ Plan:__________________________________________________________________ Solve:_________________________________________________________________ Check and Look back:____________________________________________________ Keep Moving! Solve the following word problems 1. Joel and Harry love playing marbles. Joel has 60 marbles while Harry has 80 marbles . They plan to keep their marbles in a clay jar. How many clays are there? 2. What is the smallest number of avocados that can be placed in baskets with 50 and 75 pieces ? 3. Joseph has some chocolates. If he shares them equally among 4 friends or 5 friends, there are always 2 exrta chocolates left. What is the possible number of chocolates Joseph Could have? Apply Your Skills! Try solving more problems. Read and analyze more problems. Then write your solutions and answers in your notebook. 1. Lorna earns Php 10,000 a month. How much does she earn in 2 years? 2. A farmer planted 180 monggo seeds equally in 3 big bowls. How many monggo were planted each row?
  17. 17. Lesson 8: Creates Problem (with Reasonable Answers) Factors, Multiples and Divisibility Rules Explore and Discover! Arrange the sentences to form a word problem Get Moving! Use the data inside the box to complete the problems below. Solve the problem in your notebook. 1. The average of five consecutive odd numbers is 155. What are the five odd numbers? 2. I am thinking of a number . Twice the number plus . What is my number? 3. How many are there on a n 8-by-8 checkerboard? 4. The average of consecutive numbers is 112. What is the largest number? and the total payment of T-shirts Ronald paid P155.00 each T-shirts for his indigent students for the to use as a uniform and the total payment of T-shirts he bought is P1,240.00. How many T- shirts did he buy? How many T-shirts did he buy? P he bought is P1,240.00. Ronald paid P155.00 each T-shirts Answer: for his indigent students for the to use as a uniform 115 equals 52 squares 5 even
  18. 18. Keep Moving! Study the story problems given below. Complete each problem by creating a question for what is asked. Then, solve the problem. 1. Karen collected 28 recipes of salad. She devided them equally into different categories. Fruit salad is her favourite category. Question:_____________________________________________________________? Solution and Answer: 2. Mike 42 seashells. He places an equal number of seashells in different boxes. Question:_____________________________________________________________? Solution and Answer: 3. Sarah wants to invite her cousins to see a volleyball game with her. She has Php500.Each ticket costs Php85 Question:_____________________________________________________________? Solution and Answer: Apply Your Skills! Create a problem using the given data. Then solve the problem. 1. Given : 31 sachet of shampoos / month 1 year Asked: total number of sachet of shampoos in 1year Problem:_____________________________________________________ Solution and answer: 2. Given : 12 apples / day 3 months Asked: total number of apples in 3 months Problem:_____________________________________________________ Solution and answer: 3. Given : 36 red mangoes for Anny 40 green mangoes for Sonia 4 mangoes a day Asked: total number of mangoes mangoes last individually. Problem:_____________________________________________________ Solution and answer:
  19. 19. Lesson 9: Stating, Explaining, and Interpreting Parenthesis, Multiplication, Division, Addition, Subtraction (PMDAS) or Grouping, Multiplication, Division, Addition, Subtraction (GMDAS) rule. Explore and Discover! Study the rules in the order of operations. Examples: 1. 12 ÷ 6 × 2 + 4 – 5 2. 6 ÷ 3 × 2 + 5 – 1 3. 3 ×[4 - 2 × (10 -8) + 12 ÷ 6 × 1] How will you solve the order of operations? To solve the order of operations, follow the rules listed above. Solutions: 1. 12 ÷ 6 × 2 + 4 – 5 2 × 2 + 4 – 5 1. Perform the operations within each pair of grouping symbols (parenthesis, brackets, and braces) beginning with the innermost pair. 2. Simplify the expression with exponents. 3. Perform multiplication and division as they occur from left to right. 4. Perform addition and subtraction as they occur from left to right. 4 + 4 -5 8 - 5 3 Rule 3 Rule 3 Rule 4
  20. 20. 2. 6 ÷ 3 × 2 + 5 – 1 3. 3 ×[4 - 2 × (10 -8) + 12 ÷ 6 × 1] 2× 2 + 5 – 1 4+ 5 – 1 9– 1 8 Rule 3 Rule 3 Rule 4 3 × 2 3 × [4 - 2 × 2 + 12 ÷ 6 × 1] 3 × [4 – 4 + 12 ÷ 6 × 1] 3 × [4 – 4 + 2 × 1] 3 × [4 – 4 + 2] 3 × [o + 2] 3 × 2 6 Rule 1 Rule 3 Rule 3 Rule 4 Rule 1 Rule 3
  21. 21. Get Moving Solve the expression below by following the rules. 1. 32 ÷ 2 × 2 2. 6 ÷ 2 +1 × 4 3. (15 – 6) + (4 – 1) × 23 4. 3 × [3 + 2 × (10 -3)] 5. 12 + 3 × 3 {3 × [4 +(9 – 8) – 2] – 3} Keep Moving Perform the indicated operations. 1. (12 + 3) – 7 = N 2. 4 (6 + 8) = N 3. 25 ÷ 5 + 9 = N 4. (18 – 4) + (5 + 3) = N 5. (6 ÷ 3) + (10 × 3) = N Apply Your Skills! A. Place parenthesis in the equation so that each equation will be a true statement. 1. 16 – 7 + 8 = 1 2. 3 × 5 – 4 = 3 3. 18 ÷ 6 × 3 = 1 4. 16 – 7 + 8 = 17 5. 12 ÷ 2 + 4 = 2 B. Use the numbers 3, 4, 6, and 8 once in each exercise to make a true statement. ( ______ × _______ ) ÷ ( _____ + ______ ) = 2 ______ × _______ ÷ ( ______ × _______ ) = 1 ______ × ( ______ × ______ ) ÷ _______ = 18 ______ ÷ ( _______ - _______ ) + _______ = 14
  22. 22. Lesson 10 : Simplifies a series of operations on whole numbers involving more than two operations using the PMDAS or GMDAS rule. Explore and Discover! A lot of problems in mathematics involve more than one operation. Some may contain a series of operations and different grouping symbols such as parenthesis ( ), brackets[ ], and braces { }  Simplify 4 + 32 . You need to simplify the term with the exponent before trying to add in the 4: 4 + 32 = 4 + 9 = 13  Simplify 4 + (2 + 1)2 . You have to simplify inside the parentheses before I can take the exponent through. Only then can I do the addition of the 4. 4 + (2 + 1)2 = 4 + (3)2 = 4 + 9 = 13  Simplify 4 + [–1(–2 – 1)]2 . You shouldn't try to do these nested parentheses from left to right; that method is simply too error-prone. Instead, you will try to work from the inside out. First you will simplify inside the curvy parentheses, then simplify inside the square brackets, and only then take care of the squaring. After that is done, then you can finally add in the 4: 4 + [–1(–2 – 1)]2 = 4 + [–1(–3)]2 = 4 + [3]2 = 4 + 9 = 13
  23. 23. Get Moving! A. Simplify the following expressions in your notebook following the PEMDAS or GEMDAS rule. 1. 3 + 52 – 2 2. (2 – 5 ) + 42 – 10 ÷ 5 3. ( 4 – 1 )2 + 15 ÷ 3 – 1 4. 10 – ( 3 + 4 ÷ 2 )2 + 15 5. (3 + 2 ) + 8 ÷ 2 x 4 B. Complete the table. Write the order of operations to simplify the given expression. Expression Operation first to perform Answer 6) 6 + 5 x 3 – 7 7 ) 6 + 15 - 7 8) 14 – 7 + 18 ÷ 3 To simplify series of operations on whole numbers involving more than two operations using PEMDAS or GEMDAs rule.  First, perform operations inside the innermost grouping symbols, if any.  Next, evaluate powers.  Then, perform multiplication/division from left to right.  Finally, perform addition/subtraction from left to right.
  24. 24. 9) 7 + (15 - 6 x 2) 10) 2 ( 2 + 5 ) 2 Keep Moving! A. Simplify the following expressions in your notebook following the PEMDAS or GEMDAS rule. 1. (25 + 5) x 3 – 13 2. 19 + 12 x 3 – 5 3. 54 + 23 ÷ 2 4. 21 + 34 x 3 ÷ 2 5. (5 + 3) x (3 + 8) 6. 2 + 16 x 7 – 3 7. 11 + 5 x 5 – 10 8. 31 – 24 ÷ 1 -7 9. 21 + 16 – 8 ÷ 9 10.(19 – 3 ) x 3 Apply Your Skills! A. Write the expression and solve the given problems. 1. Peter has 450 pesos. He spends 210 pesos on food. Later he divides all the money into four parts out of which three parts were distributed and one part he
  25. 25. keeps for himself. Then he found 50 pesos on the road. Write the final expression and find the money he has left? 2. You pay 10.00 pesos to buy a package of paper napkins costing 640 pesos. How much change will you get back? Give the expression also. 3. Liza has 1,000 pesos to be distributed among two groups equally. Later, the first part is divided among five children and second part is divided among two brothers. Give the expression that represents how the money distribution between two groups was dispersed? Challenge yourself with this problem! Read the problem and then write the answers to the questions in your notebook. 1) Flora bought 3 notebooks for 10 pesos each, a box of pencils for 21.00 pesos, and a box of pens for 35.00 pesos. 2) Darwin had 35 500 pesos and withdrew 5200 pesos from his bank account. He bought a pair of trousers for 340 pesos, 2 shirts for 360 pesos each, and 2 pairs of shoes for 540 each. Give the final expression, and determine how much money Darwin had at the end of the shopping day.
  26. 26. 1 Lesson 11: Finding the common factors and the GCF of two - four numbers using continuous division You find the common factors and Greatest Common Factor or (GCF) of 24, 30 and 42. Study the solution below. Using Continuous Division 2 24 30 42 3 12 15 21 3 5 7 A. Find the common factors and GCF of the following numbers. 1) 24 32 4) 4 6 20 2) 12, 30 42 5) 8 56 84 112 3) 28 32 40 Mrs. Ragas bought 24 mangoes, 30 apples and 42 bananas. If she is going to group these equally, what is the greatest number of mangoes, apples and bananas in each group? GCF: 2 x 3 = 6 The greatest number of mangoes, apples and bananas is 6. Explore and Discover! Get Moving!
  27. 27. 2 B. Find the GCF of the following problems using continuous division. 1) Miss Dela Cueva has to prepare number of exercises for her lesson for the day. She has three classes. One class has 48 pupils, another class has 50, and another has 46. What must be the largest number of exercises she should prepare so that each class will have the same number of pupils working on different problems? 2) There are 10 green, 14 blue, 20 red and 24 yellow bulbs to be used for a birthday party. They are to be placed in plastic bags so that each bag contains the same number of green, blue, red and yellow bulbs. What is the largest number of plastic bags that will be needed? A. Determine the GCF. 1) 3 72 99 126 GCF = ________ 3 24 33 42 8 11 14 2) 5 90 135 180 195 GCF = ________ 8 17 36 39 3) 2 42 56 70 98 GCF = ________ 7 21 28 35 49 3 4 5 7 A. Find the common factors and GCF the following word problems. 4) The mathematics teacher in a certain elementary school is planning to have an educational tour for four grade levels with 800 pupils in Grade II, 560 Keep Moving!
  28. 28. 3 pupils in Grade III, 480 pupils in Grade IV and 400 pupils in Grade V. What is the largest number of pupils in a group in each grade level so that each group has the same number of pupils? 5) A group of 45 dancers will march behind a group of 30 clowns in a parade. You want to arrange the two groups in rows with the same number of people in each row, but without mixing the group. What is the greatest number of people you can have in each row? 6) A group of 45 dancers will march behind a group of 30 clowns in a parade. You want to arrange the two groups in rows with the same number of people in each row, but without mixing the group. What is the greatest number of people you can have in each row? Read and solve the common factors and GCF the following word problems. 1) The mathematics teacher in a certain elementary school is planning to have an educational tour for four grade levels with 800 pupils in Grade II, 560 pupils in Grade III, 480 pupils in Grade IV and 400 pupils in Grade V. What is the largest number of pupils in a group in each grade level so that each group has the same number of pupils? 2) The parents are making sandwiches for the class picnic. They have 72 ham slices, 48 cheese slices, and 96 tomato slices. What is the greatest number of sandwiches they can make if each sandwich has the same filling? Apply Your Skills!
  29. 29. 4 Challenge yourself with this problem! Read the problem and then write the answers to the questions in your notebook. 1) Gina has two pieces of cloth. One piece is 72 inches wide and the other piece is 90 inches wide. She wants to cut both pieces into strips of equal width that are as wide as possible. How wide should she cut the strips? 2) The GCF of 40 and a number 8. What is the number if it lies between 70 and 80? 3) Two numbers have a GCF of 6. If their difference is also equal to their GCF, what are the numbers? 4) Find three consecutive even numbers such that their GCF is the lowest of the three even numbers.
  30. 30. Lesson 12: Finds the common multiples and LCM of two - four numbers using continuous division Explore and Discover! To solve the problem, you need to find the least common multiple or LCM of 6 and 9 using continuous division. Here’s how you do it. 3 6 9 2 3 LCM = 2 x 3 x 3 = 18  Notice that 18 is the least common multiple or LCM of 6 and 9. Therefore, the smallest number of roses and daisies that she will need for her bouquets is 18.  You do not include when dealing with common multiples. Get Moving! A. Write the letter of the correct answer in your notebook. 1) The common multiples of 6 and 4 are a. 2, 3, 4 b. 4, 6, 8 c. 8, 12, 16 d. 12, 24, 36 2) The common multiples of 4, 5 and 8 are a. 8, 10, 16 b. 16, 20, 24 c. 40, 80, 120 d. 50, 90, 100 Lovelyn and Zerma are going to prepare bouquets with 6 roses to a bouquets and with 8 daisies to a bouquet. What will be the smallest number of roses and daisies that she will need for their bouquets?
  31. 31. 3) The LCM of 15 and 9 is a. 3 b. 15 c. 45 d. 135 4) The LCM of 2, 3, 4 and 5 is a. 20 b. 30 c. 50 d. 60 5) A common multiple of 3, 5, 9 and 10 is a. 30 b. 50 c. 90 d. 100 B. Determine the LCM. 1) 3 9 12 LCM = ________ 3 4 2) 5 5 10 30 45 LCM = ________ 1 2 6 9 3) 2 12 16 20 28 LCM = ________ 2 6 8 10 14 3 4 5 7 Keep Moving! A. Find the Least Common Multiple (LCM) of the given sets of numbers use continuous division. 1) 3 15 21 LCM = ________ 2) 4, 8, 16, 20 LCM = ________ 3) 5, 10, 25, 30 LCM = ________ 4) 6, 12, 15, 60 LCM = ________ 5) 2, 6, 10, 14, LCM = ________
  32. 32. B. Find the Least Common Multiple (LCM) the following word problems using continuous division. 1. What is the least number of candies that can be divided equally among 8, 9, and 12 children? 2. You bring the drinks for your basketball team every sixth game. Every third game is a home game. When will you first bring the drinks to a home game? If there are 20 games in an annual sportsfest, how many times will you bring the drinks to a home game? Apply Your Skills! Read and solve the common factors and GCF the following word problems. 1. Chill water her petchay every 2 days, and her cabbage every 3 days. Not counting the first day, when is the first time both plants are waters on the same day? When is the next time? 2. Efren goes home every other day. His wife Fely goes home every 4 days. His daughter Edlin goes home every 6 days. If they see each other today, when will they see each other again at home? Challenge yourself with this problem! Read the problem and then write the answers to the questions in your notebook. A. Mr. Placido, a security guard, has 3 successive night duties a week? His wife who is a nurse has 2 successive night duties. When will they see again if they are together now?
  33. 33. B. Two films were played at the same time. But the length of time of each film is different from each other. Film A took 120 minutes while Film B took minutes. After how many minutes will the two films be played at the same time again? C. Find the LCM of each pair of number. a. 33 and 23 b. 23 and 42 c. 8, 16, 24 and 48 d. 12, 30, 42, and 66
  34. 34. Lesson 13: Solves real life problems involving GCF and LCM of 2-3 given numbers. Explore and Discover! Elmer wants to cut as many pieces of wood of equal lengths from three pieces with lengths 35dm, 49dm, and 56 dm. What is the longest that he could cut each piece? How will you solve for the answer to the problem? You can use the 4 - step plan in solving for the answer. Understand: What does the problem? The longest that he could cut each piece. What facts are given? 35 dm, 49 dm, 56 dm of wood. Plan How will you solve the problem? By finding the Greatest Common Factor (GCF) and Least Common Multiple (LCM) Solve: How is the solution done? By listing the factors 35: 1, 5, 7, 35 49: 1, 7, 49 56: 1, 2, 4, 7, 8, 14, 28, 56 GCF: 7 By Prime Factorization 35: 5 x 7 49: 7 x 7 56: 7 x 2 x 2 x 2 GCF: 7 Check and Look Back: What is the answer to the problem? 7 dm is the longest cut can be done in the wood. Can you think of other ways to solve the problem? Get Moving! Read each problem and answer the questions that follow. Write your answers in your notebook. 1. Mr Ramos has to prepare a number of exercises for his lesson for the day. He has three classes. One class has 48 students, another class has 50, and another has 46. What must be the largest number of exercises he should prepare so that each class will have the same number of students working on different problems? a. What is asked in the problem? __________________________________________ b. What facts are given? _________________________________________________ c. How will you solve the problem? _________________________________________ d. What is the answer to the problem? ______________________________________
  35. 35. 2. Yesterday Tony bought 4 “Monay Bae” for Php. 5.00. He sold 3 “Monay Bae” for Php. 5.00. How many “Monay Bae” did he have to sell in order to make a profit of Php. 5.00.? a. How will you solve the problem? ______________________________________ b. What is the answer to the problem? ___________________________________ Keep Moving! Read and solve each problem. Write the solution in your notebook. 1. There are 14 blue and 20 red bulbs to be used for a birthday party. They are to be placed in the plastic bags so that each bag contains the same number of blue and red bulbs. What is the largest number of plastic bags that will be needed? 2. Liza has bought eight hair clips for Php. 10.00 and has sold them at 6 clips for Php.10.00. How many hair clips have to be sold to make a profit of Php. 10.00? Apply Your Skills! Challenge yourself by solving these problems. Write your answers in your notebook. 1. Serena wants to create snack bags for a trip she is going on. She has 6 granola bars and 10 pieces of dried fruit. If the snack bags should be identical without any food left over, what is the greatest number of snack bags Serena can make? 2. Evelyn is packing equal numbers of apple slices and grapes for snacks. Evelyn bags the apple slices in groups of 18 and the grapes in groups of 9. What is the smallest number of grapes that she can pack?
  36. 36. Lesson 14: Create problems (with reasonable answers) involving GCF and LCM of 2-3 given numbers. Explore and Discover! How will you create a problem involving Greatest Common Factor (GCF) or Least Common Factor (LCM) given the following information? You can create a problem by following this guide:  Familiarize yourself with the concepts of GCF and LCM and their application to real life situations.  Think of the type of problem you want to create.  Read some problems and study their solutions. Problem 1: Arielle is making flower arrangements. She has 7 roses and 14 daisies. She wants to make all the arrangements identical and have no flowers left over. Problem 2: Tayli wishes to advertise her business, so she gives packs of 13 red flyers to each restaurant owner and sets of 20 blue flyers to each clothing store owner. Tayli realizes that she gave out the same number of red and blue flyers. Study the following problems as examples for the above information. Problem 1 involves finding the Greatest Common Factor (GCF) Arielle is making flower arrangements. She has 7 roses and 14 daisies. She wants to make all the arrangements identical and have no flowers left over. What is the greatest possible number of flower arrangements she can make? Problem 2 involves finding the Least Common Multiple (LCM) Tayli wishes to advertise her business, so she gives packs of 13 red flyers to each restaurant owner and sets of 20 blue flyers to each clothing store owner. Tayli realizes that she gave out the same number of red and blue flyers. What is the minimum number of flyers of each color she distributed? Can you make another problem similar to these examples?
  37. 37. Get Moving! A. Write a question to complete each item. Then, solve each problem. 1. Nathan is stocking bathrooms at the hotel where he works. He has 18 rolls of toilet paper and 9 bars of soap. If he wants all bathrooms to be stocked identically, with the same combination of supplies in each one and nothing left over, what is the greatest combination of bathrooms Nathan can stock? 2. Sarah’s Shipping and Ryan’s Mail Services both ship packages. Sarah’s trucks will only carry loads of 18 packages. In contrast, Ryan’s trucks will only carry loads of 11 packages. If both businesses ended up shipping the same number of packages this morning, what is the minimum number of packages each must have shipped? B. Create some problems involving GCF and LCM. Keep Moving! Write a problem for the numbers and phrases in the box. 1. 2. 3. 4. Apply Your Skills! Create problems involving GCF and LCM based on the following situations: 1. Alaiza arranged the fruits in a box. 2. Luisa shared her toys with her playmates. 3. Anthony is selling newspaper every morning. 4. Volunteers gives clothes in the orphanage. 5. Joey is preparing cake for her friends. 30 and 48 cookies Biggest numberPut inside the identical container 32, 24, 16 balloons Arranged in a table Greatest number 5, 10 and 15 pictures Smallest numberCollected photographs 5, 6, 30 books Least numberNumber of books in a shelve
  38. 38. Lesson 15: Adds fraction and mixed fraction without and with regrouping Explore and Discover! A. Musician practiced very well for the concert. He practiced hours yesterday and hours today. How many hours did he practice in two days? The mathematical sentence is: + = n Step 1 Step 2 Step 3 Find the LCD of the add the fractional Add the whole numbers Given fractions and rename parts reduce in lowest term These to similar fraction if needed = = = 5 + 5 + = = = = = ______ ______ = 5 Will become While Will become the answer will be
  39. 39. And will become in lowest term. Get Moving! Find the sum. Express your answer in lowest terms if possible. 1. 2. 18 3. 4. 5. + + + + + _________ _________ _________ _________ _________ Keep Moving! Add. Rename the sum in lowest terms if possible. 1. 2. 3. 4. 5. + 216 + + + + _________ _________ _________ _________ _________ Apply Your Skills! Read each Problem then, answer the question that follow. 1. Joshua picked 2½ buckets of strawberries. Joe picked 3½ buckets of strawberries. How many buckets of strawberries did the two boys pick? a. What is asked? b. What are given? c. What is the operation to be used? d. What is the number sentence? e. How is the solution done? Show your solution? f. What is the complete answer?
  40. 40. 2. Mrs. Gonzales used 2¼ cups of flour to make a plain cake, 3 ½ cups to make brownies and 2 ¾ cups to make doughnuts. How many cups of flour did she use? a. What is asked? b. What are given? c. What is the operation to be used? d. What is the number sentence? e. How is the solution done? Show your solution? f. What is the complete answer? 3. Three hogs weigh respectively kilograms, kilograms and kilograms. What is the total weight? a. What is asked? b. What are given? c. What is the operation to be used? d. What is the number sentence? e. How is the solution done? Show your solution? f. What is the complete answer?
  41. 41. Lesson 16: Subtracting Fractions and Mixed fractions without and with Regrouping Explore and Discover! Karen bought kilogram of lanzones and kilograms of banana. How many more kilograms of lanzones than banana did she buy? How will you answer the question in the problem? To answer the question, subtract . The number sentence is = Change and to similar fractions by first finding = the LCD OF 2 and 4. Subtract the numerators. Write the sum over the least common denominator So, Karen bought kilogram more lanzones than banana. Get Moving Subtract the following fractions 1. 2. 3. 4. 5. 6. 7. 8. LCD LCD
  42. 42. Keep Moving Subtract. Reduce the difference to lowest terms whenever possible. 1. 2. 3. 4. 5. Apply Your Skills! A. Read and solve each problem. 1. Jerrie can repair her car in hours. A mechanic can do the same job in 8/12 hour. How much longer does it take Jerrie to do the job? 2. Pia spent hours in her grandparents’ house. This was of an hour more than the time she spent at the mall. How much time did she spend at the mall? 3. Ana bought kg of grapes for her younger sister. They ate kg of it. How many kilograms of grapes were left? B. Read and solve each problem 1. Lailani has meters of yarn on a ball. After meters were unwound, how many meters of yarn remained on the ball? 2. There are 5 pitchers of fruit juiced arranged in a row. The first pitcher contains cups of juice. If each pitcher has cups less juice than the one before it, find the amount of juice in each of the other pitchers. 3. Alvin weeded the garden in hours and watered the plants in hours. How much longer did he spend weeding the garden than watering the plants?
  43. 43. First Quarter- Week 6 Lesson 17:Solving Routine and non routine problems involving addition and/ or subtraction of fraction using appropriate problem solving strategies and tools. EXPLORE AND DISCOVER Darwin painted his room using 5/6 liter of blue paint and 2/3 liter of white paint. What color of paint was used more than the other? How much more of it was used than the other? You can solve the problem using the following steps. Understand:  Know what is asked : The paint color that was used more and by by how much more  Know the given facts: 4/6 liter of blue paint; 4/5 liter of white paint Plan:  Draw a picture : 5/6 2/3 = 4/6 1/6  Identify the operation to be use: Subtraction  Write the number sentence : 5/6 – 2/3 = n 5/6 – 2/3= 5/6 – 4/6 = 1/6 Solve:  Solution: Check and Look back:  Answer: a. more blue paint was used b. by 1/6 liter Get Moving
  44. 44. Read each problem carefully and then solve. 1. Mark wash his car in 4/5 of an hour, cleaned the garage in 2/6 of an hour, and painted the garden fence in 2 hours. How long did it take him to do all the tasks? 2. Anthony walked ¼ of a kilometer to Jane’s house and 7/8 of a km to the park. How far did he walk? 3. Jenny spends ¼ of her daily allowance for snacks, ½ for lunch, 1/8 for transportation, and saves the rest. What part of her daily allowance does she save? Keep Moving Read and solve each problem. 1. Liza spent ¾ hour preparing the soil and 2/3 hour planting. How much time did she spend in the garden? 2. In a fruit basket, 4/5 of the fruits are bananas and 3/8 are mangoes, which are more- the bananas or the mangoes? 3. Ronnie had 7/8 gallon of paint. He used 4/5 of it. What fraction of a gallon of paint was used? How much paint remained? Apply Your Skills 1. Four fifths of a group of rallyists were students, If 3/8 of the students were female, what part of the rallyists were male students? 2. Angie covered ¾ of a bulletin board with white paper. Then, she made a Math poster on 2/3 of the white paper. What part of the board was covered by the poster? 3. A water tank was 20/21 full. If 3/5 of it was used to water the plants, what fraction of the tank was used in watering the plants?
  45. 45. Lesson 18: Creating problems (with reasonable answers) involving addition and/or subtraction Fraction using appropriate problem strategies Explore and Discover How do you create a word problem involving addition, subtraction, or addition and subtraction of fractions? You can create a word problem by observing the following guide:  Familiarize yourselves with the concept of addition and subtraction of fractions and their application to real- life situations  Think of the problem you want to write.  Read some problems and study their solutions. You also consider the following when creating a problem: a. Characters b. Situation/ setting c. Data d. Key question Study the table below: Name Ribbons used/ left Quantity Unit Liza White ribbon 2/8 meter yellow 2/4 meter Ribbons left 3/6 meter Study the problem as an example for the given data. Liza bought 2/8 m of white ribbon and 2/4 m of yellow ribbon to make flowers. After making 5 flowers, she found out she had 3/6 m of ribbons left. How many meters of ribbon did she use for the flowers? Get Moving! Use the data below to create a one-step word problem involving subtraction of fractions. Name Color of Paint used in the classroom Quantity Unit James Blue 4/5 liter Harold Green 3/6 liter
  46. 46. Keep Moving! Use the data below to create a two- step word problem involving addition and subtraction of fractions. Name Quantity Unit Color of cloth needed in science project Carmen 3/5 Meter White Rowena 2/8 Meter Red Aileen 5/6 Meter yellow Apply Your Skills! Using the table below, create a problem for each of the following. 1. One- step word problem involving addition of fractions (Group 1) 2. One-step word problem involving subtraction of fractions (Group 2) 3. Two-step word problem involving addition and subtraction of fractions (Group 3) Name Quantity Quantity ( in kilograms) Sharon Grapes 1/2 Vilma Papaya 3/4 Nora Lansones 4/8
  47. 47. 1 x 1 = 1 5 2 10 LESSON 19 Visualizes Multiplication Of Fractions Using Models Explore and Discover! Darwin had a piece of plastic cover ½ meter long. He used 1/5 of it to cover his book. What fractional part of the plastic cover did he use? To find the answer, get 1of 1. 5 2 The diagram below will help you find the answer. If the rectangle represents 1 metre, the shaded part represents the plastic cover of Darwin. To find 1 of 1 , we have to divide the shaded parts into 5 equal parts and take 1 of the equal parts 5 2 The part of the whole representing the product of 1/5 x 1/2 is the region that has been shaded twice. Notice that the rectangle has been divided into 10 equal parts and 1 part is shaded twice so 1/5 x 1/2 must be 1/10, Darwin used 1/10 metre of plastic cover. STUDY THESE EXAMPLE Let us use a region to find 1/3 of 2/5 or 1/3 x 2/5. The region at the left has been divided vertically into 5 parts of the same size. Therefore each parts is 1/5 of the whole region. Ask. How many fifths are shaded? What part of the region is shaded?
  48. 48. Thus: 1 2122 3 of 5 equals 3 x 5 = 15 Get Moving 1. Write a multiplication equation for each visualization and find the answer a X = = _________ b. X = = _________ c. x = = ____ Next picture 2 horizontal lines have been drawn to divide each 1/5 into 3 equal parts. Into how many equal parts is the region now divided? How many small regions are shaded? Next , 1/3 of the shaded part has been shaded in another direction. How many of the small regions are now shaded twice ? What part of the whole region is shaded twice?
  49. 49. Keep Moving ! Match the picture in Column A with the multiplication sentence in Column B. Write your answer in your notebook. A B Apply Your Skills: Write the multiplication equation for each and find the answer. a. 11 2 of 4 b. 13 3 of 4 c. 11 5 of 2
  50. 50. x = = A. Illustrate and Find the Product 1 323 5. 31 3 45 4 5 4 x = x = x = x = = 3. 4. 1. 2.
  51. 51. LESSON 20: MULTIPLIES A FRACTION AND A WHOLE NUMBER AND ANOTHER FRACTION First Quarter : Week 7 EXPLORE AND DISCOVER! A. Michelle bought kg of carrots for her pet rabbit. Her pet ate of this how many carrots did her pet eat? To know the amount of carrots the rabbit ate, let us compute of . How do we right of in a number sentence ? x = N Let’s solve this in two ways First let us use an illustration to get the product. 3 4 133 1 3 4 12 4 The double shaded parts show the parts of the carrot eaten by the rabbit. .When reduced to lowest terms is So, Michelle’s pet ate ¼ of the carrots. 1 3 1 3 1 3 3 4 3 4 x = = 3 12 1 4 1 3 3 4
  52. 52. 3 12 Let’s solve x again, this time through computations. Multiply the numerators x = Multiply the denominators x = Reduce the product to lowest terms ÷ = Study these other examples: of == or x 8 If we have a whole number like 8 we can also write it as a fraction with a denominator of 1. 1 4 because 0r 2 GET MOVING Direction : Cut each strip. You may paste them in a chipboard or cartolina to make them harder. STEP 1 1 3 3 4 3 STEP 2 1 3 3 4 3 12 STEP 3 3 3 1 4 1 4 8 1 4 1 4 1 8 so4 x 8 = 4 = 2 X 8 = 2, 1 4 x 8 1 = 8 4
  53. 53. KEEP MOVING ! Read the problem: A. Ramona has yard of a beautiful lace. She gave of it to her friend for their project. If 2/3 of the apples above are green, then how many are green apples ? Color them to show your answer ? If 6/7 of the socks are black, then how many pieces are not black ? Color them to show ofof the pizza shown will be given to my classmate. Draw line/s on it to show the part to be given. 1 2 3 4 4 6 2 3
  54. 54. What part of the lace did Ramona give to her friend ? B. Bon bought 8 kilos of mango in the market. He shared of it with his relatives for their outing. How many kilos of mango did he share? C. One fifth of the 40 pupils of Miss Ramos are Math Club members. How many pupils are Math Club members ? APPLY YOUR SKILLS ! Find the product. Always express answers in lowest terms. 1. What is 2,andof ? __________________ 2. What is the product of 3/4 ,4 and ½ ? __________ 3. What is the value of N ? 5 x ¾ x = N 4. Multiply, and 4.The answer is ________. 5. What is the product of 5 , ½ and? _________ 2 3 5 6 3 4 2 4 3 4 2 6 3 6
  55. 55. Lesson 21: Multiplying Mentally Proper Fractions with the Denominators Up to 10. Explore and Discover! Nelia has ½ piece of a cartolina. She shares 1/3 of it to Joe who needs it very badly for his Science project. What part of the cartolina did Nelia Share? How will you solve for the product of the fractions mentally? Here’s how to do it. Do these steps in your mind. 11 1x1 =1 2 x 3 = 2x3 =6 Step 1: Multiply the numerators. 1x1 = 1 Step 2: Multiply the denominators. 2x3 = 6 Step 3: Express the answer in lowest terms if needed. Get Moving! Solve the following mentally. 13318541 2 1 5 × 4 = 7 × 3 = 10 × 6= 9× 2 = 8×3 = A. Find the product mentally. 7461256379 9 x 5 = 10x6 = 3x9 = 8x 5 = 8x 10 = B. Find the value of N. 1237548134 2 x 3 =N 5 x 8 =N 6 x 9 =N 9 x 3 =N 7 x 5 =N Apply Your Skills! A. Read the problems, then solve them mentally. 1. Roy harvested 5/6 crates of mangoes. He sold 4/5 of them. What part of the crate of mangoes was sold? 2. Dino bought ½ L of white paint. He used ½ of this to paint the doghouse that he made. How many litres of paint did he use? B. Understand the equations carefully, then answer it.
  56. 56. 1. In the equation 2/3 x ½ =N, what is the value of N? 2. If you multiply ¼ and 2/3, what will be the product? 3. Multiply 2/5, 3/4 and 4/5. It will give a product of_____. 4. What is the product of 2/7,3/8, and ½ ? _______ 5. Multiply 2/3, 5/6 and ¾. The answer is _______
  57. 57. 1kilo o 1kilo o 1kilo o 1kilo o 1kilo o 1kilo o 1kilo o Lesson 22: Solving Routine or Non-routine Problems Involving Multiplication Without or With  Addition or Subtraction of Fractions and Whole Numbers Using Appropriate Problem Solving Strategies or Tools. Explore and Discover! Problem 1: Lucy’s mother worked in her boutique for 2 ½ hours each day for 2 weeks. How many hours did she work in all? You can solve the problem using the steps below:  Understand Know what is asked: No. of hours she worked in all. Know the given facts: 2 ½ hours and 14 days = 2 weeks  Plan Determine the operation to be used: Multiplication Write the number sentence: 2 ½ × 14 = N  Solve: Show your solution: 2 ½ × 14 = N 2 ½ × 14/1 = N 5/2 × 14/1 = N 1 7 5/1 × 7/1 = 35/1 or 35 hours Lucy’s mother worked 35 hours in 2 weeks or 14 days.  Check and look back: Did I do the operation correctly? Is my answer reasonable? Did I write my answer in a complete sentence? Problem 2: Jose harvested 15 kilograms of guavas from the orchard. He gave 2/5 of them to his neighbors. How many kilograms of guavas did he share to his neighbors?  Understand Know what is asked: No. of kilograms he shared to his neighbors. Know the given facts: 15 kilograms of guava and 2/5 part shared to his neighbors  Plan: Make a diagram or drawing.  Draw 15 kilograms of guavas
  58. 58. 1kilo o 1kilo 1kilo 1kilo o 1kilo o 1kilo o 1kilo o 1kilo o 1kilo o 1kilo o 1kilo o Divide 15 kilograms of guavas into group of 5. There will be 3 kilograms per group. Circle 2 parts of it to show 2/5. Each group shows 1/5 or 3 kilograms of guavas. There are 2 groups of 1/5 and this shows 2/5. So, 2 × 3 = 6 kilograms of guavas he shared to his neighbors.  Look back: To check 15 × 2/5 = 6 kilograms. 15 × 2/5 = 3 15 × 2 =6 or 6 kilograms of guavas 1 5 1 1 Answer: He shared 6 kilograms of guavas to his neighbors. Can you try solving the following problems? Do this with your partner. 1. One – fourth meter of the cloth was left from Evelyn’s uniform. Her friend asked 3/5 of it to her Science project. What part of the cloth did her friend get? 2. Mrs. Albano gathered 50 eggs from her poultry. She gave 4/8 of these to her co- teachers. How many eggs were given to her co-teachers? Get Moving! Solve the following problems. 1. A recipe for doughnuts needs 1 ¼ cups of flour. Mother will prepare 1 1/3 times the recipe. How much flour will she need? 2. On Jenny’s birthday, her mother prepared 48 cupcakes. If ¾ of the cupcakes were served, how many cupcakes were served? 1kilo 3 kilo 1kilo1kilo1kilo o 1kilo 1kilo 3 kilo 3 kilo 3 kilo 3 kilo 3 kilo 1kilo 1kilo 1kilo 1kilo 1kilo 1kilo 1kilo 1kilo1kilo
  59. 59. 3. Nelson had 3 ½ liters of paint. He used 2/3 of it to paint their fence. What part of the paint did he used? 4. Remy had ¾ meter long of lace. She gave 1/3 of it to her classmate to decorate her Science project. What part of the lace was given to her classmate? 5. Everyday Alvin spends 3 ½ hours reading books. How many hours does he spend in a week reading books? Keep Moving! Solve the following problems. Write your solutions and answers in your notebook. 1. Anselmo spent 6/8 of his time in morning studying Math and Science. He spent ¼ of this time studying Science. What fraction of the total time did he spend studying Science? 2. What is the area of a rectangle whose length is 8/10 m and width is 2/3 m? 3. Aling Aning planted vegetables on 4/7 of her vacant lot. Two thirds of it was planted with pechay. What fraction of the vacant lot had pechay? 4. Lorna had 2 ½ liters of beef broth. She used 3/5 of it to make soup. How much beef broth did she use to make soup? 5. A recipe calls for 1 1/3 litres of milk. How many litres of milk do you need to make 2 recipes? Apply Your Skills! Try solving more problems! 1. Joanne signed up for 24 dancing lessons. She took ¾ of them by April. How many dancing lessons did she take by April? 2. Father’s monthly salary amounts to ₱ 20,500. Every time he receives his salary, he deposits 1/5 of it. How much is father’s monthly savings? How much is his annual savings? 3. How far can father go in 8 ½ hours if he travels at an average speed of 15 kilometers an hour? 4. Six pitchers each filled with ¾ liter of juice were served to Luisa’s visitors. Find the total amount of juice served. 5. The school Home Economics Club had a buko pie sale. The member sold 2/3 of their pies in the morning and 1/6 of their pies in the afternoon. If 150 pies were left, how many pies had been sold?
  60. 60. Alice used ¼ teaspoon of salt on her cake recipe. How much salt is needed if she will make 8 recipes of it? Lesson 23: Creating Problems (with reasonable answer) Involving Multiplication of Fractions Explore and Discover! How do you create a word problem involving multiplication of fractions? Observe the guide below in creating a word problem:  Familiarize yourselves with the different Mathematical concepts especially multiplication of fractions.  Analyse the data and think of the type of problems you want to create.  Read and study some sample problems and be familiar with the organization of data on the problem.  Learn about the basic terms or word clues often used in mathematical problems. The following data is important to be considered in creating a problem:  Name/Character  Situation/Setting  Data  Unit  Key question Study the given data below: teaspoon of salt for cake recipe 8 recipes to make Study the problem as an example for the data given.
  61. 61. Get Moving! Create a one-step word problem involving multiplication of fractions using the data given. 1. – part of Mrs. Marco’s class who joined the field trip 30 - total number of pupils 2. kg- mixed nuts bought by Ana of it given to Alma 3. 12 km- distance of Elmo’s house to school of total distance is being travelled by jeepney 4. Php 24,000- amount raised by PTA of Del Mundo Elementary School spend for completing the school’s fence 5. 5 kg of rice bought by mother cooked for dinner Keep Moving Create a one-step word problem involving multiplication of fractions using the data given. 1. kg meat bought by Mr. Guanson kg cooked 2. Php 420 earnings of Gab every day in working at a printing house for transportation allowance 3. 5 m ribbon bought by Kim for gift wrapping used in wrapping square boxes used in wrapping rectangular boxes
  62. 62. Apply Your Skills! Create a word problem involving multiplication of fractions for each of the following. Use the data below. 1. One-step word problem involving multiplication of fractions. 2. Two or more step word problem involving multiplication of fractions. Name Monthly Salary Monthly Savings Randy Php 12,000 Ryan Php 15, 000
  63. 63. 4 x 𝟏 𝟒 = 𝟒 𝟏 x 𝟏 𝟒 = 𝟒 𝟒 = 1 𝟏 𝟐 𝟑 x 𝟑 𝟓 = 𝟓 𝟑 x 𝟑 𝟓 = 𝟏𝟓 𝟏𝟓 = 1 𝟑 𝟕 x 𝟐 𝟏 𝟑 = 𝟑 𝟕 x 𝟕 𝟑 = 𝟐𝟏 𝟐𝟏 = 1 Lesson 24: Show that multiplying a fraction by its reciprocal is equal to 1 Explore and Discover! Janice shared the pizza she made among her 5 friends. Each one received of the pizza. Nothing was left for her. How much pizza did she make? Find: 5 x Solution: 5 x = x = = 1 Answer: Janice made 1 whole pizza divided among her five friends. Study some more examples:  Two numbers whose product is 1 are reciprocals of each other.  To find the reciprocal of a fraction make the numerator of the fraction the denominator of the reciprocal and the denominator of the fraction the numerator of the reciprocal.  Mixed fractions must first be converted to improper fractions before the method can be applied.  Write the reciprocal of a whole number as fraction.
  64. 64. Get Moving! Give the reciprocal of each number. 1. 51 6. 11. 2 2. 3 7. 12. 35 3. 8. 13. 5 4. 9. 14. 12 5. 24 10.5 15. Keep Moving! Write the missing factor. 1. x = 1 6. x = 1 2. x = 1 7. x = 1 3. x = 1 8. 5 x = 1 4. 15 x = 1 9. x = 1 5. x = 1 10. x = 1 Apply Your Skills! 1. The reciprocal of a number is , and their product is 1. What is the number? 2. Two numbers are reciprocals of each other. One number is 36 times as large as the other. What are the numbers? X = 1 3. What is the reciprocal of a number whose numerator is 8 times as great as 3 and the denominator is half the numerator?
  65. 65. Lesson 25: Visualizing Division of fraction Explore and Discover! Janella helps her mother cut meter long ribbon from meter ribbon. How many strips can she cut? Study the illustration and solution below. Number sentence : ÷ = __________ From the figure we can see that there are twenty-eight in . Therefore, the answer is 28. Get Moving! Use illustrations to answer each question. 1. How many are there in 9? 2. How many s are there in ? 3. How many are there in 24? 4. How many are there in ? 5. 6. How many are there in ? Keep Moving! Illustrate to find the quotient. 1. ÷ = 2. ÷ = 3. ÷ = 4. ÷ = 5. ÷ =
  66. 66. Apply your Skills! Use a model to solve the problem. 1. Camille needs m of cloth for a banner. If she has m of cloth, how many banner can she make? 2. Mrs. Dator needs4 liters of fresh milk. The store has liter packs of fresh milk. How many packs does she need to buy? 3. Mario has 8 logs to be cut in fourths to make fence posts. How many fence post can he make? 4. Mother bought 5 apples. She divided them into halves. How many pieces of apple were there?
  67. 67. Lesson 26: Dividing Simple Fractions and Whole Number and a Fraction Explore and Discover! Nathan wants to share his buko pie with his friends. He has of the buko pie, and he wants to give each friend of the buko pie. How many friends can Nathan feed? Solution: Without any illustration we can solve the problem following the steps in dividing simple fraction. Solution: ÷ = n ÷ = n Write the reciprocal of the divisor x = n Change the division sign into multiplication sign x = Multiply the numerators then the denominators ÷ = 4 Express in lowest term if necessary Therefore ÷ = 4 Nathan can feed 4 of his friends. Problem 2. Jane received 3 guavas from her friend. She cut it into pieces. How many halves did she have? Use real guava to solve the problem Problem 3 Lina has of a chocolate bar. It will be divided equally among 4 persons, what part of the chocolate bar will each one get? We can solve the problem following these steps: Step 1. Write thee number sentence. ÷ 4 = ___ Step 2. Rename the whole number in fraction form ÷ = ___ Step 3. Get the reciprocal of the divisor then proceed to Multiplication of fractions. ÷ =
  68. 68. Step 4. Write the product of the numerators over the product of the denominators; and reduce the fractions if needed Get Moving! Read and analyze each question then solve. 1. What is the quotient of and ? 2. If you divide by times, what is the answer? 3. What is the quotient of divided by ? 4. ÷ = 5. ÷ = n Find the quotient. Show your solution. 1) 6  = n 2) 16  = n 3) 14  = n 4) 8 = n 5) 30 = n Keep Moving! Find each quotient. 1. ÷ = n 2. ÷ = n 3. ÷ = n 4. ÷ = n 5. ÷ = n Find the quotient. 1. 10 = n 2. 15 = n 3. 45 = n 4. 36 = n 5. 28 = Apply your Skills! 1. Find the number of eights ( ) in 2. AlingNarda repacked kg of pepper into kg bags . How many bags of pepper can she make? 6 5 4 3 7 2 8 1 4 3
  69. 69. 3. There are 4 kilograms of rice. Each girl scout can consume kg of rice per meal. For how many girl scouts is the rice enough for a meal? 5 1
  70. 70. Lesson 27 : Solving Routine or Non-Routine Problems Involving Division Without or With Any of the Other Operations of Fractions and Whole Numbers Using Appropriate Problem Solving Strategies and Tools. Explore and Discover! Read the problems below. Can you solve the problem? Here are the steps in analyzing and solving the problems. Study the solution below. Problem 1 A 4-meter piece of wood is to be divided into pieces, each 2/3 m long. How many pieces can be cut from it? Nicole has 42 meters of ribbon. She uses meters for every box she makes. How many boxes can she make from the ribbon?  Understand Know what is asked: Number of pieces that can be cut Know the given facts: 4 meter piece of wood m each long  Plan Determine the operation to be used: Division Write the number sentence: 4 = n  Solve Show your solution: 4 = n x = or 6  Check and Look back Review and check your answer Answer: There were 6 pieces of wood  Check and look back Did I do the operations correctly? Is my answer reasonable?
  71. 71. Problem 2 Can you try solving the following problems? Do this with your partner. 1. If a skirt requires 1 ¼ meters of cloth, how many skirts can be made from 21 meters of cloth? 2. Linda made a trip of 112 kilometers in 2 ½ hours. What was her average speed? Get Moving! Solve the following problems. 1. A log 5 ¾ meters long will be cut into 6 equal pieces. How long will each piece be?  Understand: _____________________________________________  Plan:___________________________________________________  Solve: __________________________________________________  Look back: ______________________________________________ 2. Andrea has 35 meters of cloth. How many aprons can she make if each apron requires meters?  Understand: _____________________________________________  Plan:___________________________________________________  Solve: __________________________________________________  Look back: ______________________________________________  Understand Know what is asked: The number of boxes that can be make from the ribbon Know the given facts: 42 meters of ribbon meters for each box  Plan Determine the operation to be used: Division Write the number sentence: 42 = n Solve Show your solution: 42 = n = = = 18 Using cancellation = x = or 18  Check and Look back Review and recheck your answer: Answer: Nicole can make 18 boxes from the ribbon.  Check and Look back Review and check your answer Answer: There were 6 pieces of wood
  72. 72. 3. Calix needs to divide cups of flour among 3 recipes. How many cups of flour does each recipe need?  Understand: _____________________________________________  Plan:___________________________________________________  Solve: __________________________________________________  Look back: ______________________________________________ 4. The class of Lora is repacking goods for the outreach. How many kg packs of sugar can they make out of a bag that contains 15 kg of sugar?  Understand: _____________________________________________  Plan:___________________________________________________  Solve: __________________________________________________  Look back: ______________________________________________ 5. Nikki has 8 meters of fabric to make shirts. If each shirt requires m of fabric, how many shorts can she make?  Understand: _____________________________________________  Plan: ___________________________________________________  Solve: __________________________________________________  Look back: ______________________________________________ Keep Moving! Solve the following problems. Write your solutions and answers in your notebook. 1. Jeff has meters of rope. He wants to make 3 pieces of clothes hanger out of it. How long will each clothes hanger be? 2. A farmer bought kilograms of fertilizer for his rice, camote, and potato crops. If the fertilizer will be used equally on the three crops, how much will be used for each crop? 3. Mr. Reyes has a coconut plantation that measures hectares. If the entire plantation is to be subdivided among 36 tenants, how much would be each tenant’s share ? 4. Donald was able to harvest 2 ¼ kg of tomatoes from each of 4 plots. Then he divided them equally into 6 piles. How many kilograms of tomatoes did each pile have? 5. Lucy equally poured 4/5 liter of lemonade into 6 cups. How much lemonade did each cup have? Apply Your Skills! Try solving more problems! Read and analyze the following problems. Solve them in any method you like 1. Mrs. Gibe has to pack 50 kg of rice. How many plastic bags are needed if each bag can contain kg of rice? 2. Merllie makes hand towels for sale. How many hand towels can she make from 6 meters of cloth if meter is used for 1 hand towel? 3. How many meter of cloth can be cut from 40 meters of ribbon?
  73. 73. 4. On their trip to Laguna, Mr. Santos’ family bought 4 baskets of lanzones. Each basket contained kg of lanzones. The family shared the 4 baskets of lanzones among 8 persons. How many kilograms of lanzones did each one receive? 5. How many m pieces of ribbon can be cut from a 50 m of ribbon?
  74. 74. Lesson 28 : Creating Problems (with reasonable answers) Involving Division or With Any of Other Operations of Fractions and Whole Numbers Explore and Discover! How do you create a word problem involving division or with any of other operations of fractions and whole number? You can create a word problem by observing the following guide:  Familiarized yourselves with the concepts division with other operation of fractions and whole number and their application to real-life situations.  Think of the problem you want to write.  Read some problems and study their solutions. You also consider the following when creating a problem: a. Characters b. Situation/Setting c. Data d. Key Question Look at the given data below.  60 kilograms of rice  kg of rice in each plastic bag  Number of plastic bags needed for repacking Can you now complete the word problem below and solve for the correct answer, too? Do this in your notebook. Mrs. Ana has to pack _____________. How many plastic bags are needed if each bag can contain______________? Get Moving! Create a word problem from the given data below. Solve the problem in your notebook. 1. 12 kilograms of flour ¾ kilograms in each plastic bag Number of plastic bags used Problem:______________________________________________________________ Solution and Answer:____________________________________________________ 2. 30 meters long of wood 1 ½ meters long for each piece The pieces of woods that can be cut Problem:______________________________________________________________ Solution and Answer:____________________________________________________
  75. 75. 3. meters long of electric wire 6 equal pieces The length of each wire Problem:______________________________________________________________ Solution and Answer:____________________________________________________ 4. of a pie 4 persons The part of the pie each one gets Problem:______________________________________________________________ Solution and Answer:____________________________________________________ 5. 5 meters of cloth 2/3 meters for each scarf The number of scarves that can be make Problem:______________________________________________________________ Solution and Answer:____________________________________________________ Keep Moving! Complete each problem by creating a question for what is asked. Then, solve the problem. 1. Ella has 15 kilograms of rice for sale. She placed these in plastic bags. Each bag contains kilograms. Question:________________________________________________________ Solution and Answer: ______________________________________________ 2. A log meters long will be cut into 7 equal pieces. Question:________________________________________________________ Solution and Answer: ______________________________________________ 3. Nene has cake. She divided it among her 6 friends. Question:________________________________________________________ Solution and Answer: ______________________________________________ 4. Michelle needs to divide cups of flour among 3 recipes. Question:________________________________________________________ Solution and Answer: ______________________________________________ 5. A tailor has a bolt of cloth 20 meters long. Each uniform needs meters of cloth. Question:________________________________________________________ Solution and Answer: ______________________________________________
  76. 76. Apply You Skills! Create a problem using the given data. Then, solve the problem. 1. Given: 50 kilograms of cholcolate kilograms packed in each box Asked: Number of boxes used Problem: _____________________________________________________ Solution and Answer: ___________________________________________ 2. Given: 12 meters of fabric meters for each shirt Asked: Number of shirts that can make Problem: _____________________________________________________ Solution and Answer: ___________________________________________ 3. Given: 15 meters of cloth meters for each cloth Asked: Number of blouses that can make Problem: _____________________________________________________ Solution and Answer: ___________________________________________ 4. Given: 24 kilograms of rice kilograms in each bag Asked: Number of bags used Problem: _____________________________________________________ Solution and Answer: ___________________________________________ 5. Given: 8 meters piece of wood meters long for each piece of wood Asked: Pieces of woods that can be cut Problem: _____________________________________________________ Solution and Answer: ___________________________________________
  77. 77. Lesson 29: Giving the Place Value and the Value of a Digit of a Given Decimal Number through Ten Thousandths Explore and Discover! Study the chart below. PlaceValue Tens Ones Decimal point Tenths Hundredths Thousandths Ten thousandths Digits 0  5 9 8 7 Value 0  .5 .09 .008 .0007 In 0.5987 the digit 0 is a place holder of ones place. The digit 5 is in tenths place. Its value is .5. The digit 9 is in the hundredths place. Its value is 0.09. The digit 8 is in the thousandths place. Its value is 0.008 and digit 7 is in the ten thousandths place, its value is .0007. Hence, 0.5987 means five thousand nine hundred eighty-seven ten thousandths. Here are other examples: 1.3984 Digit Place Value Value 1 Ones 1 3 tenths 0.3 9 hundredths 0.09 8 Thousandths 0.008 4 Ten thousandths 0.0004
  78. 78. Get Moving! Write each in symbols, then give the value and place value of the underlined digit. Symbol Value Place Value 1. Five and three hundred ten thousandths 2. Twenty-five and two hundred ten thousands 3. Fifteen hundredths 4. One hundred one and one tenths 5. Five hundred and three ten thousandths 6. Ten and ten hundredths 7. Ninety-nine ten thousandths 8. One and fifteen ten thousandths 9. Fifty-nine and four hundred ninety-eight ten thousandths 10. Eight ten thousandths
  79. 79. Keep Moving! A. Give the place value of the underlined digit. 1. 6.28 6. 4.3763 2. 0.0028 7. 0.7659 3. 0.827 8. 2.7854 4. 21.843 9. 3.9681 5. 9.375 10. 19.0365 B. Write the place value of the digit 8 in each number. 1. 29.378 6. 86. 047 2. 908.176 7. 45.801 3. 471.081 8. 567.3278 4. 57.8012 9. 67.8703 5. 870.2194 10. 0.2358 C. In 50 678.39241, identify the digit in the …. a. Hundreds place _________ b. Thousandths place _______ c. Tenths place ________ d. Ten thousands place ______ e. Hundredths place _________
  80. 80. Apply Your Skills! Read and answer the questions that follows: 1. Men’s gymnastics is divided into compulsory and optional events. In 1984, the United States team members won the gold medal. Their score in the optional events was 296.0391. in the compulsory events they scored 259.3127. a. Read 296.0391 259.3127 b. Identify the place value of each decimal numbers. 2. Copy all decimals that have 2 in ten thousandths place. Give the place value and value of the digit before the digit in the ten thousandths place. a. 6.28 d. 8.2902 b. 0.0028 e. 9.0092 c. 4.4689 3. Copy the decimals that have 5 in the ten thousandths place. Give the value and place value of the digit after the decimal point. a. 5.5543 d. 5555 b. 19.5555 e. 3.4835 c. 6.4625
  81. 81. Lesson 30: Reading and Writing Decimal Numbers through Ten Thousandths Explore and Discover! What are the numbers in the situation? 45.8 and 43.75 What kind of number is that? Decimals How do you read and write decimal numbers? The decimal 45.8 is read as forty-five and eight tenths The decimal 43.75 is read as forty-three and seventy-five hundredths Decimals are just another way of writing fractions whose denominators are powers of ten and the proper way to read them is the same as reading the corresponding fractions which they are represent. Here are other examples: Decimal Fraction Read as: 0.6 10 6 Six tenths 0.12 100 12 Twelve hundredths 0.2568 10000 2568 Two thousand five hundred sixty-eight ten thousandths In the examples “zero” and the decimal point are not read nor write in words anymore. Carl and his brother take good care of their bodies. They eat the right kinds of foods to maintain their proper weights at their age. Carl weighs 45.8 kilograms while his brother weighs 43.75 kilograms.
  82. 82. Get Moving! A. Read each decimal number correctly. 1. 0.059 4. 0.0007 2. 20.7034 5. 7. 8254 3. 46. 340 B. Write a decimal number for each. 1. two hundred forty-six ten thousandths ______________ 2. six and forty-eight thousandths ______________ 3. twenty-six and eight tenths ______________ 4. two hundred and forty-seven thousandths ______________ 5. Seven hundred twelve and eleven ten thousandths ______________ 6. thirty-one ten thousandths ______________ 7. nine and nine tenths ______________ 8. six hundredths ______________ 9. three hundred seventy and four tenths ______________ 10. ten and two thousand fifty-one ten thousandths ______________ Keep Moving! A. Write in words. 1. 3.06 _________________________________________________________ 2. 0.8009 _________________________________________________________ 3. 0.014 _________________________________________________________ 4. 15.300 _________________________________________________________ 5. 18.009 _________________________________________________________ B. Write down as decimals. 1. 10 8 6. 10000 164
  83. 83. 2. 1000 4 7. 10000 237 3. 100 45 8. 1000 258 4. 1000 17 9. 10000 10 5. 10000 69 10. 100 12 Apply Your Skills! Read and answer the following: 1. The distance between the town church and the market is one and eighty-nine thousandths kilometres. Write the distance as a decimal number. 2. How many decimal places does “one and three hundred sixteen ten- thousandths” have? 3. How many decimal places does thirty-three thousandths have? 4. I am a decimal number. My thousandths digit is three more than my tenths digit. My ones digit is 3 and so my tenths digits. All the other digits are 0 and I have four decimal places. What number I am? 5. How many hundredths are equal to 1.3?
  84. 84. Lesson 31. Rounding Decimal Numbers to the Nearest Hundredths and Thousandths Explore and Discover! James climb a 483 meter hill. If there are 1000 meters in 1 kilometer, what part of the hill and did Luis climb? Round to the nearest hundredths. To know the part of the hill Luis climb. 1. Change meter to kilometre. (1000 m=1 km) 1000 483 = .483 Rounding off number using number line .480 .481 .482 .483 .484 .485 .486 .487 .488 .489 .490 From the diagram, it is easy to see that .483 is nearer to .480 than .490. So .483 is rounded to .480. Now, let us try to round .483 to the nearest hundredths. Study the illustration below. .483 Rounding place The digit to the right is smaller than 5, so it rounds down. .483 rounded to the nearest thousandths is .480  To round decimals 1. Identify the digit to be rounded-off. 2. Inspect the digit to the right of the required place. a. If the digit is greater than 5, add 1 to the digit at the required place. b. If the digit is less than 5, retain the digit at the required place. Then drop all the digits to the right of the required place. c. Copy all the digits to the left of the required place if there are any.
  85. 85. Get Moving! A Round to the nearest hundredths. 1. 48.019 _____________________ 6. 0.925 ___________________ 2. 16.975 ______________________ 7. 4.018 ___________________ 3. 15.614 ______________________ 8. 12.3057 ___________________ 4. 12.089 ______________________ 9. 8.1749 ____________________ 5. 4.613 ______________________ 10. 1.001 ____________________ B. Round to the nearest thousandths. 1. 8.0079 ______________________ 6. 8.3056 ____________________ 2. 1.4067 ______________________ 7. 1.6149 ____________________ 3. 2.5974 ______________________ 8. 12.0192 ____________________ 4. 0.1549 ______________________ 9. 3.8315 ____________________ 5. 2.5973 ______________________ 10. 2.5615 _____________________ Keep Moving! A. Complete the table. Decimal Round to nearest hundredths Round to the nearest thousandths 1. 2. 3842 2. 0.56893 3. 2.96425 4. 5.2358 5. 0.86302
  86. 86. B. Write the letter of the number that rounds off to the given number. 1. 3.65 a. 3.624 b. 3.580 c. 3.672 d. 3.647 2. 15.27 a. 15.225 b. 15.278 c. 15.278 d. 15. 273 3. 10.85 a. 10.859 b. 10.857 c. 10.851 d. 10.856 4. 32.548 a. 32.5476 b. 32.5488 c. 23.534 d.32.6437 5. 211.78 a. 211.789 b.211.784 c. 211.786 d. 211.7865 C. Get the quotient up to the nearest thousandths plce. Then round the decimal to the nearest thousandths. Number 1 is done for you. 1. 36 ÷7 = 5.1425.14 4. 73÷ 8 = ______ ________ 2. 47 ÷ 8 = ____ ____ 5. 78 ÷ 9 = ______ ________ 3. 71 ÷ 8 = ____ _____ 6. 34 ÷ 9 = ______ ________ Apply Your Skills! Answer the following: 1. a. What are the smallest and largest decimals in hundredths that rounds to 0.5? b. What is the largest decimal in hundreths round to 0.5? 2. One centimeter is equivalent to about 0.3937 inch. Round off the given equivqlent to the nearest hunderdths. 3. Mrs. Edlagan has a total deposit of 50 766.25. The annual interest at 3% simple interest is 1 522.9875. Round off interest to the nearest hundredths and thousandths. 4. The decimal rounds to 3.2. The digit in the thousandths place is 4 times that in the hundredths place. The sum of the digits is 15. What decimal is it?
  87. 87. Lesson 32: Comparing and Arranging Decimal Numbers How do you compare decimal numbers? There are three ways to compare decimal numbers. The first one is by using a number line for small scale or difference between numbers and place value chart for numbers that cannot be represented in a number line. The third way is by adding zero to make the digits of decimal numbers the evenly. Study the example below. Start at the left side. The number line starts with 12.326. It is the smallest value in the set which is located at the leftmost part of the number line. The number line ends with 12.346. It is the greatest value in the set which is located at the rightmost part of the number line. In the number line we can clearly locate that 12.329 is at the left side while 12.341 is located at the right side. So, 12.341 is greater than 12.329. We can write it in symbol as 12.341 > 12.329. Let’s try another example using different strategy. We can add 0 to make the number of digits equally. Which is greater 0.2 or 0.198? Let’s compare it using the table below. Original Number 0 2 0 1 9 8 New Number Formed by Adding 0 0 2 0 0 0 1 9 8 Explore and Discover! Which is less 12.341 or 12.329? 12.326 12.327 12.328 12.329 12.330 12.331 12.332 12.333 12.334 12.335 12.336 12.337 12.338 12.339 12.340 12.341 12.342 12.343 12.344 12.345 12.346
  88. 88. Which is greater, 12.789 or 12.765? Now, let’s take another look. The given decimals have the same number of digits. Which is greater 0.200 or 0.198? In this example, 0.200 is greater than 0.198. In symbol, we can write this as 0.200 > 0.198. Study another set of example using the place value chart. A. Compare the following. Write >, <, or = in to make the sentence true. 1. 1.396 0.95 9. 2.35 2.53 2. 0.29 0.3 10. 0.1 0.99 3. 6.5 6.500 11. 4.07 4.017 4. 7.4 7.049 12. 10.07 10.067 5. 27.5 27.492 13. 1.0 1.01 6. 2.098 2.904 14. 2 2.00 7. 0.30 0.300 15. 3.607 3.670 8. 8.10 8.1 B. Order the following decimals from least to greatest. 1. 3.21, 3.021, 3.12, 3.121 2. 1.3, 1.309, 1.03, 1.39 3. 0.09, 0.012, 0.0089, 0.0189 4. 4.01, 4.0011, 4.011, 4.101 PlaceValue Tens Ones Decimal Point Tenths Hundredths Thousandths Value 10 1  Digits 1 2  7 8 9 Digits 1 2  7 6 5 Get Moving!
  89. 89. 5. 5.5, 5.059, 5.0090, 5.05 6. 1.7, 0.9, 1.07, 1.9, 0.7 7. 2.0342, 2.3042, 2.3104, 2.4 8. 5, 5.012, 5.1, 0.502 9. 0.6, 0.6065, 0.6059, 0.6061 10. 12.9, 12.09, 12.9100, 12.9150 A. Write <, >, or = on the blank to make the sentence true. 1. 0.1114 ____ 0.2202 9. 0.0120 _____ 0.012 2. 0.1090 ____ 0.1009 10. 16.8930 _____ 16.893 3. 0.999 ____ 0.1000 11. 0.7985 _____ 0.7895 4. 4.8934 ____ 4.8943 12. 12.1 _____ 12.0100 5. 0.6390 ____ 0.639 13. 40.04 _____ 40.041 6. 0.55 _____ 0.055 14. 8.627 _____ 8.649 7. 0.7894 _____ 0.7658 15. 0.213 _____ 0.0213 8. 0.3937 _____ 0.3198 B. Order numbers from greatest to least. 1. 3.756 37.56 375.6 0.3756 2. 0.2468 0.2486 0.2648 0.2846 3. 11.010 11.011 11.0110 1.1101 4. 2313.2 23.132 2.3132 231.32 5. 555.555 55.5555 5.5555 5555.55 6. 0.481 0.38 0.256 0.7349 7. 2.461 2.3392 2.6789 2.7666 8. 0.93 6.87 5.241 6.786 9. 62.1254 26.2351 262.351 26.5321 10. 905.928 95.7654 5.8642 5.6248 Keep Moving!
  90. 90. A. Read and solve the following. 1. Jeremiah and Catherine are both honor pupils in their school. For the first quarter, Jeremiah’s average is 93.1 while Catherine’s average is 93.095. Who topped the first quarter? 2. Team Narra and Team Mahogany undergo a water challenge. Their task is to transfer the water in a cup from the first player to the tenth player without spilling within the allotted time. After the task, the team captain measure the water collected using a measuring cup. Team Narra collected 1. 402 liters while Team Mahogany collected 1. 045 liter of water, which team got more water? 3. Robert was asked to arrange the following numbers from least to greatest. Which number comes last? 4. In a bazaar, different items are sale for big discounts. Irene is looking for a school bag. She visited three stalls to buy one for his younger brother. The stall offered the school bag of the same quality but differs in price. The first stall offered if for P 749. 25, the second stall sold it for P 792.45 and third stall gave it P 724. 95. If she wanted to save, from which stall will she buy school bag? 5. Aling Mila bought 0.82 m of red fabric, 0.79 m of yellow fabric, 0.805 m of blue fabric and 0.782 m of white fabric. Which ribbon is the longest? the shortest? Arrange the lengths of the fabric form longest to shortest? Apply Your Skills 2.099 2.9 2.99 2.109 2.5
  91. 91. Lesson 33: Visualizing Addition and Subtraction of Decimals Gab and Sassa goes to school together by walking. The school is 2 km from their house. For first five minutes Sassa and Gab has walked and reached 0.28 kilometer, after the next 8 minutes they recorded 0. 59 km. How far are they from school? How can we solve the problem? First identify the given. We have the following. 2 km – distance of school from Gab and Sassa’s house 0.28 km – the distance they have walked and reached for the first 5 minutes 0. 59 km – the distance covered by them for the next 8 minutes What is asked in the problem? The problem is looking for the distance from the school that they need to cover after driving for 13 minutes. So, let’s add the distance they have walked for 5 minutes and the distance covered by them for the next 8 minutes. Use the model below. Each square represents 0.001. A. Add or subtract the following. Use drawing or illustration if possible. 0.028 0.087 Explore and Discover! 0.059 + = Get Moving!
  92. 92. 1. 0.27 + 0.61 6. 0.8 – 0.3 2. 0.13 + 0.22 + 0.45 7. 0.57 – 0.4 3. 0.261 + 0.003 8. 0.095 – 0.002 4. 0.005 + 0.024+ 0.314 9. 0.631 – 0.385 5. 0.421 + 0.06 + 0.104 10. 0.457 – 0.104 B. Find the sum or difference. 1. 0.549 – 0.014 6. 0.31 + 0.42+ 0.16 2. 0.653 – 0.128 7. 0.473 – 0. 251 3. 0.56 + 0.23 + 0.2 8. 0.927 – 0.302 4. 0. 783 – 0.53 9. 0.07 + 0.009 + 0.4 5. 0.205 + 0.612 10. 0.365 + 0.13 + 0.283 C. Find the sum or difference. 1. 0.684 2. 0.83 3. 0.73 4. 0.9002 + 0.295 + 0.567 + 0.3073 + 0.8634 5. 0.84 6. 0.84 7. 0.540 8. 0.3 + 0.8056 - 0.6358 - 0.2365 - 0.076 9. 0.6 10. 0.9702 - 0.1858 - 0.1694 A. Add or subtract the following. 1. 2.198 – 1.439 6. 2.67 + 8.94 + 6.43 2. 38.026 – 49.183 7. 12.652 – 9.758 3. 5.072 – 3.861 8. 45.006 – 39. 248 4. 45.349 – 29. 465 9. 6.89 + 23. 574 + 16.045 5. 18.860 + 34. 257 10. 7.14 + 8.432 + 9.77 B. Find the sum or difference of the following. 1. 37.813 – 27.654 6. 9.87 + 10.163 + 19.054 2. 12.095 + 9.389 7. 98.764 – 87.365 3. 43.702 + 18. 419 8. 63.007 – 48.642 4. 16.206 – 13.076 9. 9.71 + 52.075 5. 89.652 + 17. 378 10. 84.349 – 49.182 C. Add or subtract. 1. 0.38 + 0.47 = n 6. 0.23 – 0.16 = n Keep Moving!
  93. 93. 2. 0.412 + 0.638 = n 7. 0.97 – 0.178 = n 3. 0.529 + 0.646 = n 8. 0.232 – 0.046 = n 4. 0.412 + 0.473 = n 9. 0.76 – 0.057 = n 5. 0.284 + 0.325 = n 10. 0. 200 – 0.099 = A. Read, analyze and solve the following. 1. During a vacation, Ben’s records showed gasoline purchases of 19.75 gallons, 15.4 gallons, 13.85 gallons and 21.06 gallons. How many gallons of gasoline did he buy? 2. The perimeter of a triangle is equal to the sum of the length of its sides. Find the perimeter of a triangle whose sides are 8.75 cm, 9.6 cm and 10.375 cm. 3. Rachel has P 3 316.40 in her savings account. If she made withdrawals of P 285.00, P 472.46 and P 1 042.25, how much money is left in her account? 4. One week a jogger ran the following distances : 15.3 km , 18.75 km , 19 km , 21.5 km, 25.375 km and 30.25 km. If his weekly average is 150 km, did he run less or more? 5. Romeo has P 20 000 in available credit on his Visa charge card. If she purchases a portable CD player for P 8 139.55, a boom box for P 399.95 and two way speakers for P 3 425.05, how much available credit does she have left ? Apply Your Skills!
  94. 94. Lesson 34: Adding and Subtracting Decimal Numbers through Thousandths Without and With Regrouping Mr.Acapulco acquired a lot in a remote area in Batangas to be planted by different kinds of fruit bearing trees. He already acquired 105.652 square meters in Barangay Masikap and 91.246 square meters of lands in Brgy. Matamis. If Mr. Acapulco needs 398.166 square meters, what part of land area does he need to acquire? Step 1: How do we solve the problem? To solve the problem, we must need to add the first two given data, 105.692 square meters of land in Barangay Masikap and 91.246 square meters of land in Barangay Matamis. The number sentence is 105.652 sq. m + 98.276 sq. m = N. Without Regrouping Step 2: After getting the sum. We must now answer the question raised in the problem. To know the part of land Mr. Acapulco still needs to acquire. We may now subtract the sum that we get to the land area intended to plant with different fruit bearing trees. Here’s the number sentence to use: 398.166 sq. m – 196.898 sq. m = N. With Regrouping Hundreds Tens Ones Decimal Points Tenths Hundredths Thousandths 9 1  2 4 6 1 0 5  6 5 2 1 9 6  8 9 8 Hundreds Tens Ones Decimal Points Tenths Hundredths Thousandths 2 18 7 10 15 16 3 9 8  1 6 6 1 9 6  8 9 8 1 9 5  2 6 8 + Sum Difference- Explore and Discover! Get Mo
  95. 95. A. Find the sum of the following. 1. 3.76 2. 23. 347 3. 37.786 + 4.356 + 8.92 + 2. 632 4. 4. 762 5. 5. 703 6. 87.652 + 1.69 + 17.74 + 51.764 7. 0.9154 8. 92.65 7 9. 15.421 + 0.2515 + 24.57 3 + 37.88 10. 0.3276 + 0.1178 B. Find the difference. A. Solve for the sum or difference. 1. 75.267 2. 59.246 3. 43.823 4. 86. 576 - 63.122 - 28.132 - 21.51 + 53.123 5. 98.364 6. 21. 924 7. 85.376 8. 58.148 - 72. 225 - 17. 379 - 49. 528 + 67.251 1. 93. 152 - 29. 184 2. 61.41 - 37.532 3. 57.31 - 46. 653 4. 154. 76 - 85.493 5. 380.205 - 278.398 Keep Moving!
  96. 96. 9. 70.542 10. 59. 647 - 53.891 - 27.958 A. Read, analyze and solve. 1. Alex traveled 41.3 kilometers on Monday and 53.75 kilometers on Tuesday. How many kilometers did he travel in two days? 2. In a midnight sale, a radio cassette player was sold at P 1 449.95. If it’s regular price was P 1 950.50, how much less was the sale price? 3. Anna bought a bunch of flowers for P 125.50. If she gave a P 100 bill and P 50 bill, how much was her change? 4. The rainfall on four consecutive days during a typhoon was 10.31 cm, 12.72 cm, 18.39 cm and 9.84 cm. Find the total rainfall during the typhoon. 5. Mother bought 2.35 kg of pork, 3.75 kg of chicken, 1.1 kg of beef, and 1 kg of liver. How many kilograms of meat did Mother buy in all? Apply Your Skills!
  97. 97. Lesson 35: Estimating the Sum or Difference of Decimal Numbers with Reasonable Results Explore and Discover A. Nancy wants to buy a blouse for Php.118.50, a t-shirt for Php.99.75 and a pair of shoes for Php.215.50. If she has Php.500-bill, does she have enough money to pay for them? To answer the question, we need to estimate. We can use the rounding method. Php.118.50Php.120 Php.99.75 Php.100 Php.215.50Php.220 Php.440 Yes, Nancy has enough money to buy the three items. B. A salesman drove 17.65 km to one town and 15.86 km to a second town. How much farther is the first town than the second town? 17.6518 km 15.8616 km 2 km The first town is less than 2 km farther than the second town. Get Moving! A. Using the rounding off technique, find the estimated sum of the given decimals. 1. 23.45 + 8.63 + 2.75 2. 8.05 + 7.93 + 1.62 3. 112.56 + 23.63 + 12.45 4. 0.91 + 0.86 + 8.75 5. 2.843 + 15.624 + 13.56
  98. 98. B. Using the rounding off technique, find the rough estimated difference of the given decimals. 1. 634.58 – 436.79 2. 37.86 – 19.92 3. 14.39 – 8.59 4. 7.45 – 2.93 5. 15.63 – 8.79 Keep Moving! A. Round to the greatest place value and estimate each sum. 1. 2347.081 + 5834.501 2. 9452.8 + 4671.2 3. 23.5 + 15.03 + 9.54 4. 7.45 + 8.83 + 6.55 5. 12.4 + 14.8 + 21.53 B. Round to the greatest place value and estimate each difference. 1. 678.23 – 451.2 2. 818.9 – 489.06 3. 951.4 – 568.19 4. 7512.2 – 3725.9 5. 9301.67 – 4878.8 Apply Your Skills! Estimate the answer to each problem. 1. Gloria bought a t-shirt for Php.95.75 and a book for Php.175.60. how much more did the book cost than the t-shirt? 2. A salesman traveled 78.45 km in the morning and 25.24 km in the afternoon. Did he cover at least 100 km? 3. A household consumes 222.5 liters of water a day. One faucet leaks 12.25 liters of water a day. Estimate how many liters of water a day a household consumes when the faucet is fixed? 4. The Math Club raised Php 1 225.00 during their fund raising campaign. The club will be buying 3 items worth Php495.00, Php347.50 and Php862.90. How much more money does the club need to buy the items? 5. A rectangular garden measures 22.7 meters by 16.6 meters. Estimate how many meters of fencing material are needed to enclose it.
  99. 99. Lesson 36- Solving Routine or Non-routine Problems Involving Addition and Subtraction of Decimal Numbers Including Money Using Appropriate Problem Solving Strategies and Tools Explore and Discover Study the solution below. Problem 1 Problem 2 Which of the two problems is easier to solve? Why? Get Moving Solve the following problems. 1. The perimeter of a quadrilateral is 412.95 cm. If the three known sides measures 85.56cm, 112.77 cm, and 85.26 cm, how long is the fourth side? 2. I bought 4 items worth P39.90, P68.60, P 58.75 and P120.25. How much change will I get from P 500-bill? 3. A rectangle is 13.8cm. long and and 9.7 cm wide. Find its perimeter. 4. Obed and Dario hiked 15.1 km. In one day and 13.75 km in the next day. How many kilometres did they hiked in all? Mang Isko has 18.48 pesos . If she has to devide it into her 6 children, How much will each one receive? Marlene opened her math book and found that the sum of the pages facing her was 243. What pages did she open to? Understand Know what is asked? The amount of money each child receive? Know the given facts: 18.48 pesos, 6 children Plan Determine the operation to be used: Division Write the number sentence: 18.48÷6=n Solve Show your solution: 18.48÷6=3.08 Check and look back Review and re check your answer: you can use calculator to divide 18.46 by 6 or multiply 3.08 by 6 Understand Know what is asked: The pages of the book Know the given facts: The sum of two pages was 243 Plan Determine the operation to be used: Addition Write the number sentence: n+(n+1)= 243 Solve Show your solution: Trial and error method If n=121, then 121+(121+1)= 243 121+122 =243 243 = 243 Review and check your answer: you cannot have a page that is 121 r. 1
  100. 100. 5. Mr. De Guzman and the boys spent P 567.75 for food and P 175.50 for transportation during the Science Fair Camp. If they had P 800.00 to spend, how much money was left? Keep Moving Analyze and sole the ff. Problems. 1) The diameter of the earth is 12 763.29 kilometers. If Mercury’s diameter is about 7 913.04 kilometers shorter than that of the earth, what is the diameter of Mercury? 2) Luz wants to buy a bag that costs 375.95. If she has saved 148.50 for it, how much more does she need? 3) Martha bought 2.5 m of yellow ribbon, 3.4 m of red, 8.75 m of white, and 3.70 m of blue. How many metres of ribbon did she buy altogether? Apply Your Skills Write the number sentence and solve. 1. Delia filled the container with 3.5 litres of water. Her mother used 0.75 litres of water for cooking and 1.25 litres for palamig. How much water was left in the container? 2. Mang Caloy cut four pieces of bamboo. The first piece was 0.75 metre; the second was 2.278 metres, the third was 6.11 metres, and the fourth was 6.72 metres. How much longer were the third and fourth pieces put together than the first and second pieces put together?
  101. 101. Lesson 37- Creating Problems (with reasonable answers)Involving Addition and Subtraction of Decimal Numbers Including Money Second Grading Period, Week 3 Explore and Discover How do you create a word problem involving addition and subtraction of decimals including money? You can create a word problem by observing the following guide: a. Familiarize yourself with the concept and their application to real life situation. b. Think of the problem you want to create. c. Read some problems and study their solutions You also consider the following when creating a problem. 1. Characters 2. Situation/Setting 3. Data 4. Key Questions Study the table below Name Things bought Price Shane T-shirt 250.75 kg. Lito Shoes 1,999.99 kg. Study the problem as an example for the data given. Get Moving Use the data below to create a two-step word problem involving addition and subtraction of decimals. Name Items bought Price Carlo 10 note books P80.65 Lolit Bag P617.35 Jane Shoes P1,250.08 Shane and Lito went to the Department Store. Shane bought a T-shirt cost P 250.75. Lito bought a shoes cost 1,999.99kg. How much more does Lito spend than Shane?
  102. 102. Keep Moving Use the data below to create a two-step word problem involving addition and subtraction of decimals. Name Foods Ordered Price Amie Spaghetti P50.75 Zet Palabok P48.25 Precy Regular Yum P30.75 Apply Your Skills Use the data below to create a problem for each of the ff. 1. One- step word problem involving addition of fraction 2. One -step word problem involving subtraction of fraction 3. Two- step word problem involving addition and subtraction of fraction Name Amount Deposited in the Bank Allan P 2,978.88 Amiel P 4, 656.75 Raquel P 7, 665.50
  103. 103. Lesson 10: Visualizing Multiplication of Decimal Numbers Using Pictorial Models Explore and Discover! Sophia’s rides the bus to and from school each day. A one-way trip is 8.12 kilometers. How many kilometers does he travels in 5 days? Can you visualize how far Sophia travels? One way of visualizing how far Sophia travels is through number line. Get Moving! Show the following multiplication equations by using number lines. 1.) 0.3 x 0.6 = 2.) 0.5 x 0.8 = 3.) 0.7 x 0.4 = 4.) 0.2 x 0.9 = 5.) 0.8 x 0.3 =
  104. 104. Keep Moving! Directions: Illustrate the given equation in a grid. 1. 0.7 x 0.6 = n 4. 0.2 x 0.3 = n 2. 0.4 x 0.8 = n 5. 0.3 x 0.5 = n 3. 0.6 x 0.6 = n Use number lines to find the answer. 1.) Nichole needs 0.95 m of ribbon to trim a shirt. If the ribbon costs ₱ 0.75 per meter. How much did she has to pay? 2.) JR can swim 12 meters in one minute. How far can he swim in 30 minutes? Apply Your Skills! Read and solve the following. Use your own pictorial model to answer the following. 1.) Looking after my baby cousins after classes, my Aunt Abing gives me ₱ 45.00 a day. How can I save a week if I spend ₱ 100.00 for my snacks in school? 2.) Realyn bought 2.5 kg of meat at ₱ 100.00 per kg. she gave the seller a ₱ 500.00 bill. How much change did she get? 3.) Each potted plant in a nursery costs ₱ 25.50. How much will be left on of my ₱ 400.00 if I buy 10 potted plants.
  105. 105. Lesson 11: Multiplying decimals up to 2 decimal places by 1 to 2 digit whole numbers. Explore and Discover! Look at this square. What is its perimeter? 3.5 cm How can you find the perimeter? How many sides has a square? What can you say about its side? Because there are 4 equal sides and each measures 3.5 cm, we can compute this as 4 x 3.5 = N. Here’s how this is done.  Multiply as with whole numbers. Regroup if necessary. 3.5 X 4 140  Count the number of decimal places in the factors. 3.5 X 4 140  Place the decimal point in the product. The decimal place in the product is equal to the total number of decimal places in the factors. 3.5 X 4 1.40 1 decimal place

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