2. Lesson Quiz: Part I Write each in standard form, expanded form and words. 1. 8.0342 2. 10 + 8 + 0.3 + 0.006 3. eight and twelve hundredths 18.306; eighteen and three hundred six thousandths 8 + 0.03 + 0.004 + 0.0002; eight and three hundred forty-two ten thousandths 8.12; 8 + 0.1 + 0.02
3. A number is in exponential form when it is written with a base and an exponent. 7 3 = 7 7 7= 343 An exponent tells how many times a number called the base is used as a factor. Base Exponent
4. Additional Example 1: Writing Numbers in Exponential Form Write each expression in exponential form. A. 5 5 5 5 B. 3 3 3 3 3 5 is a factor 4 times. 5 4 3 is a factor 5 times. 3 5
5. Lesson Quiz Write each expression in exponential form. 1. 12 12 12 2. 9 9 9 9 9 9 9 Find each value. 3. 20 2 4. 6 4 5. In a phone tree, each of three people will call three people, and then each of those will call three more. If there are five levels of the tree, how many people will be called? 9 7 12 3 400 1,296 243
6. Additional Example 1B: Using the Order of Operations Evaluate the expression. 9 + (21 ÷ 7) 5 9 + (21 ÷ 7) 5 9 + 3 5 9 + 15 24 Perform operations within parentheses. Multiply. Add.
7. Check It Out: Example 1B Evaluate the expression. 7 + (24 ÷ 6) 3 7 + (24 ÷ 6) 3 7 + 4 3 7 + 12 19 Perform operations within parentheses. Multiply. Add.
8. Additional Example 2B: Using the Order of Operations with Exponents Evaluate the expression. 24 ÷ (9 – 6) 3 2 – 10 8 9 – 10 72 – 10 62 Perform operations within parentheses. Multiply. Divide. Find the value of the number with the exponent. 24 ÷ (9 – 6) 3 2 – 10 24 ÷ 3 3 2 – 10 24 ÷ 3 9 – 10 Subtract.
9. Lesson Quiz Evaluate each expression. 1. 15 + 4 2 2. (12 – 5) 2 – 10 3. 3 + 9 2 – 5 4. 4 3 – 30 ÷ 2 5. Chaz bought 4 football cards for $2 each and 8 baseball cards for $3 each. Evaluate the expression to find the amount Chaz spent on cards: 4 2 + 8 3. 39 23 16 49 $32
10. Lesson Quiz Identify a pattern in each sequence, and then find the missing terms. 1. 12, 24, 36, 48, , , , … 2. 75, 71, 67, 63, , , ,… Identify a pattern in each sequence. Name the missing terms. 3. 1000, 500, , 125,… 4. 100, 50, 200, , 400, ,… subtract 4; 59, 55, 51 add 12; 60, 72, 84 divide by 2; 250 divide by 2 then multiply by 4; 100, 200
11. Lesson Quiz Estimate each product or quotient. 3 14 80 3. 6.75 1.82 4. 10.5 ÷ 3.42 5. The snowfall in December, January, and February was 18.26 cm, 29.36 cm, and 32.87 cm, respectively. About how many total centimeters of snow fell during the three months? Estimate by rounding to the indicated place value. 3 4.5 1. 3.07442 + 1.352; tenths 2. 7.305 – 4.12689; nearest whole number
12. Lesson Quiz Find each sum or difference. 1. 8.3 + 2.7 2. 9.7 – 4 3. 22.6 + 8.4 4. Evaluate 12.76 – x for x = 8.41. 5. During an ice-skating competition, Dawn received the following scores: 4.8, 5.2, 5.4. What was Dawn’s total score? 5.7 11 Insert Lesson Title Here 31 4.35 15.4 Course 1 3-3 Adding and Subtracting Decimals
13. Lesson Quiz Find each product. 1. 0.8 2. 0.006 0.07 Evaluate 8 x for each value of x . 0.00042 0.056 Insert Lesson Title Here 21.64 6.432 0.07 $87.40 3. x = 2.705 4. x = 0.804 5. “Pick your own” peaches sell for $0.95 per pound. You picked 92 pounds of peaches. How much were you charged? Course 1 3-5 Multiplying Decimals
14. Lesson Quiz Find each quotient. 1. 49 ÷ 0.7 2. 21.63 ÷ 2.1 3. 38.43 ÷ 6.1 4. 16.9 ÷ 5.2 5. John spent $13.44 renting 4 videos for the weekend. What was the cost per video? 10.3 70 Insert Lesson Title Here 6.3 3.25 $3.36 Course 1 3-7 Dividing by Decimals
15. Lesson Quiz Solve each equation. Check your answer. 1. x – 3.9 = 14.2 2. = 8.3 3. x – 4.9 = 16.2 4. 7 x = 47.6 5. The area of the floor in Devon’s room is 35.7 m 2 . If the width is 4.2 m, what is the length of the bedroom? Insert Lesson Title Here x = 18.1 x = 33.2 x = 21.1 x = 6.8 8.5 m Course 1 3-9 Solving Decimal Equations x 4
16. Lesson Quiz Use the following data set: 18, 20, 56, 47, 30, 18, 21. 1. Find the range. 2. Find the mean. 3. Find the median. 4. Find the mode. 5. Bonnie ran a mile in 8 minutes, 8 minutes, 7 minutes, 9 minutes, and 8 minutes. What was her mean time? 38 30 21 18 8 minutes
17. Lesson Quiz: Part 1 Use the bar graph to answer each question. 1. Which animal was least popular among students? 2. Which pet was more popular to twice as many students as rabbits were? dog bird Student Pet Survey
18. Check It Out: Example 2 Step 1 : Draw a number line. Step 2 : For each aluminum can, use an x on the number line to represent how many were collected. Students collected aluminum cans for a project. The number of cans collected by the students is recorded in the table. Make a line plot of the data. x x x x x x x x x x x x Cans Collected 5 7 11 14 11 5 7 14 14 5 15 11 5 6 7 8 9 10 11 12 13 14 15 16
19. 1. Evaluate the expression to find the missing values in the table. Lesson Quiz 2. A rectangle is 6 units wide. How many square units does the rectangle cover if it is 2, 3, 4, or 5 units long? 95 44 20 12 18 24 30 l w l x w 2 6 3 6 4 6 5 6 x x 2 – 5 10 7 5
20. 1. Let x represent the number of minutes Kristen works out in one week. Write an expression for the number of minutes she works out in 4 weeks. Lesson Quiz Write each phrase as a numerical or algebraic expression. 2. 7 less than x 3. The product of 12 and w 4 x x 7 12 w x more than 17 or x added to 17 n divided by 12 or the quotient of n and 12 Write a phrase for each expression. 4. 17 + x 5. n 12
21. Determine whether the given value of each variable is a solution. 1. 85 = 13 x for x = 5 2. w + 38 = 210 for w = 172 3. 8 y = 88 for y = 11 4. 16 = w 6 for w = 98 Lesson Quiz no yes yes no no 5. The local pizza shop charged Kylee $172 for 21 medium pizzas. The price of a medium pizza is $8. Determine if Kylee paid the correct amount of money. ( Hint : $8 • pizzas = total cost.)
22. Solve each equation. 1. x + 15 = 72 2. 81 = x + 24 3. x + 22 = 67 4. 93 = x + 14 Lesson Quiz x = 57 x = 57 x = 45 x = 79 56 inches 5. Kaitlin is 2 inches taller than Reba. Reba is 54 inches tall. How tall is Kaitlin?
23. 1. x – 9 = 21 2. 14 = x – 3 3. x – 7 = 11 4. 16 = x – 14 5. x – 9 = 11 Lesson Quiz 6. Susan is taller than James. The difference in their height is 4 inches. James is 62 inches tall. How tall is Susan? x = 30 x = 17 x = 18 x = 30 x = 20 66 inches
24. 1. 10 y = 300 2. 2 y = 82 3. 63 = 9 y 4. 78 = 13 x Lesson Quiz 5. The area of a board game is 468 square inches. Its width is 18 inches. What is the length? y = 30 y = 41 y = 7 x = 6 26 inches
25. 1. = 7 2. 8 = 3. = 11 4. = 7 Lesson Quiz 5. The area of Sherry’s flower garden is one- fourth the area of her vegetable garden. The area of the flower garden is 17 square feet. Let x represent the area of her vegetable garden. Find the area of her vegetable garden? x = 70 x = 32 x = 99 x = 105 68 square feet Solve each equation. Check your answers. x 4 x 9 x 10 x 15
