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November 14, 2012



                    Today:

   Warm-Up: Review Fractions & GCF
          Decimals: +, -, x, ÷
             STAR Math
  Khan Academy: Nov. 10th & 17 Topics
Warm-Up:
Khan Academy Help: Dividing Fractions Word Probs.
Warm-Up:

3. Which Fraction is larger: 4/6 or 7/10?

4. 2/5 + 7/8 =           5.   3 3/7 + 2 3/8 =
6. 6/11 - 5/12 =         7.   3 2/7 - 2 1/8 =
8. 8/15 • 3/11 =         9.   3 2/7 • 2 1/8 =
10. 8/15 ÷ 3/11         11.   3 2/7 ÷ 2 1/8 =
  =
 12. Find the Prime Factorization of 60

 13. Simplify, using GCF: 144/150
Decimals: Objectives

1.   Read decimals          6.  Add decimals
2.   Write decimals         7. Subtract decimals
3.   Compare the size of    8. Multiply decimals
     decimals to one        9. Divide decimals
     another                10. Round decimals to
4.   Convert fractions to       nearest tenth
     decimals               11. Round decimals to
5.   Convert decimals to        nearest hundredth
     fractions
Decimals: Definition

 A decimal is a fraction with a denominator that is a
  multiple of 10. The decimal (.) is used to indicate place
  value. Examples:
       3
             equals 0.3 stated as "three tenths"
       10
       18
              equals 0.18 stated as "eighteen hundre dths"
       100

   Caution: each decimal expression with a value
     less than 1 is preceded by a leading zero to
      emphasize the presence of a decimal. For
        example, .7 is correctly written as 0.7
Decimals: Place values
Decimals: Reading

 Reading
  1. Read the whole number on the left
  2. Read the decimal point as the word
     “and”
  3. Read the decimal fraction on the right
  Example: 8.3 = “eight and three tenths”
         4.06 = “four and six hundredths”
          0.5 = “five tenths
Decimals: Writing

   Write as follows

1. The whole number (if none, then write a zero - (“0”)

2. The decimal point to indicate the place of value

3. The decimal fraction portion of the number
    Examples: “Seven and five tenths” = 7.5
    “One hundred twenty-five thousandths” = 0.125
Decimals: Comparing Values

 Zeros do not change the value of the number
 whether added at the beginning or the end,
 but they are unsafe as trailers.

  Ex:  .7 is the same numerical value as 0.7
   12.6250 is the same value as 12.625
   but, 30.0 can be misinterpreted as 300!

     Use leading zeros; AVOID trailing zeros
Decimals: Comparing Values (cont’d)


 Zeros added within a decimal number
 change the value dramatically

  Example:   0.375 is NOT the same as 0.0375
              2.025 is NOT the same as 20.025
Decimals: Comparing Values (cont’d)

 Different whole numbers
  Ifwhole numbers are present and different,
   whole numbers are compared to determine
   largest
  Example: 4.8 is greater than 2.9



 Same or no whole number
  The number in the tenths place determines
   largest
  Example: 0.45 is larger than 0.37
Decimals: Comparing Values (cont’d)


 Same or no whole number, and the number
  in the tenths place is the same
 The decimal with the highest number in the
  hundredths place is the largest

  Examples:    0.67 is larger than 0.66
               0.17 is larger than 0.14
               0.09 is larger than 0.08
Decimals: Adding and Subtracting

 Place the numbers in the columns so the decimals
 are lined up. Add or subtract from left to right.
    Examples:

   16.4             .7
   21.8             .750           .7
  + 3.0           + .324         - .050



         Safety Point: Zeros may be added to help line up
        decimals – don’t include in final answer!
Decimals: Multiplying
 Place decimal correctly!
 Multiply numbers; in the product (answer), count
 decimal places right to left equal to the total
 decimal places in the numbers being multiplied.
    Example:

                 1.2
                                     .7
                x 3.2
                                   x .050
                  24
                 36
                384.    =   3.84
Decimals: Multiplying (cont’d)

 Add zeros where needed to ensure correct
 placement of decimal in answer
  Example: 0.11 x .33


           0.11
                               .12
          x 0.33
                             x .14
             33
            33

           0363. = 0.0363
Multiplying by Decimal Movement


 Multiplying by 10, 100, 1,000 can be done by
 moving decimal to the right one space for each
 zero in the number by which multiplying
  Example:     1.6 x 10 = 1.6 = 16

                 5.2 x 100 = 5.20 = 520


     .7 • 10 =               .8 • 100 =
Decimals: Dividing


 Same as for whole numbers


              Q uotient
      Divisor Dividend
    Example:    9 27   = 27 divided by 9
Decimals: Dividing a Decimal

 To divide by a whole number, place decimal in
 quotient directly above decimal in dividend

         3 .5
     5 1 7 .5
                       8 22.3
     - 15
         25             4 35.7
     -   25

            0
Decimals: Dividing by a Decimal

 Move the decimal in the divisor to the right
 until the number is a whole number. Then move
 the decimal in the dividend the same number of
 spaces.                           2 3 .2
                    .            3   6 9 .6

             0.3 6.96            -   6
                                         9
                                 -       9

          .8 12.1                            6
                                             -6

                                              0
Class Work:


       Decimal Handout:
Every Other Problem
Girls: Begin with First Problem
Gents: Begin with Second
Problem
November 14
Decimals: Changing from Fractions
 Rewrite fraction in division format
 Divide the numerator by the denominator and add
  zeros as needed
 Method can be used to compare fraction size

           0.4
     2             1                  1
         5 2.0         0.333... and        0.166...
     5             3                  6
                              1                    1
                  Therefore       is larger than
                              3                    6

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November 14

  • 1. November 14, 2012 Today: Warm-Up: Review Fractions & GCF Decimals: +, -, x, ÷ STAR Math Khan Academy: Nov. 10th & 17 Topics
  • 2. Warm-Up: Khan Academy Help: Dividing Fractions Word Probs.
  • 3. Warm-Up: 3. Which Fraction is larger: 4/6 or 7/10? 4. 2/5 + 7/8 = 5. 3 3/7 + 2 3/8 = 6. 6/11 - 5/12 = 7. 3 2/7 - 2 1/8 = 8. 8/15 • 3/11 = 9. 3 2/7 • 2 1/8 = 10. 8/15 ÷ 3/11 11. 3 2/7 ÷ 2 1/8 = = 12. Find the Prime Factorization of 60 13. Simplify, using GCF: 144/150
  • 4. Decimals: Objectives 1. Read decimals 6. Add decimals 2. Write decimals 7. Subtract decimals 3. Compare the size of 8. Multiply decimals decimals to one 9. Divide decimals another 10. Round decimals to 4. Convert fractions to nearest tenth decimals 11. Round decimals to 5. Convert decimals to nearest hundredth fractions
  • 5. Decimals: Definition  A decimal is a fraction with a denominator that is a multiple of 10. The decimal (.) is used to indicate place value. Examples: 3 equals 0.3 stated as "three tenths" 10 18 equals 0.18 stated as "eighteen hundre dths" 100 Caution: each decimal expression with a value less than 1 is preceded by a leading zero to emphasize the presence of a decimal. For example, .7 is correctly written as 0.7
  • 7. Decimals: Reading  Reading 1. Read the whole number on the left 2. Read the decimal point as the word “and” 3. Read the decimal fraction on the right Example: 8.3 = “eight and three tenths” 4.06 = “four and six hundredths” 0.5 = “five tenths
  • 8. Decimals: Writing  Write as follows 1. The whole number (if none, then write a zero - (“0”) 2. The decimal point to indicate the place of value 3. The decimal fraction portion of the number Examples: “Seven and five tenths” = 7.5 “One hundred twenty-five thousandths” = 0.125
  • 9. Decimals: Comparing Values  Zeros do not change the value of the number whether added at the beginning or the end, but they are unsafe as trailers.  Ex: .7 is the same numerical value as 0.7 12.6250 is the same value as 12.625 but, 30.0 can be misinterpreted as 300! Use leading zeros; AVOID trailing zeros
  • 10. Decimals: Comparing Values (cont’d)  Zeros added within a decimal number change the value dramatically  Example: 0.375 is NOT the same as 0.0375 2.025 is NOT the same as 20.025
  • 11. Decimals: Comparing Values (cont’d)  Different whole numbers  Ifwhole numbers are present and different, whole numbers are compared to determine largest  Example: 4.8 is greater than 2.9  Same or no whole number  The number in the tenths place determines largest  Example: 0.45 is larger than 0.37
  • 12. Decimals: Comparing Values (cont’d)  Same or no whole number, and the number in the tenths place is the same  The decimal with the highest number in the hundredths place is the largest  Examples: 0.67 is larger than 0.66 0.17 is larger than 0.14 0.09 is larger than 0.08
  • 13. Decimals: Adding and Subtracting  Place the numbers in the columns so the decimals are lined up. Add or subtract from left to right.  Examples: 16.4 .7 21.8 .750 .7 + 3.0 + .324 - .050 Safety Point: Zeros may be added to help line up decimals – don’t include in final answer!
  • 14. Decimals: Multiplying  Place decimal correctly!  Multiply numbers; in the product (answer), count decimal places right to left equal to the total decimal places in the numbers being multiplied.  Example: 1.2 .7 x 3.2 x .050 24 36 384. = 3.84
  • 15. Decimals: Multiplying (cont’d)  Add zeros where needed to ensure correct placement of decimal in answer  Example: 0.11 x .33 0.11 .12 x 0.33 x .14 33 33 0363. = 0.0363
  • 16. Multiplying by Decimal Movement  Multiplying by 10, 100, 1,000 can be done by moving decimal to the right one space for each zero in the number by which multiplying  Example: 1.6 x 10 = 1.6 = 16 5.2 x 100 = 5.20 = 520 .7 • 10 = .8 • 100 =
  • 17. Decimals: Dividing  Same as for whole numbers Q uotient Divisor Dividend  Example: 9 27 = 27 divided by 9
  • 18. Decimals: Dividing a Decimal  To divide by a whole number, place decimal in quotient directly above decimal in dividend 3 .5 5 1 7 .5 8 22.3 - 15 25 4 35.7 - 25 0
  • 19. Decimals: Dividing by a Decimal  Move the decimal in the divisor to the right until the number is a whole number. Then move the decimal in the dividend the same number of spaces. 2 3 .2 . 3 6 9 .6 0.3 6.96 - 6 9 - 9 .8 12.1 6 -6 0
  • 20. Class Work: Decimal Handout: Every Other Problem Girls: Begin with First Problem Gents: Begin with Second Problem
  • 22. Decimals: Changing from Fractions  Rewrite fraction in division format  Divide the numerator by the denominator and add zeros as needed  Method can be used to compare fraction size 0.4 2 1 1 5 2.0 0.333... and 0.166... 5 3 6 1 1 Therefore is larger than 3 6