Lesson 5 3 Identifying and Writing Proportions Class Notes by S21VtHr

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									 5-3 Identifying and Writing Proportions


    Preview

               Warm Up
               California Standards
               Lesson Presentation




Holt CA Course 1
 5-3 Identifying and Writing Proportions
   Warm Up
   Find the unit rate.
                            Evaluate.
   1. 18 miles in 3 hours
                            3(15 – 6) + (18 – 12)2
      6 mi/h
   2. 6 apples for $3.30      A. 36
      $0.55 per apple
   3. 3 cans for $0.87        B. 45
      $0.29 per can           C. 63
   4. 5 CDs for $43
      $8.60 per CD            D. 75

Holt CA Course 1
 5-3 Identifying and Writing Proportions

                   California
                   Standards
         Number Sense (NS1.2) - Interpret and
         use ratios in different contexts (e.g.,
         batting averages, miles per hour) to show
         the relative sizes of two quantities,
         using appropriate notations
                             ( a , a to b, a:b ).
                                b



Holt CA Course 1
 5-3 Identifying and Writing Proportions




        Objective: You will learn how to
        find equivalent ratios and identify
        proportions.




Holt CA Course 1
 5-3 Identifying and Writing Proportions

                    Vocabulary
        equivalent ratios
        proportion




Holt CA Course 1
 5-3 Identifying and Writing Proportions


     Students are measuring the
     width w and the length l of their
     heads. The ratio of l to w is 10
     inches to 6 inches for Jean and
     25 centimeters to 15
     centimeters for Pat.




Holt CA Course 1
 5-3 Identifying and Writing Proportions



         These ratios can be written as the
                      10
         Fractions     6
                          and 25 . Since both ratios
                              15
         simplify   to 5, they are equivalent.
                        3
         Equivalent ratios are ratios that name the

         same comparison.




Holt CA Course 1
 5-3 Identifying and Writing Proportions


     An equation stating that two ratios are
     equivalent is called a proportion. The equation,
     or proportion, below states that the ratios 10
                                                  6
     and 25 are equivalent.
            15
                                     10 = 25
                                      6   15
             Reading Math
             If two ratios are equivalent, they are said to be
             proportional to each other, or in proportion.


Holt CA Course 1
 5-3 Identifying and Writing Proportions
           Example 1: Comparing Ratios in Simplest Forms

    Determine whether the ratios are proportional.

        24 , 72
        51 128

       24 ÷ 3    8      Simplify   24
              =                    51
       51 ÷ 3   17

        72 ÷ 8   9                  72
               =        Simplify
       128 ÷ 8   16                128

     Since     8 ≠ 9 , the ratios are not proportional.
               17  16


Holt CA Course 1
 5-3 Identifying and Writing Proportions
           Example 2: Comparing Ratios in Simplest Forms

    Determine whether the ratios are proportional.

        150 ,         90
        105           63

       150 ÷ 15   10        Simplify   150
                =                      105
       105 ÷ 15    7

        90 ÷ 9   10                    90
               =            Simplify
        63 ÷ 9    7                    63

                   10 10
       Since         =   , the ratios are proportional.
                   7   7

Holt CA Course 1
 5-3 Identifying and Writing Proportions
                         Check It Out! Example 3

     Determine whether the ratios are proportional.
        54 , 72
        63 144
        54 ÷ 9   6         Simplify   54
               =                      63
        63 ÷ 9   7

        72 ÷ 72 1
               =           Simplify    72
       144 ÷ 72 2                     144

                   6   1
       Since         ≠   , the ratios are not proportional.
                   7   2

Holt CA Course 1
 5-3 Identifying and Writing Proportions
                           Check It Out! Example 4

    Determine whether the ratios are proportional.
        135 , 9
         75   4

        135 ÷ 15   9         Simplify   135
         75 ÷ 15 =                       75
                   5

                       9     9 is already in simplest form.
                       4     4

                   9   9
       Since         ≠   , the ratios are not proportional.
                   5   4

Holt CA Course 1
 5-3 Identifying and Writing Proportions
   Example 5: Comparing Ratios Using a Common Denominator
  Directions for making 12 servings of rice
  call for 3 cups of rice and 6 cups of     Servings Cups of Cups of
  water. For 40 servings, the directions    of Rice   Rice   Water
  call for 10 cups of rice and 19 cups of     12        3       6
  water. Determine whether the ratios of
                                              40       10      19
  rice to water are proportional for both
  servings of rice.
   Write the ratios of rice to water for 12 servings and for 40 servings.
                                              3
   Ratio of rice to water, 12 servings:       6    Write the ratio as a fraction.
                                              10
   Ratio of rice to water, 40 servings:            Write the ratio as a fraction.
                                              19
                                                    Write the ratios with a
   3 = 3 · 19      = 57       10 = 10 · 6 = 60
                                                    common denominator,
   6   6 · 19        114      19   19 · 6   114     such as 114.
            57     60
    Since       ≠     , the two ratios are not proportional.
            114   114


Holt CA Course 1
 5-3 Identifying and Writing Proportions
                         Check It Out! Example 6
     Use the data in the table to determine whether the ratios of beans
     to water are proportional for both servings of beans.

          Servings of Beans        Cups of Beans          Cups of Water
                   8                       4                      3
                   35                      13                     9
   Write the ratios of beans to water for 8 servings and for 35 servings.
                                           4
   Ratio of beans to water, 8 servings:             Write the ratio as a fraction.
                                           3
                                               13
   Ratio of beans to water, 35 servings:            Write the ratio as a fraction.
                                                9
                                                    Write the ratios with a
             4 = 4·3     = 12              13       common denominator,
             3   3·3       9                9       such as 9.

    Since 12 ≠ 13 , the two ratios are not proportional.
            9      9


Holt CA Course 1
 5-3 Identifying and Writing Proportions



               You can find an equivalent ratio by
               multiplying or dividing the numerator
               and the denominator of a ratio by the
               same number.




Holt CA Course 1
 5-3 Identifying and Writing Proportions
    Example 7: Finding Equivalent Ratios and Writing Proportions
     Find a ratio equivalent to each ratio. Then use the ratios
     to find a proportion.
     A. 3               Multiply both the
        5
                        numerator and
        3    3·2 = 6
           =            denominator by any
        5    5 · 2 10 number, such as 2.
        3 = 6
        5    10 Write a proportion.
     B. 28
        16               Divide both the
        28 = 28 ÷ 4 = 7 numerator and
                         denominator by any
        16 16 ÷ 4     4
                         number, such as 4.
        28 = 7
        16    4 Write a proportion.


Holt CA Course 1
 5-3 Identifying and Writing Proportions
                     Check It Out! Example 8

     Find a ratio equivalent to each ratio. Then use the ratios
     to find a proportion. Possible Answers:

     A. 2              Multiply both the
         3
                       numerator and
         2   2·3 = 6
           =           denominator by any
         3   3·3     9 number, such as 3.
        2 = 6
        3    9 Write a proportion.
     B. 16
        12              Divide both the
        16 = 16 ÷ 4 = 4 numerator and
        12 12 ÷ 4     3 denominator by any
                        number, such as 4.
        16 = 4
        12   3 Write a proportion.


Holt CA Course 1
 5-3 Identifying and Writing Proportions

                                    On-Line
                                    Tutoring




Holt CA Course 1
 5-3 Identifying and Writing Proportions
                         Lesson Quiz: Part I
     Determine whether the ratios are proportional.

          9    12                    12 10
     1. 30 , 40                   2. 21 , 15
          3 , 3 ; proportional        4 , 2 ; not proportional
          10 10                       7 3

    Find a ratio equivalent to each ratio. Then use
    the ratios to write a proportion.

           3   15 ; 3 = 15         4. 3    9 ; 3 = 9
     3.    8   40   8   40            7   21 7     21




Holt CA Course 1
 5-3 Identifying and Writing Proportions
                     Lesson Quiz: Part II

   5. In one pre-school, there are 5 children for every
     teacher. In another pre-school, there are 20
     children for every 4 teachers. Determine whether
     the ratios of children to teachers are proportional
     in both pre-schools.
        5 = 20
        1    4




Holt CA Course 1

								
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