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					5-1 Ratios

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   Evaluating Algebraic Expressions

       Warm Up
       California Standards
       Lesson Presentation
5-1 Ratios


   Evaluating Algebraic Expressions
 Warm Up
 Write each fraction in lowest terms.

 1. 14   7          2. 24   3
    16   8             64   8


 3. 9    1          4. 45   3
   72    8            120   8
5-1 Ratios


   Evaluating Algebraic Expressions
        California
        Standards
   Preparation for MG1.1 Compare
   weights, capacities, geometric
   measures, times, and temperatures
   within and between measurement
   systems (e.g., miles per hour and feet
   per second, cubic inches to cubic
   centimeters).
5-1 Ratios

            Vocabulary
    Evaluating Algebraic Expressions
   ratio
   equivalent ratios
5-1 Ratios


   Evaluating Algebraic Expressions
   A ratio is a comparison of two quantities.



   Ratios can be written in several ways. 7
   to 5, 7:5, and 7 name the same ratio.
                  5
5-1 Ratios
 Additional Example 1: Writing Ratios in Simplest
                      Form
    Evaluating Algebraic Expressions
 Write the ratio 15 bikes to 9 skateboards in
 simplest form.

     bikes    = 15                Write the ratio
  skateboards   9                 as a fraction.

                 15 ÷ 3
               =        = 5       Simplify.
                 9÷3      3

                                        5
 The ratio of bikes to skateboards is     , 5:3, or 5 to 3.
                                        3
5-1 Ratios
               Check It Out! Example 1

    Evaluating Algebraic Expressions
 Write the ratio 24 shirts to 9 jeans in
 simplest form.

    shirts = 24                 Write the ratio as
    jeans    9                  a fraction.

               24 ÷ 3
           =            = 8    Simplify.
               9÷3        3

                                    8
  The ratio of shirts to jeans is     , 8:3, or 8 to 3.
                                    3
5-1 Ratios


   Evaluating Algebraic Expressions

   When simplifying ratios based on
   measurements, write the quantities
   with the same units, if possible.
5-1 Ratios
  Additional Example 2: Writing Ratios Based on
                 Measurement
    Evaluating yards to 12 feet in simplest
 Write the ratio 3 Algebraic Expressions
 form.
 First convert yards to feet.
 3 yards = 3 ● 3 feet   There are 3 feet in each yard.
          = 9 feet      Multiply.

 Now write the ratio.
  3 yards = 9 feet          9÷3=3
                         =              Simplify.
  12 feet      12 feet      12 ÷ 3 4
  The ratio is 3 , 3:4, or 3 to 4.
               4
5-1 Ratios
             Check It Out! Example 2
 Write the ratio 36 inches to 4 feet in
    Evaluating Algebraic Expressions
 simplest form.
 First convert feet to inches.
 4 feet = 4 ● 12 inches   There are 12 inches in each
                          foot.
       = 48 inches        Multiply.
 Now write the ratio.
 36 inches = 36 inches = 36 ÷ 12 = 3     Simplify.
  4 feet     48 inches     48 ÷ 12 4
  The ratio is 3 , 3:4, or 3 to 4.
               4
5-1 Ratios


   Evaluating Algebraic Expressions
  Ratios that make the same comparison
  are equivalent ratios. Equivalent
  ratios represent the same point on the
  number line. To check whether two
  ratios are equivalent, you can write both
  in simplest form.
5-1 Ratios
 Additional Example 3: Determining Whether Two
              Ratios Are Equivalent
   Evaluating Algebraic Expressions
 Simplify to tell whether the ratios are
 equivalent.

  A. 3 and 2     3   3 ÷ 3 =1          1= 1
                   =             Since       ,
     27    18    27 27 ÷ 3 9           9 9
                                 the ratios are
                 2   2 ÷ 2 =1
                   =             equivalent.
                 18 18 ÷ 2 9

  B. 12 and 27 12 = 12 ÷ 3 = 4   Since 4  3 ,
     15     36 15 15 ÷ 3 5             5 4
                                 the ratios are not
                27 = 27 ÷ 9 3
                                 equivalent.
                36 36 ÷ 9 = 4
5-1 Ratios
            Check It Out! Example 3

 Simplify to tell whether the ratios are
   Evaluating Algebraic Expressions
 equivalent.


 A. 3 and 9     3   3÷3= 1            1= 1
                  =             Since       ,
    15    45    15 15 ÷ 3 5           5 5
                                the ratios are
                9   9÷9= 1
                  =             equivalent.
                45 45 ÷ 9 5

                14 = 14 ÷ 7 2
 B. 14 and 16                   Since 2  4 ,
                49 49 ÷ 7 = 7         7 9
    49     36                   the ratios are not
                16 = 16 ÷ 4 4
                                equivalent.
                36 36 ÷ 4 = 9
5-1 Ratios
 Additional Example 4: Earth Science Application

  At 4°C, four cubic feet of silver has the same
     Evaluating Algebraic Expressions
  mass as 42 cubic feet of water. At 4°C,
  would 20 cubic feet of silver have the same
  mass as 210 cubic feet of water?
                                Since 2 = 2 ,
     4    ? 20       ft3 silver        21      21
          =
     42     210      ft3 water
                                210 cubic feet of water
 4÷2                            would have the same
          = 20 ÷ 10 Divide.
          ?
 42 ÷ 2     210 ÷ 10            mass at 4°C as 20 cubic
                                feet of silver.
    2     =  2
    21       21       Simplify.
5-1 Ratios
             Check It Out! Example 4

 At 4°C, two cubic feet of silver has the same
    Evaluating Algebraic Expressions
 mass as 21 cubic feet of water. At 4°C,
 would 105 cubic feet of water have the same
 mass as 10 cubic feet of silver?

  2 = 10
     ?            ft3 silver Since 2 = 2 ,
  21   105        ft3 water        21  21

   2 = 10 ÷ 5
      ?                    105 cubic feet of water
                Divide.    would have the same
   21   105 ÷ 5
                           mass at 4°C as 10 cubic
  2 = 2          Simplify. feet of silver.
  21  21
5-1 Ratios
              Lesson Quiz: Part I
 Write each ratio in simplest form.
     Evaluating Algebraic Expressions
                            1
 1. 22 tigers to 44 lions
                            2
 2. 5 feet to 14 inches    30
                            7
 Find two ratios that are equivalent to each
 given ratio.

 3. 4   Possible answer: 8 , 12
   15                    30 45

 4. 8   Possible answer: 16 , 24
   21                    42 63
5-1 Ratios
                Lesson Quiz: Part II
 Simplify to tell whether the ratios are
     Evaluating Algebraic Expressions
 equivalent.
 5. 16 and 32 8 = 8; yes
    10     20 5 5

6. 36 and 28    3 14 ; no
   24     18    2 9
 7. Kate poured 8 oz of juice from a 64 oz bottle.
    Brian poured 16 oz of juice from a 128 oz bottle.
    Are the ratios of poured juice to starting amount
    of juice equivalent?
     8 and 16 ; yes, both equal 1
    64      128                    8

				
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