compare quantities as percentages by LHqv7zW

VIEWS: 7 PAGES: 7

									                               Percentages

Objectives:
       D Grade       Express one quantity as a percentage of another


Prior knowledge:
   Understand how to:
      Convert fractions to equivalent fractions
      Convert fractions to decimals
      Convert decimals to percentages
                               Percentages

What is a percentage?
                          percent
                          percent
                        out of
                        hundred

    So we can think of percentages also as fractions with a denominator
    of 100:
      e.g. 65 percent           This helps us to understand that
                                finding a percentage of a quantity
        per    65               is the same as finding a fraction of a
       cent    00
               00               quantity
                                 Percentages

Expressing one quantity as a percentage of another

  Compare one quantity with the other.
    e.g. compare 20 with 25
    Write:                      20
             compare with
                                25
  Write as an equivalent fraction with the denomination 100
                   20      80
                        ≡
                   25     100
         This is now 80%        because 80 is the same as 80%
                                       100
                                 Percentages

Sometimes you might need to have an intermediate equivalent fraction
    e.g. compare 4 with 40
    Write:                      4
             compare with
                               40
    Simplify as an equivalent fraction
                      4      1
                          ≡
                     40     10
   Now write as an equivalent fraction with the denominator of 100
                     1    10
                       ≡
                    10   100

       This is now 10%       because 10 is the same as 10%
                                    100
                                Percentages

Now do these:
                                                   4        20
      1.        Write 4 as a percentage of 20         ≡
                                                  20       100
                                                   50       25
      2.        Write 50 as a percentage of 200       ≡
                                                  200      100
                                                   21       3     10
      3.        Write 14 as a percentage of 28        ≡        ≡
                                                   28       4 100
      4.        Write 4 as a percentage of 25      4        16
                                                       ≡
                                                  25       100
      5.        Write 18 as a percentage of 45    18       2     40
                                                      ≡       ≡
                                                  45       5     100
                                 Percentages

Harder percentages of quantities can be found using a calculator.
                            24
         compare with                     can be read as ÷
                            34

  Convert from a fraction to a decimal:

      Using a calculator:   24 ÷ 34 = 0.7059

   Convert from a decimal to a percentage:

                     0.7059 × 100 = 70.59

                             70.59 %
                                Percentages

Now do these:

      1.        Write 3 as a percentage of 72        3 ÷ 72 = 0.04167
                                              0.04167 × 100 = 4.167 %
                                                    42 ÷ 76 = 0.5526
      2.        Write 42 as a percentage of 76
                                               0.5526 × 100 = 55.26 %
                                                   45 ÷ 135 = 0.3333
      3.        Write 45 as a percentage of 135
                                               0.3333 × 100 = 33.33 %
                                                     37 ÷ 52 = 0.7115
      4.        Write 37 as a percentage of 52 0.7115 × 100 = 71.15 %
                                                     92 ÷ 56 = 1.6429
      5.        Write 92 as a percentage of 56 1.6429 × 100 = 164.29 %

								
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