Relating Decimals, Fractions, and Percents by BR19t9Xp

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									  Relating Decimals, Fractions,
  and Percents

               8.1




Pre-Algebra
                Warm Up

Evaluate.

1. 2 + 3    1      2. 7 – 3
                                 1
   15 15    3         12 12      3

3. 4    7 14 or 2 4 4.   1
                            1   14
                       3
   5    2 5       5      2   4
Learn to relate decimals, fractions, and
percents.
          Vocabulary

percent
Percents are ratios that compare a number
to 100.

         Equivalent Ratio with
 Ratio                           Percent
          Denominator of 100
   3             30
  10             100              30%
  1              50
                 100
                                  50%
  2
   3             75
                 100
                                  75%
   4
Reading Math
Think of the % symbol as meaning /100.
0.75 = 75% = 75/100
To convert a fraction to a decimal, divide
the numerator by the denominator.
          1
            = 1 ÷ 8 = 0.125
          8

To convert a decimal to a percent, multiply by
100 and insert the percent symbol.

        0.125      100  12.5%
Example: Finding Equivalent Ratios
          and Percents
Find the missing ratio or percent equivalent
for each letter a–g on the number line.




          10   1
 a: 10% =    =
          100 10
Example: Finding Equivalent Ratios
          and Percents
Find the missing ratio or percent equivalent
for each letter a–g on the number line.




      1
 b:     = 0.25 = 25%
      4
Example: Finding Equivalent Ratios
          and Percents
Find the missing ratio or percent equivalent
for each letter a–g on the number line.




          40   4   2
 c: 40% =    =   =
          100 10   5
Example: Finding Equivalent Ratios
          and Percents
Find the missing ratio or percent equivalent
for each letter a–g on the number line.




      3
 d:     = 0.60 = 60%
      5
Example: Finding Equivalent Ratios
          and Percents
Find the missing ratio or percent equivalent
for each letter a–g on the number line.




         2            2
 e: 66     %= 0.666 =
         3            3
Example: Finding Equivalent Ratios
          and Percents
Find the missing ratio or percent equivalent
for each letter a–g on the number line.




         1            875
 f: 87     %= 0.875 =      = 7
         2            1000   8
Example: Finding Equivalent Ratios
          and Percents
Find the missing ratio or percent equivalent
for each letter a–g on the number line.




           125   5     1
 g: 125% =     =   = 1
           100   4     4
                   Try This
Find the missing ratio or percent equivalent
for each letter a–g on the number line.
         1         c         e
    12     % 25%       50%       75%    g
         2

                             5          1
      a      b     3   d          f
                   8         8


                             125
         a: 12 1 % = 0.125 =      = 1
               2             1000   8
          Try This Continued
Find the missing ratio or percent equivalent
for each letter a–g on the number line.
         1         c         e
    12     % 25%       50%       75%   g
         2

                             5         1
      a      b     3   d         f
                   8         8


                      25    1
             b: 25% =     =
                      100   4
          Try This Continued
Find the missing ratio or percent equivalent
for each letter a–g on the number line.
         1         c         e
    12     % 25%       50%       75%   g
         2

                             5         1
      a      b     3   d         f
                   8         8


               3             1
            c:   = 0.375 = 37 %
               8             2
          Try This Continued
Find the missing ratio or percent equivalent
for each letter a–g on the number line.
         1         c         e
    12     % 25%       50%       75%   g
         2

                             5         1
      a      b     3   d         f
                   8         8


                      50    1
             d: 50% =     =
                      100   2
          Try This Continued
Find the missing ratio or percent equivalent
for each letter a–g on the number line.
         1         c         e
    12     % 25%       50%       75%   g
         2

                             5         1
      a      b     3   d         f
                   8         8


               5             1
            e:   = 0.625 = 62 %
               8             2
          Try This Continued
Find the missing ratio or percent equivalent
for each letter a–g on the number line.
         1         c         e
    12     % 25%       50%       75%   g
         2

                             5         1
      a      b     3   d         f
                   8         8


                      75    3
             f: 75% =     =
                      100   4
          Try This Continued
Find the missing ratio or percent equivalent
for each letter a–g on the number line.
         1         c          e
    12     % 25%        50%       75%   g
         2

                              5         1
      a      b     3     d        f
                   8          8


                      100 100%
             g: 1 =       =
                      100
     Example: Finding Equivalent
  Fractions, Decimals, and Percents
Find the equivalent fraction, decimal, or percent
for each value given on the circle graph.

               Fraction Decimal        Percent
                15
                    = 3     0.15   0.15(100) = 15%
                100 20
                35 = 7     7 = 0.35
                100 20                    35%
                          20
                38 19     19 = 0.38
                    =                    38%
                100 50    50
                   3       3 = 0.12
                          25        0.12(100) = 12%
                  25
         Example Continued
 You can use information in each column to
 make three equivalent circle graphs. One
 shows the breakdown by fractions, one shows
 the breakdown by decimals, and one shows the
 breakdown by percents.




The sum of the     The sum of the    The sum of the
fractions should   decimals should   percents should
be 1.              be 1.             be 100%.
               Try This
Fill in the missing pieces on the chart below.


  Fraction Decimal          Percent
    1                   0.1(100) = 10%
   10           0.1
 45 = 9      45 =0.45       45%
 100 20      100
    1        25 =0.25 0.25(100) = 25%
    4        100
    1         1 = 0.2
              5        0.2(100) = 20%
    5
     Example: Physical Science
           Application
Gold that is 24 karat is 100% pure gold. Gold
that is 14 karat is 14 parts pure gold and 10
parts another metal, such as copper, zinc,
silver, or nickel. What percent of 14 karat gold
is pure gold?
parts pure gold      14 = 7     Set up a ratio and
  total parts        24 12      reduce.
 7 =
     7  12 = 0.583 = 58.3%     Find the percent.
12
                                 1
So 14-karat gold is 58.3%, or 58 3 % pure
gold.
                  Try This
A baker’s dozen is 13. When a shopper
purchases a dozen items at the bakery they
get 12. It is said that the baker eats 1 item
from every batch. So, what percentage of the
food the baker cooks is eaten without being
sold?
   items eaten           1      Set up a ratio and
     total items        13      reduce.
  1 =
         1  13 = 0.077 = 7.7%  Find the percent.
 13

So the baker, eats 7.7% of the items they
bake.
                Lesson Quiz
Find each equivalent value.
1. 3 as a percent       37.5%
    8
                         1
2. 20% as a fraction     5
     5
3.     as a decimal        0.625
     8
4. 14 as a percent         56%
    25
5. About 342,000 km2 of Greenland’s total area
   (2,175,000 km2) is not covered with ice. To the
   nearest percent, what percent of Greenland’s
   total area is not covered with ice?
   16%

								
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