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Ratios,
 Proportions
and Percents
A ratio is a comparison of two quantities.



Write a ratio comparing the number of squares to
the number of circles.

     3 to 2

     3:2

      3
      2
Two equal ratios form a proportion.



 Circles        2                     4
 squares        3                     6

                       2=4
                       3 6
                    proportion
Solving proportions
        x3
       3= n        n=9       Look for a multiplier
       4 12                     (scale factor)

        x3

  30          7n
                             No obvious multiplier -
       5= n
                                 Cross multiply
       7 6         7n = 30
                   7     7
                         2
                   n=47
Three out of every 10 adults segregate their food.

a) Write this information as a ratio.
       Segregators          3
          total             10
b) In a group of 90 people, how many would you
   expect to be food segregators?
                       x9

Segregators          3 = x
                                   x = 27
   total             10 90
                       x9
The scale on a map is 1 inch = 20 miles.

a) If two towns are 4 ½ inches apart on the map, how
many miles apart are they?
       1x         20 · 4 ½
                               x = 20 · 9 = 180 = 90
Inch      1 = 4½                        2    2
Mile      20    x               90 miles apart

b) If two towns are 75 miles apart, how far apart will
they be on the map?
        75        20x      20x = 75 3 ¾ inches apart
Inch       1 = x           20 20
Mile      20    75           x = 75 5 = 15
                                 20 5    4
Percents
• “Percent” means “out of 100”
• Percents are rational numbers
            41
     41% =
           100
           260
    260% =
           100
           0.2 10       2
    0.2% =
           100 10     1000
           100 1
    100% =
           100
Fractions/Decimals/Percents

Percents    Fractions
      16     4
16% =
      100    25
                         Move decimal point
Percents    Decimals     two places left
      16
16% =     = 0.16        175% = 1.75
      100

                        0.05% = 0.0005
Fractions      Percents
 5 x5      25
              = 25%
 20 x5    100                       16
                                  3 50
                  6x = 100          3
  1       x
                   6     6          20
  6      100
                  x = 50            18
                       3             2
                          2
                     = 16     %
                          3
Decimals     Percents   Move decimal point
                        two places right
         37
0.37        = 37%
        100


       0.0004 = 0.04%

        36.7 = 3670%
The Percent Proportion

    percent   part
            =
      100     whole

 What is 20% of 18?

  20        x            100x = 360
      =                  100 100
  100      18

                          x = 3.6
3 is 6% of what number?
part    percent       whole


       percent    part
               =
        100      whole

         6        3
            =
        100       x

       6x = 300
       6     6
        x = 50
A dress that normally sells for $80 is on sale for $52.
What is the “percent off”?

1)   Find the markdown
          80 – 52 = 28

2)   Percent: x         Part: 28         Whole: 80

           x    28
              =
          100   80
           80x = 2800
             x = 35
                                   35 % off

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1150 day 11

  • 2. A ratio is a comparison of two quantities. Write a ratio comparing the number of squares to the number of circles. 3 to 2 3:2 3 2
  • 3. Two equal ratios form a proportion. Circles 2 4 squares 3 6 2=4 3 6 proportion
  • 4. Solving proportions x3 3= n n=9 Look for a multiplier 4 12 (scale factor) x3 30 7n No obvious multiplier - 5= n Cross multiply 7 6 7n = 30 7 7 2 n=47
  • 5.
  • 6. Three out of every 10 adults segregate their food. a) Write this information as a ratio. Segregators 3 total 10 b) In a group of 90 people, how many would you expect to be food segregators? x9 Segregators 3 = x x = 27 total 10 90 x9
  • 7. The scale on a map is 1 inch = 20 miles. a) If two towns are 4 ½ inches apart on the map, how many miles apart are they? 1x 20 · 4 ½ x = 20 · 9 = 180 = 90 Inch 1 = 4½ 2 2 Mile 20 x 90 miles apart b) If two towns are 75 miles apart, how far apart will they be on the map? 75 20x 20x = 75 3 ¾ inches apart Inch 1 = x 20 20 Mile 20 75 x = 75 5 = 15 20 5 4
  • 8. Percents • “Percent” means “out of 100” • Percents are rational numbers 41 41% = 100 260 260% = 100 0.2 10 2 0.2% = 100 10 1000 100 1 100% = 100
  • 9. Fractions/Decimals/Percents Percents Fractions 16 4 16% = 100 25 Move decimal point Percents Decimals two places left 16 16% = = 0.16 175% = 1.75 100 0.05% = 0.0005
  • 10. Fractions Percents 5 x5 25 = 25% 20 x5 100 16 3 50 6x = 100 3 1 x 6 6 20 6 100 x = 50 18 3 2 2 = 16 % 3
  • 11. Decimals Percents Move decimal point two places right 37 0.37 = 37% 100 0.0004 = 0.04% 36.7 = 3670%
  • 12. The Percent Proportion percent part = 100 whole What is 20% of 18? 20 x 100x = 360 = 100 100 100 18 x = 3.6
  • 13. 3 is 6% of what number? part percent whole percent part = 100 whole 6 3 = 100 x 6x = 300 6 6 x = 50
  • 14. A dress that normally sells for $80 is on sale for $52. What is the “percent off”? 1) Find the markdown 80 – 52 = 28 2) Percent: x Part: 28 Whole: 80 x 28 = 100 80 80x = 2800 x = 35 35 % off