1. Ratios,
Proportions
and Percents

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

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