Ratio and proportion can be expressed in different ways. A ratio compares two numbers using a colon or fraction. A proportion states that two ratios are equal, also using a colon or equal fractions. To solve proportions, use cross multiplication. Word problems can involve finding an unknown value given ratios or proportions related to distances, times, enrollments and other quantities.

1. Ratio and
Proportion

2. Ratio
- a comparison of two numbers
- can be written in any form:
• the two numbers in a ratio are separated by
colon (:)
a:b 2:3 25:56
• as a fraction
a 2 25
b 3 56

3. • the child to books

4. • the bananas to monkeys

5. • the number of the apple trees to the number of apples

6. Proportion
- a statement that two ratios are equal
- can be written in any form:
• using a colon
a:b = c:d 2:6 = 1:3
• two equal fractions
a a
c 2 1
a
= =
b d
b 6 b
3

7. a:b = c:d
means
extremes
Remember:
The means is always equal to the extremes.

8. - use the cross products
3 12
6 24
3 x 24 = 12 x 6
72 = 72

9. Find n in the proportion.
20 60
30 n
20 x n = 60 x 30
20 n = 1800
20 20
n = 90

10. Word Problems
Jane ran 2 meters in 3 seconds. How long
can she take to run 50 meters?
2 50
=
3 n
Distance
2xn = 3 x 50
Time
Let n be our time. 2n = 150
2 2
n = 75 seconds

11. a. In 1995, 120 girls were enrolled in a certain
elementary school while 100 boys were enrolled. What
was the ratio of girls to boys? Boys to girls?
girls to boys
120:100
boys to girls
100:120

12. b. In 1996, the ratio of girls to boys enrolled in the
same school stayed the same as in 1995. How many girls
were enrolled in 1996 when there where 130 boys
enrolled?
120 n
=
100 130
girls to boys
120:100 100 x n = 120 x 130
Let n be the 100 n = 15600
number of girls. 100 100
n = 156 girls

13. Are there any questions?
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