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5.1_5.3 Ratios and Proportions Lesson - Kutz
Contributed by: Kutz

Ratio - A ratio compares two quantities by division.

Ratios can be simplified just like fractions.

18
15
÷
3
3
=
5
6
Simplify -
4
10
6
5
=
=
2
10
25
18
8
=
=

Ratios compare like quantities - Sometimes the

quantities appear different but are like. One

example would be measurement.

12 inches = 1 foot

When simplifying ratios involving measurement

the units must be the same.

3 feet = 1 yard

36 inches = 1 yard

2 yards
9 feet

12 inches = 1 foot

3 feet = 1 yard

36 inches = 1 yard

Example -
Simplify the ratio 2 yards to 9 feet.
x       feet per yard = 6 feet
9 feet
÷
3
=
3

Let's convert yards to feet. Every yard = 3 feet, so

multiply 4 yards x 3 feet per yard. So 4 yards = 12 feet.

36 inches = 1 yard

12 inches = 1 foot
3 feet = 1 yard

Write the ratio 4 yards to 15 feet in simplest form. You

have to convert the measurements to the same unit.

15 feet
4 yards
x 3 ft./yd.             ft.
=
ft.
÷

3

3
=

Let's convert inches to feet. Every foot = 12 inches, so

divide 36 in. by 12 in. per ft. So 36 inches = 3 feet.

36 inches = 1 yard

12 inches = 1 foot
3 feet = 1 yard

Write the ratio 36 inches to 15 feet in simplest form.

Convert the measurements to the same unit.

15 feet

36 in.

÷ 12 in./ft.             ft.
=
ft.
÷

3

3
=

When two ratios are set equal to each other they

form a proportion. Two ratios are said to be

proportional is their cross products are equal.

Does 3 x 24 = 9 x 8?
3
8
=

?

24
9
15
15 x
45
=

?

yes or no?
18

6

=  6 x
?
=
?

75

75 x

100

=

?

yes or no?

8

4

=  4 x
?
=
?

7

7 x

2

=

?

yes or no?

6

21

=  21 x
?
=
?
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