IDENTIFYING AND WRITING PROPORTIONSObjective: Learn to find equivalent ratios and identify proportions.

RATIO RECAPA ratio is a comparison of two quantities(numbers) using division

Three Ways to Write a RatioFraction With “to” With “:”

a

b to a b :a b

TRY THIS!What is the ratio of shaded squares to unshaded squares?

box 1 box 27

5

28

20

7

5

4

4

These 2 ratios are

called equivalent

ratios

GCF of 20 and 28

EQUIVALENT RATIOSWhat are Equivalent Ratios?Equivalent ratios are ratios that make the same comparison

Examples:9

27

9

9

1

3

9

27

3

3

27

81

Multiply by any number

These

equivalent

ratio

s are

proporti

onal.

PROPORTIONALWhat is a Proportional or in

Proportion?Proportions are equivalent ratios that are identical when in simplest form.Examples:2 8

and 16 64

4 2 and

12 4

1 1 = proportional

8 81 1

not proportional3 2

TRY THIS!Determine whether the ratios are proportional.

A. .

B. .

2 6,

7 21Already reduced

3

3

2

7

2 2Since , the ratios

7 7are proportional

8 6,

24 208

8

1

3

3

10

6

20

8

24 2

2

and

Simplify

1 3Since , the ratios are not proportional

3 10

TRY THESE!

Find a ratio that is equivalent to each given ratios.

481

27

42

18

2

2

8

36

3

3

16

9

possible answers

your answers may be different

Divide both the numerator and the denominator by a common factor

Multiply both the numerator and the denominator by any number

Write the proportion

Write the proportion

48 16

27 9

4 8

18 36

EXAMPLE 1:Determine whether the ratios are proportional.

24 72A ,

51 128

150 90B ,

105 63

EXAMPLE 2: Directions for making 12 servings of rice call for 3 cups of rice and 6 cups of water. For 40 servings it calls for 10 cups of rice and 19 cups of water. Are the ratios of rice to water proportional for both servings of rice.

EXAMPLE 3: Find an equivalent ratio. Then write the proportion.

3A

5

28B

16