1. 5-4 Identifying and Writing Proportions Warm Up Problem of the Day
Course 2
Warm Up
Problem of the Day
Lesson Presentation

2. Identifying and Writing Proportions
Course 2
5-4
Identifying and Writing Proportions
Warm Up
Find the unit rate.
1. 18 miles in 3 hours
2. 6 apples for $3.30
3. 3 cans for $0.87
4. 5 CD’s for $43
6 mi/h
$0.55 per apple
$0.29 per can
$8.60 per CD

3. Identifying and Writing Proportions
Course 2
5-4
Identifying and Writing Proportions
Problem of the Day
Bob made a square table top with 100 white square tiles. He painted the tiles along the edge of the table red. How many tiles are red? 36

4. Identifying and Writing Proportions
Course 2
5-4
Identifying and Writing Proportions
Learn to find equivalent ratios and to identify proportions.

5. Vocabulary 5-4 Identifying and Writing Proportions equivalent ratios
Course 2
5-4
Identifying and Writing Proportions
Vocabulary
equivalent ratios
proportion

6. Identifying and Writing Proportions
Course 2
5-4
Identifying and Writing Proportions
Students in Mr. Howell’s math class are measuring the width w and the length l of their heads. The ratio of l to w is 10 inches to 6 inches for Jean and 25 centimeters to 15 centimeters for Pat.

7. Identifying and Writing Proportions
Course 2
5-4
Identifying and Writing Proportions 10 6 25 15
These ratios can be written as the
fractions and . Since both simplify
to , they are equivalent. Equivalent
ratios are ratios that name the same comparison. 5 3

8. Identifying and Writing Proportions
Course 2
5-4
Identifying and Writing Proportions
An equation stating that two ratios are equivalent is called a proportion. The equation, or proportion, below states that the ratios and are equivalent. 10 6 25 15 10 6 25 15 =
Read the proportion by saying “ten is to six
as twenty-five is to fifteen.”
Reading Math 10 6 = 25 15

9. Identifying and Writing Proportions
Course 2
5-4
Identifying and Writing Proportions
If two ratios are equivalent, they are said to be proportional to each other, or in proportion.

10. Additional Example 1A: Comparing Ratios in Simplest Forms
Course 2
5-4
Identifying and Writing Proportions
Additional Example 1A: Comparing Ratios in Simplest Forms
Determine whether the ratios are proportional. 24 51 , 72
128
Simplify . 24 51
24 ÷ 3
51 ÷ 3 = 8 17
72 ÷ 8
128 ÷ 8 = 9 16
Simplify 72
128 8 17
Since = , the ratios are not proportional. 9 16

11. Additional Example 1B: Comparing Ratios in Simplest Forms
Course 2
5-4
Identifying and Writing Proportions
Additional Example 1B: Comparing Ratios in Simplest Forms
Determine whether the ratios are proportional. ,
150
105 90 63
Simplify
150
105
150 ÷ 15
105 ÷ 15 = 10 7
90 ÷ 9
63 ÷ 9 = 10 7
Simplify . 90 63 10 7
Since = , the ratios are proportional.

12. Identifying and Writing Proportions
Course 2
5-4
Identifying and Writing Proportions
Check It Out: Example 1A
Determine whether the ratios are proportional. 54 63 , 72
144
Simplify . 54 63
54 ÷ 9
63 ÷ 9 = 6 7
72 ÷ 72
144 ÷ 72 = 1 2
Simplify 72
144 6 7
Since = , the ratios are not proportional. 1 2

13. Identifying and Writing Proportions
Course 2
5-4
Identifying and Writing Proportions
Check It Out: Example 1B
Determine whether the ratios are proportional.
135 75 , 9 4
135 ÷ 15
75 ÷ 15 = 9 5
Simplify
135 75 9 4
is already in simplest form. 9 4 9 5
Since = , the ratios are not proportional. 4

14. Additional Example 2: Comparing Ratios Using a Common Denominator
Course 2
5-4
Identifying and Writing Proportions
Additional Example 2: Comparing Ratios Using a Common Denominator
Directions for making 12 servings of rice call for 3 cups of rice and 6 cups of water. For 40 servings, the directions call for 10 cups of rice and 19 cups of water. Determine whether the ratios of rice to water are proportional for both servings of rice.
Servings of Rice
Cups of Rice
Cups of Water 12 3 6 40 10 19
Write the ratios of rice to water for 12 servings and for 40 servings. 3 6
Ratio of rice to water, 12 servings:
Write the ratio as a fraction. 10 19
Ratio of rice to water, 40 servings:
Write the ratio as a fraction
Write the ratios with a
common denominator,
such as 114. 3 6
3 · 19
6 · 19 57
114 10 19
10 · 6
19 · 6 60
114 = = = = 57
114 60
114
Since = , the two ratios are not proportional.

15. Identifying and Writing Proportions
Course 2
5-4
Identifying and Writing Proportions
Check It Out: Example 2
Use the data in the table to determine whether the ratios of beans to water are proportional for both servings of beans.
Servings of Beans
Cups of Beans
Cups of Water 8 4 3 35 13 9
Write the ratios of beans to water for 8 servings and for 35 servings. 4 3
Ratio of beans to water, 8 servings:
Write the ratio as a fraction. 13 9
Ratio of beans to water, 35 servings:
Write the ratio as a fraction
Write the ratios with a
common denominator,
such as 27. 4 3
4 · 9
3 · 9 36 27 13 9 39 27 = =
13 · 3
9 · 3 = = 36 27 39 27
Since = , the two ratios are not proportional.

16. Identifying and Writing Proportions
Course 2
5-4
Identifying and Writing Proportions
You can find an equivalent ratio by multiplying or dividing the numerator and the denominator of a ratio by the same number.

17. Insert Lesson Title Here
Course 2
5-4
Identifying and Writing Proportions
Insert Lesson Title Here
Additional Example 3: Finding Equivalent Ratios and Writing Proportions
Find a ratio equivalent to each ratio. Then use the ratios to find a proportion. Possible Answers: 3 5 A. 3 5
3 · 2
5 · 2 6 10 = =
Multiply both the numerator and
denominator by any number such as 2. 3 5 6 10 =
Write a proportion. B. 28 16 28 16
28 ÷ 4
16 ÷ 4
Divide both the numerator and
denominator by any number such as 4. 7 4 = = 28 16 7 4 =
Write a proportion.

18. Insert Lesson Title Here
Course 2
5-4
Identifying and Writing Proportions
Insert Lesson Title Here
Check It Out: Example 3
Find a ratio equivalent to each ratio. Then use the ratios to find a proportion. Possible Answers: 2 3 A. 2 3
2 · 3
3 · 3 6 9
Multiply both the numerator and
denominator by any number such as 3. = = 2 3 6 9 =
Write a proportion. B. 16 12
Divide both the numerator and
denominator by any number such as 4. 16 12
16 ÷ 4
12 ÷ 4 4 3 = = 16 12 = 4 3
Write a proportion.

19. Identifying and Writing Proportions Insert Lesson Title Here
Course 2
5-4
Identifying and Writing Proportions
Insert Lesson Title Here
Lesson Quiz: Part I
Determine whether the ratios are proportional. 9 30 12 40 12 21 10 15 1. 2. , ,
, ; proportional 3 10
, ; not proportional 4 7 2 3
Find a ratio equivalent to each ratio. Then use the ratios to write a proportion. 3 8 15 40 ; = 3 8 3 7 9 21 ; = 3 7 3. 4.

20. Identifying and Writing Proportions Insert Lesson Title Here
Course 2
5-4
Identifying and Writing Proportions
Insert Lesson Title Here
Lesson Quiz: Part II
5. In pre-school, there are 5 children for every
one teacher. In another preschool there are 20 children for every 4 teachers. Determine whether the ratios of children to teachers are proportional in both preschools.
20 4
5 1 =