1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. 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. 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. Learn to find equivalent ratios and to identify proportions.

5. Vocabulary
equivalent ratios
proportion

6. Students in Mr. Howell’s math class are measuring the width w and the length l of their faces. The ratio of l to w is 6 inches to 4 inches for Jean and 21 centimeters to 14 centimeters for Pat.

7. 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. 6 4 21 14 3 2

8. An equation stating that two ratios are equivalent is called a proportion. The equation, or proportion, below states that the ratios and are equivalent. 6 4 21 14 6 4 21 14 =
Reading Math
Read the proportion by saying “six is to four
as twenty-one is to fourteen.” 6 4 = 21 14

9. 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
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
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. 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. 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
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. 19 10 40 6 3 12
Cups of Water
Cups of Rice
Servings of Rice
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. 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. 9 13 35 3 4 8
Cups of Water
Cups of Beans
Servings of Beans
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. You can find an equivalent ratio by multiplying or dividing both terms of a ratio by the same number.

17. 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. 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. Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems

20. Determine whether the ratios are proportional.
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.

21. 5. In preschool, there are 5 children for every
Lesson Quiz: Part II
5. In preschool, 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.
5 1 =

22. Lesson Quiz for Student Response Systems
1. Determine whether the ratios are proportional. ,
A. proportional
B. not proportional
12 20
18 30

23. Lesson Quiz for Student Response Systems
2. Determine whether the ratios are proportional. ,
A. proportional
B. not proportional
21 56
14 49

24. Lesson Quiz for Student Response Systems
2 9
3. Identify a ratio equivalent to . Then use
the ratios to write a proportion.
A. ; = C. ; =
B. ; = D. ; =
10 35
2 9
10 35
5 35
2 9
5 35
10 45
2 9
10 45
5 45
2 9
5 45

25. Lesson Quiz for Student Response Systems
4 5
4. Identify a ratio equivalent to . Then use
the ratios to write a proportion.
A. ; = C. ; =
B. ; = D. ; =
12 15
4 5
12 15
12 20
4 5
12 20
12 18
4 5
12 18
15 20
4 5
15 20

26. Lesson Quiz for Student Response Systems
5. In one school, there are 12 students for every classroom. In another school, there are 36 students for every 4 classrooms. Determine whether the ratios of students to classrooms are proportional in both schools.
A. = ; C. ≠ ;
proportional not proportional
B. = ; D. ≠ ;
12 36
1 3
12 1
36 4
12 1
36 3
12 4
36 1