1. 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

2. ANSWERS 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
ANSWERS
6 mi/h
$0.55 per apple
$0.29 per can
$8.60 per CD

3. Learn to find equivalent ratios and identify proportions.
I will…
Learn to find equivalent ratios and identify proportions.

4. Vocabulary
equivalent ratios
proportion

5. THINK & DISCUSS
the next two slides

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. Equivalent ratios are ratios that name the same comparison.
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. Take more
NOTES

9. 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 =

10. You can read the proportion
Reading Math
You can read the proportion
by saying “six is to four
as twenty-one is to fourteen.” 6 4 = 21 14

11. If two ratios are equivalent, they are said to be proportional to each other, or in proportion.

12. 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
Simplify 72
128
72 ÷ 8
128 ÷ 8 = 9 16 8 17
Since = , the ratios are not proportional. 9 16

13. Example 1b ,
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.

14. I try! – Practice on the BOARD!
Determine whether the ratios are proportional. 54 63 , 72
144
Click for answers!
135 75 , 9 4

15. Determine whether the ratios are proportional.
I try! – ANSWERS!!
Determine whether the ratios are proportional. 54 63 , 72
144 6 7
Since = , the ratios are not proportional. 1 2
135 75 , 9 4 9 5
Since = , the ratios are not proportional. 4

16. (see the next slide for steps)
For the next problem…
Write the chart ONLY
…then…
Work out the problem
(see the next slide for steps)

17. 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

18. Working it Out! Ratio of rice to water, 12 servings:
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.
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.

19. I try! – Practice on the BOARD!
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
Click for answer.

20. I try! – ANSWER
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 36 27 39 27
Since = , the two ratios are not proportional.

21. You can find an equivalent ratio by multiplying or dividing both terms of a ratio by the same number.

22. 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.

23. I try! – Practice on the BOARD!
Find at least THREE ratios equivalent to each ratio.
Then use the ratios to write proportions.
3a:
3b:
3c: 2 3 16 12 38 18

24. Lesson
Quiz

25. Determine whether the ratios are proportional.9 30 12 40 12 21 10 15 1. 2. , ,
Find a ratio equivalent to each ratio. Then use the ratios to write a proportion. 3 8 3 7 3. 4.
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.