1. Pre-Algebra Homework
Page 344 #9-25

2. Ratios and Proportions
7-1
Ratios and Proportions
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra

3. Ratios and Proportions
Pre-Algebra
7-1
Ratios and Proportions
Warm Up
Write each fraction in lowest terms. 14 16 1. 7 8 24 64 2. 3 8 9 72 3. 1 8 45
120 4. 3 8

4. Problem of the Day
A magazine has page numbers from 1 to 80. What fraction of those page numbers include the digit 5? 17 80

5. Learn to find equivalent ratios to create proportions.
Today’s Learning Goal Assignment
Learn to find equivalent ratios to create proportions.

6. BrainPOP Videos

7. Vocabulary
ratio
equivalent ratio
proportion

8. Comparisons of Mass of Equal Volumes
Relative density is the ratio of the density of a substance to the density of water at 4°C. The relative density of silver is This means that silver is 10.5 times as heavy as an equal volume of water.
The comparisons of water to silver in the table are ratios that are all equivalent.
42 g
31.5 g
21 g
10.5 g
Silver
4 g
3 g
2 g
1 g
Water
Comparisons of Mass of Equal Volumes
of Water and Silver

9. Ratios can be written in several ways. A colon is often used
Ratios can be written in several ways. A colon is often used. 90:3 and name the same ratio.
Reading Math
90 3

10. A ratio is a comparison of two quantities by division
A ratio is a comparison of two quantities by division. In one rectangle, the ratio of shaded squares to unshaded squares is 7:5. In the other rectangle, the ratio is 28:20. Both rectangles have equivalent shaded areas. Ratios that make the same comparison are equivalent ratios.

11. Additional Example 1: Finding Equivalent Ratios
Find two ratios that are equivalent to each given ratio.
Multiply or divide the numerator by the same nonzero number. = 9 27 =
9 • 2
27 • 2 18 54 A. 9 27 = =
9 ÷ 9
27 ÷ 9 1 3
Two ratios equivalent to are and . 9 27 18 54 1 3 =
64 • 2
24 • 2 64 24 =
128 48
Two ratios equivalent to are and . 64 24
128 48 8 3 B. 64 24 = =
64 ÷ 8
24 ÷ 8 8 3

12. Try This: Example 1
Find two ratios that are equivalent to each given ratio.
Multiply or divide the numerator by the same nonzero number. = 8 16 =
8 • 2
16 • 2 16 32 A. 8 16 = =
8 ÷ 4
16 ÷ 4 2 4
Two ratios equivalent to are and . 8 16 32 2 4 =
32 • 2
16 • 2 32 16 = 64 32
Two ratios equivalent to are and . 32 16 64 4 2 B. 32 16 = =
32 ÷ 8
16 ÷ 8 4 2

13. Ratios that are equivalent are said to be proportional, or in proportion. Equivalent ratios are identical when they are written in simplest form.

14. Additional Example 2: Determining Whether Two Ratios are in Proportion
Simplify to tell whether the ratios form a proportion.
Since ,
the ratios are in proportion. 1 9 = 3 27 A.
and 2 18 3 27 = =
3 ÷ 3
27 ÷ 3 1 9 2 18 = =
2 ÷ 2
18 ÷ 2 1 9 12 15 B.
and 27 36 12 15 = =
12 ÷ 3
15 ÷ 3 4 5
Since ,
the ratios are not in proportion. 4 5  3 27 36 = =
27 ÷ 9
36 ÷ 9 3 4

15. Simplify to tell whether the ratios form a proportion.
Try This: Example 2
Simplify to tell whether the ratios form a proportion.
Since ,
the ratios are in proportion. 1 5 = 3 15 A.
and 9 45 3 15 = =
3 ÷ 3
15 ÷ 3 1 5 9 45 = =
9 ÷ 9
45 ÷ 9 1 5 14 49 = =
14 ÷ 7
49 ÷ 7 2 7
Since ,
the ratios are not in proportion. 2 7  4 9 14 49 B.
and 16 36 16 36 = =
16 ÷ 4
36 ÷ 4 4 9

16. Additional Example 3: Earth Science Application
At 4°C, four cubic feet of silver has the same mass as 42 cubic feet of water. At 4°C, would 210 cubic feet of water have the same mass as 20 cubic feet of silver?
Since ,
210 cubic feet of water would have the same mass at 4°C as 20 cubic feet of silver. 2 21 = 4 42 ? = 20
210
4 ÷ 2
42 ÷ 2 ? =
20 ÷ 10
210 ÷ 10 2 21 =

17. Try This: Example 3
At 4°C, two cubic feet of silver has the same mass as 21 cubic feet of water. At 4°C, would 105 cubic feet of water have the same mass as 10 cubic feet of silver?
Since ,
105 cubic feet of water would have the same mass at 4°C as 10 cubic feet of silver. 2 21 = 2 21 ? = 10
105 ? =
10 ÷ 5
105 ÷ 5 2 21 2 21 =

18. Lesson Quiz: Part 1
Find two ratios that are equivalent to each given ratio. 4 15 1. 8 30 12 45
Possible answer: , 16 42 24 63
Possible answer: , 8 21 2.
Simplify to tell whether the ratios form a proportion. 16 10 3.
32 20 8 5 =
; yes
and 36 24 4.
28 18 3 2 14 9 
; no
and

19. Lesson Quiz: Part 2
5. Kate poured 8 oz of juice from a 64 oz bottle. Brian poured 16 oz of juice from a 128 oz bottle. What ratio of juice is missing from each bottle? Are the ratios proportional? 8 64 16
128
and ; yes, both equal
1 8