1. Ratios and Proportions
7-1
Ratios and Proportions
Course 3
Warm Up
Problem of the Day
Lesson Presentation

2. Ratios and Proportions
Course 3
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

3. Ratios and Proportions
Course 3
7-1
Ratios and Proportions
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

4. Ratios and Proportions
Course 3
7-1
Ratios and Proportions
Learn to find equivalent ratios to create proportions.

5. Insert Lesson Title Here
Course 3
7-1
Ratios and Proportions
Insert Lesson Title Here
Vocabulary
ratio
equivalent ratio
proportion

6. Comparisons of Mass of Equal Volumes
Course 3
7-1
Ratios and Proportions
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

7. Ratios and Proportions
Course 3
7-1
Ratios and Proportions
Ratios can be written in several ways. A colon is often used. 90:3 and name the same ratio.
Reading Math
90 3

8. Ratios and Proportions
Course 3
7-1
Ratios and Proportions
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.

9. Additional Example 1: Finding Equivalent Ratios
Course 3
7-1
Ratios and Proportions
Additional Example 1: Finding Equivalent Ratios
Find two ratios that are equivalent to each given ratio.
Multiply or divide the numerator and denominator 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

10. Ratios and Proportions
Course 3
7-1
Ratios and Proportions
Try This: Example 1
Find two ratios that are equivalent to each given ratio.
Multiply or divide the numerator and denominator 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

11. Ratios and Proportions
Course 3
7-1
Ratios and Proportions
Ratios that are equivalent are said to be proportional, or in proportion. Equivalent ratios are identical when they are written in simplest form.

12. Additional Example 2: Determining Whether Two Ratios are in Proportion
Course 3
7-1
Ratios and Proportions
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

13. Ratios and Proportions
Course 3
7-1
Ratios and Proportions
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

14. Additional Example 3: Earth Science Application
Course 3
7-1
Ratios and Proportions
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 =

15. Ratios and Proportions
Course 3
7-1
Ratios and Proportions
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 =

16. Ratios and Proportions Insert Lesson Title Here
Course 3
7-1
Ratios and Proportions
Insert Lesson Title Here
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

17. Ratios and Proportions Insert Lesson Title Here
Course 3
7-1
Ratios and Proportions
Insert Lesson Title Here
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