1. 3rd week of the first six week
5-1
Ratios and Proportions
Course 3
3rd week of the first six week
7th pre a/p

2. Learning Objective: to find equivalent ratios to create proportions.

3. Vocabulary
ratio
equivalent ratio
proportion

4. 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.
7: :20

5. Ratios can be written in several ways
Ratios can be written in several ways. 7 to 5, 7:5, and name the same ratio.
Reading Math
7 5

6. 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

7. Check It Out: 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 16 = =
32 • 2
16 • 2 64 32
Two ratios equivalent to are and . 32 16 64 4 2 B. 32 16 = =
32 ÷ 8
16 ÷ 8 4 2

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

9. 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

10. Simplify to tell whether the ratios form a proportion.
Check It Out: 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

11. 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
Divide. 2 21 =

12. Check It Out: 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
Divide. 2 21 =

13. Demonstration of Learning page 1
Find two ratios that are equivalent to each given ratio. 4 15 1. 8 21 2.
Simplify to tell whether the ratios form a proportion. 16 10 3.
32 20
and 36 24 4.
28 18
and

14. Demonstration of learning page 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?