Course 3

5-1 Ratios and Proportions

Warm UpWrite each fraction in lowest terms.

1416

1.

972

3.

2464

2.

45120

4.

78

38

18

38

Course 3

5-1 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?1780

Course 3

5-1 Ratios and Proportions

Learn to find equivalent ratios to create proportions.

TB P. 216-219

Course 3

5-1 Ratios and Proportions

Vocabulary

ratioequivalent ratioproportion

Course 3

5-1 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.

7:5 28:20

Course 3

5-1 Ratios and Proportions

Ratios can be written in several ways. 7 to 5,

7:5, and name the same ratio.

Reading Math

7 5

Course 3

5-1 Ratios and Proportions

Additional Example 1: Finding Equivalent Ratios

Find two ratios that are equivalent to each given ratio.

B.

1854

13

12848

83

A. =927

=9 • 227 • 2

=9 ÷ 927 ÷ 9

927

= Two ratios equivalent

to are and . 927

1854

13

Two ratios equivalent

to are and . 6424

12848

83

=64 • 224 • 2

=64 ÷ 824 ÷ 8

6424

=

6424

=

Multiply or divide the numerator and denominator by the same nonzero number.

Course 3

5-1 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.

Course 3

5-1 Ratios and Proportions

Additional Example 2: Determining Whether Two Ratios are in Proportion

Simplify to tell whether the ratios form a proportion.

1215

B. and 2736

327

A. and 218

Since ,

the ratios are in

proportion.

19

= 19

19

=3 ÷ 327 ÷ 3

327

=

19

=2 ÷ 218 ÷ 2

218

=

45=

12 ÷ 315 ÷ 3

1215

=

34=

27 ÷ 936 ÷ 9

2736

=

Since ,

the ratios are not

in proportion.

45 3

4

Course 3

5-1 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?

4 ÷ 242 ÷ 2

?= 20 ÷ 10210 ÷ 10

221

= 221

442

?= 20210

Since ,

210 cubic feet of water would have the same mass at 4°C as 20 cubic feet of silver.

221

= 221

Divide.

Course 3

5-1 Ratios and Proportions

Lesson Quiz: Part 1

85

85

= ; yes

Find two ratios that are equivalent to each given ratio.

415

1.

821

2.

1610

3.

3624

4.

Simplify to tell whether the ratios form a proportion.

830

1245

Possible answer: ,

1642

2463

Possible answer: ,

and 32 20

and 28 18

32

149

; no

Course 3

5-1 Ratios and Proportions

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?

864

16128

and ; yes, both equal 1 8