Bell Ringer

Ratios and Proportions

• A ratio is a comparison of a number “a” and a nonzero number “b” using division

Example 1 Simplify Ratios

Simplify the ratio.

a.60 cm : 200 cm b. 3 ft18 in.

SOLUTION

a. 60 cm : 200 cm can be written as the fraction .60 cm200 cm

Divide numerator and denominatorby their greatest common factor, 20.

= 60 cm

200 cm60 ÷ 20

200 ÷ 20

310

Simplify. is read as “3 to 10.” = 310

Example 1 Simplify Ratios

b. Substitute 12 in. for 1 ft.

21Simplify. is read as “2 to 1.”= 2

1

Divide numerator and denominatorby their greatest common factor, 18.

= 36 ÷ 1818 ÷ 18

Multiply.= 36 in.18 in.

= 3 · 12 in.18 in.

3 ft18 in.

Example 2 Use Ratios

In the diagram, AB : BC is 4 : 1 and AC = 30. Find AB and BC.

AB + BC = AC Segment Addition Postulate

4x + x = 30 Substitute 4x for AB, x for BC, and 30 for AC.

5x = 30 Add like terms.

x = 6 Divide each side by 5.

SOLUTION

Let x = BC. Because the ratio of AB to BC is 4 to 1, you know that AB = 4x.

Example 2 Use Ratios

To find AB and BC, substitute 6 for x.

AB = 4x = 4 · 6 = 24 BC = x = 6

ANSWER So, AB = 24 and BC = 6.

Example 3 Use Ratios

The perimeter of a rectangle is 80 feet. The ratio of the length to the width is 7 : 3. Find the length and the width of the rectangle.

SOLUTION

The ratio of length to width is 7 to 3. You can let the length l = 7x and the width w = 3x.

2l + 2w = P Formula for the perimeter of a rectangle

2(7x) + 2(3x) = 80 Substitute 7x for l, 3x for w, and 80 for P.

14x + 6x = 80 Multiply.

20x = 80 Add like terms.

x = 4 Divide each side by 20.

Example 3 Use Ratios

To find the length and width of the rectangle, substitute 4 for x.

l = 7x = 7 · 4 = 28 w = 3x = 3 · 4 = 12

ANSWER The length is 28 feet, and the width is 12 feet.

Now You Try

ANSWER EF = 16; FG = 8

1. In the diagram, EF : FG is 2 : 1 and EG = 24. Find EF and FG.

ANSWER length, 24 ft; width, 18 ft

2. The perimeter of a rectangle is 84 feet. The ratio of the length to the width is 4 : 3. Find the length and the width of the rectangle.

An equation that states that two ratios are equal is called a proportion

Example 4 Solve a Proportion

5 · 6 = 3(y + 2) Cross product property

30 = 3y + 6 Multiply and use distributive property.

30 – 6 = 3y + 6 – 6 Subtract 6 from each side.

24 = 3y Simplify.

8 = y Simplify.

Solve the proportion .=y + 2

653

SOLUTION

Write original proportion.=y + 2

653

Divide each side by 3.=3y3

243

ANSWER 4

ANSWER 9

ANSWER 5

Solve the proportion.

3. = 68

3x

4. = 15y

53

5. =m + 2

51410

Now You Try

Complete #s 2-44 even only