bell ringer. ratios and proportions a ratio is a comparison of a number “a” and a nonzero number...
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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
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