6-3 Finding Percents

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California StandardsCalifornia Standards

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6-3 Finding Percents

Warm UpRewrite each value as indicated.

1. as a percent

2. 25% as a fraction(reduced)

3. as a decimal

4. 0.16 as a fraction (reduced)

48%

0.375

425

24 50

3 8

14

6-3 Finding Percents

NS1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications.

California Standards

6-3 Finding Percents

What percent of 92 is 69?

Additional Example 1: Finding the Percent One Number Is of Another (Read)

Think: What number is to 100 as 69 is to 92?

=number

100 partwhole

Set up a proportion.

Substitute. n

100 6992

=

n 92 = 100 69

92n = 6900

Find the cross products.

Method 1: Set up a proportion to find the percent.

Simplify.

6-3 Finding PercentsAdditional Example 1 Continued

n = 75

Divide both sides by 92.

69 is 75% of 92.

Simplify.

92n = 6900 92 92

6-3 Finding Percents

What percent of 92 is 69?

Method 2: Set up an equation.

p 92 = 69 Let p represent the percent.

Divide both sides by 92.

p = 0.75 Simplify.

69 is 75% of 92.

92p 92

= 69 92

Additional Example 1 Continued

percent whole = part Set up an equation.

6-3 Finding PercentsAdditional Example 1 Continued

Check

69 = 69 75% of 92 is 69.

75% 92 = 69 Substitute 75% for p.?

0.75 92 = 69 Write as a decimal and multiply.?

6-3 Finding Percents

Method 3: Show as a fraction. Convert the fraction to a percent by dividing.

What percent of 92 is 69?

69 / 92 Set up fraction. Part over whole.

69 / 92 = 0.75 Divide numerator by denominator

0.75 x 100 = 75% Multiply by 100 to get percent.

6-3 Finding Percents

What percent of 140 is 21? (Notes)

Think: What number is to 100 as 21 is to 140?

=number

100 partwhole Set up a proportion.

Let n represent the percent. n

100 21140

=

n 140 = 100 21

140n = 2100

Find the cross products.

Check It Out! Example 1

Method 1: Set up a proportion.

Simplify.

6-3 Finding Percents

n = 15

Divide both sides by 140.

21 is 15% of 140.

Check It Out! Example 1 Continued

Simplify.

140n = 2100 140 140

6-3 Finding PercentsCheck It Out! Example 1 Continued

What percent of 140 is 21?

Method 2: Set up an equation.

p 140 = 21 Let p represent the percent.

Divide both sides by 140.

p = 0.15 Simplify.

21 is 15% of 140.

140p 140

= 21 140

percent whole = part Set up an equation.

6-3 Finding PercentsCheck It Out! Example 1 Continued

21 = 21 15% of 140 is approximately 21.

15% 140 = 21 Substitute 15% for p.?

0.15 140 = 21 Write as a decimal and multiply.?

Check

6-3 Finding PercentsCheck It Out! Example 1 Continued

What percent of 140 is 21?

Method 3: Show as a fraction. Convert the fraction to a percent by dividing.

21 / 140 Set up fraction. Part over whole.

21 / 140 = 0.15 Divide numerator by denominator

0.15 x 100 = 15% Multiply by 100 to get percent.

6-3 Finding PercentsAdditional Example 2A: Recreation Application

First, change Aimee and Ken’s amounts to percents.

= 20% and 0.31 = 31%.1 5

Four friends volunteered to cut the grass around their neighbor’s house. Jay cut 23%

of the grass, Aimee cut of the grass, Ken cut 0.31 of the grass, and Bryn cut the rest. What percent of the grass did Bryn cut?

1 5

Next - since the whole lawn is 100% - subtract the percents you know from 100% to find the remaining percent.

100% – 23% – 20% – 31% = 26%.Bryn cut 26% of the grass.

6-3 Finding Percents

When solving a problem when the percent is greater than 100, the number you are looking for will be greater than the number given.

Helpful Hint

6-3 Finding PercentsCheck It Out! Example 3B

Ms. Marvin has a savings account with approximately $210,000 in it. Mr. Parson has 30% of the amount of Ms. Marvin’s savings account. What is the amount of Mr. Parson’s savings account?Choose a method: Set up a proportion.

= 30

100 x

210,000Set up a proportion.

30 210,000 = 100 x Find the cross products.

Think: 30% = 30/100 is proportionate to what part of $210,000?

= percent

100 part (is)whole (of)

6-3 Finding PercentsCheck It Out! Example 3B Continued

Mr. Parson has $63,000 in his savings account.

6,300,000 = 100x Simplify.

= 6,300,000 100

100x 100

Divide both sides by 100.

63,000 = x Simplify.

6-3 Finding PercentsLesson Quiz: Part I

Find each percent.

1. What percent of 33 is 22?

2. Of Earth’s 197 million mi2 of surface area, about

139 million mi2 is water. Find the percent of Earth’s

surface that is covered by water.

3. The Ramirez family bought a large bag of oranges

during their trip to Florida. Jorge ate of the oranges,

Ann ate 0.18 of the oranges, Mrs. Ramirez ate 22% of

the oranges, and Mr. Ramirez ate the rest. What

percent of the oranges did Mr. Ramirez eat?

70.6%

20%

66 %2 3

25

6-3 Finding PercentsLesson Quiz: Part II

4. Rada is 170% as tall as her brother Raj. Raj is 0.82 m tall. To the nearest tenth of a meter, how tall is Rada?

5. The volume of Lake Superior is 2900 mi3 and

the volume of Lake Erie is 116 mi3. What

percent of the volume of Lake Superior is the

volume of Lake Erie?

1.4 m

4%