6-3 finding percents ns1.3 convert fractions to decimals and percents and use these representations...

$: 6-3 Finding Percents NS1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications. California$
6-3 Finding Percents

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

California Standards


What percent of 92 is 66?

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

Think: What number is to 100 as 66 is to 92?

=number

100 partwhole

Set up a proportion.

Substitute. n

100 6692

=

n 92 = 100 66

92n = 6600

Find the cross products.

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

Simplify.

6-3 Finding PercentsAdditional Example 1 Continued

n ≈ 72

Divide both sides by 92.

66 is approximately 72% of 92.

Simplify.

92n = 6600 92 92



Method 2: Set up an equation.

p 92 = 66 Let p represent the percent.


p 0.72 Simplify.

66 is about 72% of 92.

92p 92

= 66 92

Additional Example 1 Continued

percent whole = part Set up an equation.

6-3 Finding PercentsAdditional Example 1 Continued

Check

66.24 66 72% of 92 is approximately 66.

72% 92 = 66 Substitute 72% for p.?

0.72 92 = 66 Write as a decimal and multiply.?



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.


n = 15


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


Method 2: Set up an equation.

p 140 = 21 Let p represent the percent.


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 PercentsAdditional Example 2A: Recreation Application

First, find what percent of the grass Aimee and Ken cut.

= 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, 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 PercentsAdditional Example 2B: Recreation Application

First, find what percent of his films are dramas and action.

= 40% and 0.325 = 32.5%2 5

Jeremy organizes his movie collection by genre. of his collection are dramas, 0.325 are action

films, 3% are documentaries, 19.5% are comedies, and the rest of his movies are independent films. What percent of his movie collection are independent films?

2 5

Next, subtract the percents you know from 100% to find the remaining percent.100% – 40% – 32.5% – 3% – 19.5% = 5%.5% of Jeremy’s movie collection are independent films.

6-3 Finding PercentsCheck It Out! Example 2B

First, find what percent of his CDs are rock and pop.

= 50% and 0.125 = 12.5%1 2

Joe organizes his CD collection by genre.

of his collection is rock, 0.125 is pop, 6% is

classical, 9.5% is country, and the rest of his CDs are jazz. What percent of his CD collection is jazz?

1 2

Next, subtract the percents you know from 100% to find the remaining percent.

100% – 50% – 12.5% – 6% – 9.5% = 22%.

22% of Joe’s CD collection is jazz.


Additional Example 3A: Finding the Percent of a Number

The city of Dallas, Texas has a population of approximately 1,189,000 people. The population of the city of Austin, Texas is 55% of the population of Dallas. To the nearest thousand, what is the population of Austin?

Choose a method: Set up a proportion.

= 55

100 p

1,189,000 Set up a proportion.

55 1,189,000 = 100 p Find the cross products.

Think: 55 is to 100 as what population is to 1,189,000?


Additional Example 3A Continued

Austin has a population of approximately 654,000 people.

65,395,000 = 100p Simplify.

= 65,395,000 100

100p 100


653,950 = p Simplify.

654,000 ≈ p Round to the nearest whole number.


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


Additional Example 3B: Finding the Percent of a Number

After a drought, a reservoir had only 66 % of the average amount of water. If the average amount of water is 57,000,000 gallons, how much water was in the reservoir after the drought?

23

Choose a method: Set up an equation.

Think: What number is 66 % of 57,000,000?23

w = 66 % 57,000,000 Set up an equation.23

w = 57,000,000 66 % is equivalent to . 23

23

23

6-3 Finding PercentsAdditional Example 3B Continued

The reservoir contained 38,000,000 gallons of water after the drought.

w = = 38,000,000 114,000,000

3 Simplify.

6-3 Finding PercentsCheck It Out! Example 3A

After a drought, a river had only 50 % of the average amount of water flow. If the average amount of water flow is 60,000,000 gallons per day, how much water was flowing in the river after the drought?

23

Choose a method: Set up an equation.Think: What number is 50 % of 60,000,000?2

3 w = 50 % 60,000,000 Set up an equation.2

3

w = 0.506 60,000,000 50 % is equivalent to 0.506. 23

w 30,400,000 Simplify.The water flow in the river was about 30,400,000 gallons per day after the drought.

6-3 Finding PercentsCheck It Out! Example 3B

Ms. Marvin has a savings account with approximately $214,000 in it. Mr. Parson has 35% of the amount of Ms. Marvin’s savings account. To the nearest thousand, what is the amount of Mr. Parson’s savings account?

Choose a method: Set up a proportion.

= 35

100 s

214,000 Set up a proportion.

35 214,000 = 100 s Find the cross products.

Think: 35 is to 100 as what amount is to $214,000.

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

Mr. Parson has approximately $75,000 in his savings account.

7,490,000 = 100s Simplify.

= 7,490,000 100

100s 100


74,900 = s Simplify.

75,000 ≈ s Round to the nearest thousand.

6-3 finding percents ns1.3 convert fractions to decimals and percents and use these representations...

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