Lesson 8.1.1Lesson 8.1.1

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California Standard:Number Sense 1.3Convert fractions to decimals and percents and use these representations in estimations, computations, and applications.

What it means for you:You’ll see what percents are and how they’re related to fractions and decimals.

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Key words:• percent• decimal• fraction• hundredth

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You hear percents used a lot in everyday life.

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A percent is really just a way to write a fraction — it tells you how many hundredths of a number you have.

You might score 83% in a test

A store might have a 20% off sale

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Percents Tell You How Many Hundredths You Have

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A percent is a way to write a fraction as a single number. It tells you how many hundredths of something you have.

The word percent means out of 100.

1% =

1 out of 100

100

110% =

10 out of 100

100

10

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Decimals can also be written as percents. The decimal 0.01 means “1 hundredth,” so it’s the same as 1%.

There’s more on converting decimals to percents next lesson.

0.01 = = 1%

1 out of 100

100decimal percent1

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Example 1

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In a box of 100 pencils, 26 are blue. What percent of the pencils are blue?

Solution

The fraction of pencils that are blue is .

Solution follows…

So you can say that 26% of the pencils are blue.

26

100

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Trace the outline of the picture onto tracing paper. Draw a 10 × 10 grid over the tracing.

The grid has 100 squares. So the mountain covers about 42% of the picture.

Example 2

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Estimate what percent of the picture on the right is covered by the mountain.

Solution follows…

It’s useful to be able to visually estimate a percent.

Solution

Count the number of squares the mountain covers. It covers 37 whole squares, 8 half squares and 4 quarter squares.

37 + (0.5 • 8) + (0.25 • 4) = 42 squares.

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Guided Practice

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In Exercises 1–3, write each fraction as a decimal and a percent.

0.05, 5% 0.25, 25% 0.62, 62%

Solution follows…

1. 2. 3.

In Exercises 4–6, write each percent as a fraction in its simplest form.

4. 1%1

100 5. 50%1

2 6. 20%1

5

100

62

100

5

100

25

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8. 9.

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Guided Practice

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In Exercises 7–9, draw a 10 by 10 square. Shade in the given percent.

Solution follows…

7. 8%

8. 27%

9. 100%

7.

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Percents Can Be Greater Than 100

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You can also have percents that are bigger than 100.

And just as 0.01 is the same as 1%, 1.5 is the same as 150%.

In the same way that is 1%, is 150%.100

150

100

1

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Percents bigger than 100 leave you with more than the original number.

Look at this orange:

That’s the same as of an orange, or 100% of an orange. 100

100

This is one whole orange.

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Now look at these oranges:

This is one and a half oranges.

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or 150% of an orange.

That’s the same as + =100

150

100

50

100

100of an orange,

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Guided Practice

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In Exercises 10–12, write each fraction as a percent.

120% 200% 1200%

Solution follows…

10. 11. 12.

In Exercises 13–15, write each decimal as a percent.

13. 1.4 140% 14. 3.6 360% 15. 22.0 2200%

100

200

100

120

100

1200

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To Find a Percent of a Number You Need to Multiply

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You already know that to find a fraction of a number, you multiply the number by the fraction.

Finding a percent of a number means finding a fraction out of 100 of the number.

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Example 3

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What is 25% of 160?

Solution

Write out the percent as a fraction: 25% =

Solution follows…

Multiply the fraction by the number

25

100

25

100× 160 =

4000

100

= 40 Simplify the answer

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Finding the Original Amount — Write an Equation

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Sometimes, you’ll know how much a certain percentage of a number is and want to find the original amount.

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Example 4

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25% of a number is 40. What is the number?

Solution

Write out the percent as a fraction: 25% =

Solution follows…

Multiply both sides by 100

25

100

25

100× x = 40

x = 160

Call the number that you’re finding x.

25x = 4000

Divide both sides by 25

40 is 25% of 160

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Guided Practice

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Find:

Solution follows…

16. 10% of 40 17. 60% of 250 18. 64% of 8004 150 512

In Exercises 19–21, find the value of x.

19. 50% of x is 30 60

20. 4% of x is 7

21. 65% of x is 130

175

200

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Guided Practice

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22. Pepe was chosen as president of his class. He got 75% of the votes, and his class has 28 members. How many people voted for Pepe?

Solution follows…

23. The school basketball team won 60% of their games this season. If they won 24 games, how many did they play altogether?

21

40

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Independent Practice

Solution follows…

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In Exercises 1–4, write the fraction as a percent.

10% 156%1. 4. 50%2. 23%3.

In Exercises 5–8, write the percent as a fraction in its simplest form.

5. 25% 6. 17% 7. 75%17100

8. 150%3

2

1

4

3

4

100

156

100

10

100

50

100

23

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Independent Practice

Solution follows…

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9. Out of 6000 nails made, 2% were faulty. How many were faulty?

30

10. 150% of the people who were expected turned up at the school fair. If 340 people were expected, how many came?

120

510

11. 20% of the students riding a bus are from Town A. If 6 students on the bus are from Town A, how many students ride the bus in total?

12. 80 students auditioned for a play. After the audition, 20% were asked to come to a 2nd audition. 50% of those who came to the 2nd audition were cast. How many were cast? What percent of the original 80 is this? 8, 10%

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Round UpRound Up

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Percents say how many hundredths of something you have.

You find a percent of a number by converting the percent to a fraction, and then multiplying this fraction by the number.