1. Percents
Lesson 8.1.1

2. 8.1.1 1.1.1 Percents California Standard: What it means for you:
Lesson
8.1.1
Lesson
1.1.1
Percents
California Standard:
Number Sense 1.3
Convert 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.
Key words:
percent
decimal
fraction
hundredth

3. You might score 83% in a test A store might have a 20% off sale
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1.1.1
Lesson
8.1.1
Percents
You hear percents used a lot in everyday life.
You might score 83% in a test
A store might have a 20% off sale
A percent is really just a way to write a fraction — it tells you how many hundredths of a number you have.

4. The word percent means out of 100.
Lesson
1.1.1
Lesson
8.1.1
Percents
Percents Tell You How Many Hundredths You Have
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 1
10% =
10 out of 100
100 10

5. Lesson
1.1.1
Lesson
8.1.1
Percents
Decimals can also be written as percents. The decimal 0.01 means “1 hundredth,” so it’s the same as 1%.
0.01 = = 1%
1 out of 100
100
decimal
percent 1
There’s more on converting decimals to percents next lesson.

6. So you can say that 26% of the pencils are blue.
Lesson
8.1.1
Percents
Example 1
In a box of 100 pencils, 26 are blue. What percent of the pencils are blue?
Solution 26
100
The fraction of pencils that are blue is
So you can say that 26% of the pencils are blue.
Solution follows…

7. It’s useful to be able to visually estimate a percent.
Lesson
8.1.1
Percents
Example 2
It’s useful to be able to visually estimate a percent.
Estimate what percent of the picture on the right is covered by the mountain.
Solution
Trace the outline of the picture onto tracing paper. Draw a 10 × 10 grid over the tracing.
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.
The grid has 100 squares.
So the mountain covers about 42% of the picture.
Solution follows…

8. Percents 8.1.1 1.1.1 Guided Practice
Lesson
1.1.1
Lesson
8.1.1
Percents
Guided Practice
In Exercises 1–3, write each fraction as a decimal and a percent.
100 5
100 25
100 62 1. 2. 3.
0.05, 5%
0.25, 25%
0.62, 62%
In Exercises 4–6, write each percent as a fraction in its simplest form. 1
100 1 2 1 5
4. 1%
5. 50%
6. 20%
Solution follows…

9. 8.1.1 1.1.1 Percents Guided Practice
Lesson
8.1.1
Lesson
1.1.1
Percents
Guided Practice
In Exercises 7–9, draw a 10 by 10 square. Shade in the given percent.
7. 8% 8. 9. 7.
8. 27% %
Solution follows…

10. Percents 8.1.1 1.1.1 Percents Can Be Greater Than 100
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1.1.1
Lesson
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Percents
Percents Can Be Greater Than 100
You can also have percents that are bigger than 100.
In the same way that is 1%, is 150%.
100
150 1
And just as 0.01 is the same as 1%, 1.5 is the same as 150%.

11. Lesson
1.1.1
Lesson
8.1.1
Percents
Percents bigger than 100 leave you with more than the original number.
Look at this orange:
This is one whole orange.
That’s the same as of an orange, or 100% of an orange.
100

12. Percents 8.1.1 1.1.1 Now look at these oranges:
Lesson
1.1.1
Lesson
8.1.1
Percents
Now look at these oranges:
This is one and a half oranges.
or 150% of an orange.
That’s the same as =
100
150 50
of an orange,

13. Percents 8.1.1 1.1.1 Guided Practice
Lesson
1.1.1
Lesson
8.1.1
Percents
Guided Practice
In Exercises 10–12, write each fraction as a percent.
100
120
100
200
100
1200
10.
11.
12.
120%
200%
1200%
In Exercises 13–15, write each decimal as a percent.
140%
360%
2200%
Solution follows…

14. Lesson
1.1.1
Lesson
8.1.1
Percents
To Find a Percent of a Number You Need to Multiply
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.

15. Multiply the fraction by the number
Lesson
8.1.1
Percents
Example 3
What is 25% of 160?
Solution 25
100
Write out the percent as a fraction: 25% = 25
100
4000
100
× 160 =
Multiply the fraction by the number
= 40
Simplify the answer
Solution follows…

16. Percents 8.1.1 1.1.1 Finding the Original Amount — Write an Equation
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1.1.1
Lesson
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Percents
Finding the Original Amount — Write an Equation
Sometimes, you’ll know how much a certain percentage of a number is and want to find the original amount.

17. Call the number that you’re finding x.
Lesson
8.1.1
Percents
Example 4
25% of a number is 40. What is the number?
Solution 25
100
Write out the percent as a fraction: 25% =
Call the number that you’re finding x. 25
100
× x = 40
25x = 4000
Multiply both sides by 100
x = 160
Divide both sides by 25
40 is 25% of 160
Solution follows…

18. Percents 8.1.1 1.1.1 Guided Practice Find: 16. 10% of 40
Lesson
1.1.1
Lesson
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Percents
Guided Practice
Find:
% of 40
% of 250
% of 800 4
150
512
In Exercises 19–21, find the value of x.
% of x is 30 60
20. 4% of x is 7
175
% of x is 130
200
Solution follows…

19. 8.1.1 1.1.1 Percents Guided Practice
Lesson
8.1.1
Lesson
1.1.1
Percents
Guided Practice
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? 21
23. The school basketball team won 60% of their games this season. If they won 24 games, how many did they play altogether? 40
Solution follows…

20. Percents 8.1.1 Independent Practice
Lesson
8.1.1
Percents
Independent Practice
In Exercises 1–4, write the fraction as a percent.
100 10
100 50
100 23
100
156 1. 2. 3. 4.
10%
50%
23%
156%
In Exercises 5–8, write the percent as a fraction in its simplest form. 1 4
5. 25%
6. 17% 17
100 3 4 3 2
7. 75% %
Solution follows…

21. Percents 8.1.1 Independent Practice
Lesson
8.1.1
Percents
Independent Practice
9. Out of 6000 nails made, 2% were faulty. How many were faulty?
120
% of the people who were expected turned up at the school fair. If 340 people were expected, how many came?
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? 30
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%
Solution follows…

22. Lesson
8.1.1
Percents
Round Up
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.