CHAPTER 7: RELATING FRACTIONS, DECIMALS,
AND PERCENTS
7.1
CONVERTING FRACTIONS TO DECIMALS p 2-3
7.2
CONVERTING DECIMALS TO FRACTIONS p 4-5
7.3
CONVERTING DECIMALS AND PERCENTS p 6-7
7.4
CONVERSIONS REVIEW p 8-9
7.5
THE PERCENT CIRCLE p 10-11
7.6
FINDING THE PART p 12-13
7.7
FINDING THE WHOLE p 14-15
7.8
FINDING THE PERCENT p 16-17
ANSWER KEY p 18-19
1
7.1
CONVERTING FRACTIONS TO DECIMALS
Key Vocabulary 7.1
Repeating decimals: _______________________________________________________
Rational numbers: ________________________________________________________
Think 7.1




a
b a
b
Add a decimal after the dividend and at least one zero. a b.0
.
Bring the decimal straight up into the quotient space. a b.0
Divide the numerator by the denominator.
Add at least 2 additional zeros to the dividend until it divides evenly or until you get a
repeating pattern.
0.25
0.33
1
1

4
1.00

3
1.00
0.4
4
2
3
 5 2.0
8
5
9
Example A:
Example B:
ExampleC:
2 0
20
10
 20
0
 9
0
0
Try It 7.1
Divide to convert the fractions to decimals.
1)
4)
3
 _____
4
2
 _____
3
2)
5)
1
 _____
8
3
 _____
10
2
3)
3
 _____
5
6)
7
 _____
8
7.1 Practice Exercises
Divide to convert the fractions to decimals.
1)
1
 _____
4
2)
3
 _____
8
3)
7
 _____
10
4)
5
 _____
6
5)
1
 _____
2
6)
3
 _____
9
7)
1
 _____
6
8)
3
 _____
5
(9 -10) Tanner spent ⅓ of his time at work stocking shelves and ⅔ of the time with
customers.
9) Write the amount of time Tanner spent stocking shelves as a decimal: _____
10) Write the amount of time Tanner spent with customers as a decimal: _____
3
7.2 CONVERTING DECIMALS TO FRACTIONS
Think 7.2
 To convert decimals to fractions, you need to write the decimal in fraction form.
Simplify the fraction by reducing to lowest terms.
Example A
0.6 

6 2 3
 
10 2 5
Example B
0.25 
Example C
25 25 1


100 25 4
0.275 
275 25 11


1, 000 25 40
For repeating fraction decimals, exclude the decimal and use just the fraction.
Example D: 0.33 or 3 3
1 1

3 3
Try It 7.2
Write each decimal as a fraction. Simplify by reducing the fraction to lowest terms.
1)
0.4 = _____
2)
0.8 = _____
3)
0.45 = _____
4)
0.55 = _____
5)
0.125 = _____
6)
0.075 = _____
4
7.2 Practice Exercises
Write each decimal as a fraction. Simplify by reducing the fraction to lowest terms.
Decimal Form
Fraction Form
Simplify Fraction
1)
0.5 =
_________
_________
2)
0.2 =
_________
_________
3)
0.15 =
_________
_________
4)
0.35 =
_________
_________
5)
0.70 =
_________
_________
6)
0.075 =
_________
_________
7)
0.220 =
_________
_________
8)
0.375 =
_________
_________
9)
0.0025 =
_________
_________
10)
Phillip walked 0.35 miles on Monday and 0.25 miles on Tuesday. Write the total
distance he walked as a fraction. _____________
5
7.3 CONVERTING DECIMALS AND PERCENTS
Key Vocabulary 7.3
Percent: _______________________________________________________________
Think 7.3
 To convert a decimal to a percent, multiply the decimal by 100. Move the decimal 2
places right. Add a decimal point to the end of whole numbers as a starting point.
 Be sure to add or remove zero placeholders as needed.

Drop the decimal and add a percent sign.
Example A:(0.2 5) 0.2 5 x100  25% Example B:

(added zero)
(0.5) 0.5 0 x 100  50%

Move decimal point right two places.
Move decimal point right two places.
1
1
1
Example C : (0.33 ) 0.33 x100  33 % Example D:(1.25) 1.25 x100 125%
3
3
3
Move decimal point right two places.
Move decimal point right two places.

To convert a percent to a decimal, divide the number by 100 (move the decimal 2 places
to the left. Add a decimal point to the end of whole numbers as a starting point.

Add or remove zeros as needed, drop the percent sign and add a decimal.
Example E: (25%) 25.%  100  0.25 Example F: (50%) 50.%  100  0.5


Move decimal point left two places.
Move decimal point left two places.
1
1
1
Example G: (33 %) 33 %  100  .33
Example H: (5%) 05.%  100  0.05
3
3
3
Add a zero placeholder. Move decimal point right two places.
Move decimal point left two places.
Try It 7.3
Convert each percent to a decimal.
1)
35% = _________
2)
8 % = __________
Convert each decimal to a percent.
4)
0.18 = __________
5)
0.8 = __________
6)
1.2= __________
6
3)
2
66 % = ________
3
7.3 Practice Exercises
Convert each decimal to a percent.
1) 0.3 = _____ %
2) 0.05 = _____ %
3) 0.45 = _____ %
4) 0.025 = _____ %
5) 2.45 = _____ %
Convert each percent to a decimal.
6) 3% = _____
7) 15% = _____
8) 90% = _____
9) 160% = _____
10) Jake ate 30% of his pizza for lunch. Write the amount he ate as a decimal. ____
7
7.4 CONVERTING FRACTIONS, DECIMALS, AND
PERCENTS
Think 7.4

Fraction →
Example A: 2 0  2 
50 5

Decimal → Percent (Simplify the fraction first as needed.)
0.4
5 2.0 
Percent →
0.4 x 100  40%
Decimal → Fraction (Simplify fraction as needed.)
Example B: 3 5%    0
35 5 7
 
100 5 20
Try It 7.4
Convert the numbers and simplify.
Fraction →
Decimal →
4

10
_____ 
1)
Percent →
2) 60% 
Decimal →
_____ 
Percent (Simplify the fraction first as needed.)
_____
Fraction (Simplify fraction as needed.)
_____
8
7.4 Practice Exercises
Fill in the chart by converting the fractions, decimals, and percents.
Percent
Decimal
Fraction
(1)
(2)
1
8
(3)
0.20
(4)
25%
(5)
(6)
(7)
(8)
4
5
(9)
0.66
(10)
2
3
9
7.5 THE PERCENT CIRCLE
Key Vocabulary 7.5
percent circle:________________________________________________________
part: ________________________________________________________________
whole: _______________________________________________________________
percent: _______________________________________________________________
Think 7.5

Using the percent circle as a guide, you can solve percent exercises with either
multiplication or division.
Part
P
Means Divide
%
Percent (as decimal)
Whole
W
Means Multiply
Sentence
Part
Percent (as
decimal)
Whole
36 is 10% of 360
36
10% (0.1)
360.
30% of 200 is 60.
60
30% (0.3)
200
Try it 7.5
Find what is missing: Part (P) Percent (%) or Whole (W)
1)
2)
3)
4)
5)
6)
What is 75% of 300?
30 is what percent of 90?
480 is 60% of what number?
20 is what percent of 100?
90 is 30% of what number?
What is 40% of 120?
P
P
P
P
P
P
%
%
%
%
%
%
10
W
W
W
W
W
W
Circle One
7.5 Practice Exercises
What’s missing? Part (P) Percent (%) or Whole (W) Circle One
1) What is 40% of 180?
P
%
W
2) 6 is what percent of 18?
P
%
W
3) 75% of what number is 25?
P
%
W
4) 30% of 300 is what number?
P
%
W
5) What percent of 60 is 20?
P
%
W
Draw lines and fill in the percent circles below.
6) 30% of 90 is 27.
7) 9.8 is 35% of 28.
8) 16 is 20% of 80.
9) 8 ½ % of $40 is $3.40
(10) A shirt that normally sells for $40 is 25% off. The discount id $10. Identify each
term.
Part _____
% _______
11
Whole _____
7.6 FINDING THE PART
Key Vocabulary 7.6
Formula: __________________________________________________________
Think 7.6


FORMULA: Part (P) = Percent (%) multplied by the Whole ( P  % x W )
Change percent to a deciaml first.
Part
P
Percent (as decimal)
%
W
Whole
Means Multiply
Example A: 60% of 180 is what number?
First change the percent to a decimal. 60% ÷ 100 = 0.06
Then multiply. Part = (0.06) (180) Answer: 108
1
Example B: 8 % of $40 is what amount?
2
1
First change the percent to a decimal. 8 %  8.5% 100  0.85
2
Then multiply. Part = (0.085) (40) Answer: $3.40
Example C: You can also change the percent to a fraction.
1
1
1
33 % 0f 90 is what number? 33 % 
3
3
3
30
1
90
30
Multiply the fraction by the whole number to find the part.
x

 30
1
3 1
1
Try It 7.6 Multiply the decimal or the fraction by the whole number to find the part.
1)
25% of 68 is _____
4)
1
8 % of $80 is _____
2
2) 15% of 300 is _____
5) 250% of 50 is ______
12
2
3) 66 of 39 is _____
3
6) 6% of $80 is _____
7.6 Practice Exercises
Use the percent to decimal method to find the part.
1)
25% of 40 is _____
2)
60% of 240 is _____
3)
1
7 % of $42 is _____
2
4)
5% of 60 is _____
5)
15% of $60 is _____
Use the percent to fraction method to find the part.
6)
1
33 % of 54 is _____
3
7)
2
66 % of 60 is _____
3
8)
Carlos was charged 6% sales tax on a shirt that cost $40. How much was the tax?
9)
Lydia bought a dress on sale for a 20% discount. The dress was originally $50. How
much was the discount? ________________
10) What was the sale price for Lydia’s dress? __________________
13
7.7 FINDING THE WHOLE
Think 7.7
FORMULA: Whole (W) = Part (P) divided by the Percent (as decimal). (W 
P
)
%
Part
P
Means Divide
Percent (as decimal)
%
?
Whole

First convert the percent to a decimal or a fractions (See 7.6)

Move the decimal point to the right the same number of spaces for the divisor and the
dividend.

Then divide the part value by the decimal value.
Example A: 20% of what number is 60? (20% = 0.2)
300  300
60
Whole 
 0.2 600  2 600
0.2
1
1
1
Example B: 25 is 33 % of what number? ( 33 % = )
3
3
3
1 25 3 75
Whole  25   x 
 75
3 1 1 1
Try It 7.7
Find the whole.
1) 30% of what number is 72? _____
2) 36 is 40% of what number? _____
3) 20% of what number is 22? _____
4) 72 is 60% of what number? _____
1
5) $5.25 is 7 % of what number? _____
2
6) $1.05 is 1 ½ % of what number? _____
14
7.7 Practice Exercises
Find the whole.
1)
18 is 30% of what number? ________________
2)
20% of what number is 50? ________________
3)
15% of what number is 27? ________________
4)
26 is 25% of what number? ________________
5)
1
7 % of what number is $15? ________________
2
6)
1
33 % of what number is 40? ________________
3
7)
1
1 % of what number is 5? ________________
4
8)
5 is 5% of what number? ________________
9)
1
Brittany paid 150.00 for the 7 % state taxes on a car she purchased. What was the
2
price of the car? ________________
10)
1
Alex earned 105.00 for 3 % interest on a deposit. How much money did he
2
deposit? ________________
15
7.8 FINDING THE PERCENT
Think 7.8
FORMULA: Percent (%) = Part (P) divided by the Whole (W) (% 
P
)
W
Part
P
Means Divide
Percent (as decimal)
%
W
Whole




Write the part divided by the whole as a fraction.
Simplify the fraction by reducing to lowest term
Convert the fraction to a decimal (See 7.1)
Multiply the resulting decimal by 100, move the decimal point two places to the right,
add zero as place holders as needed, drop the decimal and add the % sign.
Example A: What percent of 40 is 8?
P
8 8 1

  
W 40 8 5
0.2 x 100  20% ( answer )
Percent 
0.2
5 1.0
Try It 7.8
Find the percent.
1)
What percent of 16 is 12? _________________
2)
5 is what percent of 25? _________________
3)
12 inches is what percent of 1 yard? (Hint: 1 yard = 36 inches) _________________
4)
48 is what percent of 64? _________________
5)
$15 is what percent of $60? _________________
6)
66 is what percent of 99? _________________
16
7.8 Practice Exercises
Find the percent.
1)
What percent of 24 is 18? _________________
2)
8 inches is what percent of 32 inches? _________________
3)
What percent of $90 is $36? _________________
4)
18 is what percent of 60? _________________
5)
2.7 is what percent of 36? _________________
6)
What percent of 120 is 40? _________________
7)
24 is what percent of 36? _________________
8)
$135 is what percent of $180? _________________
9)
Victor deposited $300 in his savings account. He earned $3.75 on his deposit. What
is the percent he earned on his deposit? _________________
10)
Marcella bought a text book for $78 and had to pay an additional $5.85 for the tax
What percent of $78 is the $5.85 tax? _________________
17
Chapter 7 Answer Key
7.1
7.3
1) 0.25
2) 0.375
3) 0.7
1) 30%
2) 5%
4) 0.83 or 0.8
1
3
3) 45%
5) 0.5
6) 0.3 or 0.3
4) 2.5%
1
3
7) 0.16 or 0.16
5) 245%
2
3
6) 0.03
8) 0.6
9) 0.3 or 0.33
10)
1
3
0.6 or 0.66
7) 0.15
2
3
8) 0.9
9) 1.6
7.2
10) 0.3
1
2
1
2)
5
3
3)
20
7
4)
20
7
5)
10
3
6)
40
11
7)
50
3
8)
8
1
9)
400
3
10) miles
5
1)
7.4
1) 12.5%
2) 0.125
3) 20%
4)
1
5
5) 0.25
6)
1
4
7) 80%
8) 0.8
2
9) 66 %
3
10)
18
2
3
7.5
7.7.7.7
1)
P
2)
%
3)
W
4)
P
5)
%
6) P=27 W= 90
%=30
7) P=7
W= 28
%=25
8) P=16 W= 80
%=20
9) P=234 W= 40
%=8 1/2
10) P = 30 % = 25 W = 40
7.6
1)
60
2)
250
3)
180
4)
104
5)
$200
6)
120
7)
400
8)
100
9)
$2,000
10)
$3,000
7.8
1)
10
7.8
2)
144
1)
75%
3)
$3.15
2)
25%
4)
3
3)
40%
5)
9
4)
30%
6)
18
7)
40
5)
1
7 %
2
8)
$2.40
6)
9)
$10.00
1
33 %
3
10)
$40.00
7)
2
66 %
3
8)
75%
9)
1.25%
10)
1
7 %
2
19