Math Success Reproducible Worksheets
Reproducible Worksheets for:
Percents and Ratio
These worksheets practice math concepts explained in Percents and Ratios (ISBN 0-7660-1435–5),
written by Lucille Caron and Philip M. St. Jacques.
Math Success reproducible worksheets are designed to help teachers, parents, and tutors use the books in the
Math Success series in the classroom and home. Teachers, librarians, tutors, and parents are granted
permission and encouraged to make photocopies of these worksheets.
These worksheets are reproducible for educational use only and are not for resale.
2006 © Enslow Publishers, Inc.
Visit www.enslow.com and search for the Math Success series and download worksheets for the following
titles:
Addition and Subtraction
0-7660-1432-0
Multiplication and Division
0-7660-1431–2
Fractions and Decimals
0–7660–1430–4
Percents and Ratios
0–7660–1435–5
Geometry
0-7660-1433–9
Pre–Algebra and Algebra
0-7660-1434–7
Titles in this series can be purchased directly from:
Enslow Publishers, Inc.
40 Industrial Road, Box 398
Berkeley Heights, NJ 07922-0398
Phone: 1-800-398-2504
E-mail: [email protected]
Web Page: http://www.enslow.com
Name _____________________________________________
Date ___________________
Reducing Ratios
Reducing ratios is just like reducing fractions.
Example:
1. Reduce 30 to 15 to lowest terms.
Divide by 15.
2 to 1
190
2. Reduce to lowest terms.
Divide by 10.
19
1
3. Reduce 9:18 to lowest terms.
Divide by 9.
1:2
10
Write ratios using each of the above methods. Reduce these ratios to lowest terms.
Example: 8 hits for 20 at bats
8 to 20 2 to 5
8
2
20
5
8:20 2:5
a. 63 girls on 7 teams
____________ _____________ _____________
b. 20 uniforms for 10 boys
____________ _____________ _____________
c. 18 pages for 45 questions
____________ _____________ _____________
d. 40 candies for 6 boxes
____________ _____________ _____________
e. 32 pizza slices in 4 pies
____________ _____________ _____________
f. 32 ribbons for 10 girls
____________ _____________ _____________
g. 9 hamburgers for 3 people
____________ _____________ _____________
h. 5 miles represented by 3 inches ____________ _____________ _____________
i. 16 people to 4 cars
____________ _____________ _____________
j. 25 birds to 5 cages
____________ _____________ _____________
k. 6 letters in 2 mailboxes
____________ _____________ _____________
© Enslow Publishers, Inc. Based on the book Percents and Ratios by Lucille Caron and Philip M. St. Jacques,
ISBN 0-7660-1435-5, pages 8–9.
2
Name _____________________________________________
Date ___________________
Ratios and Percents
First Term
A percent compares a number to 100. The number is always the first term. The first term
can be less than 100, equal to 100, or greater than 100. The second term is always 100.
First Term Less than 100
Example:
Write 35% as a ratio.
35 to 100
Divide each number by 5.
7 to 20
Write each percent as a ratio and reduce to lowest terms.
a. 60% _____________
b. 75% ________________
c. 30% ____________
d. 25% _____________
e. 85% ________________
f. 40% ____________
First Term Greater than 100
Example:
Write 300% as a ratio.
300 to 100
Divide by 100.
3 to 1
Write each percent as a ratio and reduce to lowest terms.
a. 550% _____________
b. 600% _____________
c. 150% _____________
d. 105% _____________
e. 125% _____________
f. 175% _____________
g. 200% _____________
h. 900% _____________
i. 850% _____________
© Enslow Publishers, Inc. Based on the book Percents and Ratios by Lucille Caron and Philip M. St. Jacques,
ISBN 0-7660-1435-5, pages 10–11.
3
Name _____________________________________________
Date ___________________
Equivalent Ratios
Multiplying or dividing both terms of a ratio by the same number does not change the
value of the ratio.
8 to 1
Multiply each number by 8 (8 8 64; 1 8 8).
64 to 8
8 to 1 and 64 to 8 are equivalent ratios.
Renaming a Ratio in Higher Terms
Example:
Rename 6 to 3 in higher terms.
Multiply each number by 2.
6 to 3 12 to 6
Rename each ratio with the next higher equivalent ratio. Do not reduce your answer.
a. 20 to 10
_______________________
b. 9 to 5
_______________________
c. 3 to 2
_______________________
d. 15 to 10
_______________________
e. 8 to 6
_______________________
f. 50 to 4
_______________________
g. 35 to 11
_______________________
h. 10 to 3
_______________________
Renaming a Ratio in Lowest Terms
Example:
Rename 72 to 9 in lowest terms.
Divide each number by 9.
72 to 9 8 to 1
a. 15 to 5
_______________________
b. 18 to 10
c. 16 to 4
_______________________
d. 36 to 18 ______________________
e. 100 to 30
_______________________
f. 42 to 6
g. 150 to 50 _______________________
______________________
______________________
h. 48 to 16 ______________________
© Enslow Publishers, Inc. Based on the book Percents and Ratios by Lucille Caron and Philip M. St. Jacques,
ISBN 0-7660-1435-5, pages 12–13.
4
Name _____________________________________________
Date ___________________
Rates
285 dollars
The rate of the price of gold may be . Other rates are miles per hour and feet
1 ounce
per second.
Rates can be written in two ways:
Using a fraction bar:
__
Using words:
per
$285
1 ounce
285 dollars per ounce
Write the following rates using the word per.
$4.00
a. 12 bagels
___________________________________
5 miles
b. hour
___________________________________
16 feet
c. minute
___________________________________
Write the following rates using a fraction bar.
a. 75 miles per hour
__________________________________
b. $3.00 per 2 pounds of tomatoes
__________________________________
c. 56 houses per 2 city blocks
__________________________________
Reducing Rates to Lowest Terms
$4.80
Divide by 12.
12 donuts
Reduce these rates to lowest terms.
$0.40
donut
Example:
80 miles
a. 2 hours
14 cars
b. 7 households
___________________________________
___________________________________
c. $39.00 per 3 CDs
___________________________________
d. 100 feet per 10 seconds
___________________________________
© Enslow Publishers, Inc. Based on the book Percents and Ratios by Lucille Caron and Philip M. St. Jacques,
ISBN 0-7660-1435-5, pages 14–15.
5
Name _____________________________________________
Date ___________________
Units of Measure
Money
Example:
3 quarters
2 dimes, 1 nickel
75 cents
25 cents
3 to 1
Find the ratio of the following and reduce to lowest terms.
2 half dollars
a. 1 quarter
___________________________________________
6 dimes
b. 2 nickels
___________________________________________
4 dollars
c. 2 quarters
___________________________________________
5 nickels
d. 1 dime, 5 pennies
___________________________________________
4 dimes, 1 nickel
e. 3 nickels
___________________________________________
5 quarters
f. 3 dimes, 2 nickels
___________________________________________
Time
Example:
2 hours
20 minutes
2 60 minutes
20 minutes
120 minutes
20 minutes
12 days
a. 6 weeks
___________________________________________
4 weeks
b. 10 days
___________________________________________
6 years
c. 9 months
___________________________________________
12 hours
d. 180 minutes
___________________________________________
6 days
e. 3 weeks
___________________________________________
6 minutes
f. 40 seconds
___________________________________________
6 to 1
© Enslow Publishers, Inc. Based on the book Percents and Ratios by Lucille Caron and Philip M. St. Jacques,
ISBN 0-7660-1435-5, pages 16–17.
6
Name _____________________________________________
Date ___________________
Ratios and Fractions
Expressing Fractions as Whole Number Ratios
You can rewrite the ratio 1 to 2 with whole numbers by finding the least
2
3
common multiple (LCM) of the denominator. The LCM of 2 and 3 is 6.
1
6 3
2
2
12
6 4
3
3
The ratio 1 to 2 is 3 to 4.
2
3
Write these fraction ratios as whole number ratios.
a. 3 to 1
___________________________________________
b. 5 to 3
___________________________________________
c. 2 to 1
___________________________________________
d. 3 to 1
___________________________________________
e. 1 to 1
___________________________________________
4
3
6
8
3
5
4
2
4
6
Expressing Mixed Numbers as Whole Number Ratios
1 1 to 2 3
Example:
8
4
Change the mixed numbers to improper fractions.
9
11
to 8
4
1
Then continue as you did above. The ratio 9 to 1
changes to 9 to 22.
8
4
Write these mixed number ratios as whole number ratios.
a. 1 1 to 2 2
___________________________________________
b. 2 1 to 1 5
___________________________________________
c. 2 1 to 2 2
___________________________________________
d. 4 1 to 2 2
___________________________________________
e. 1 1 to 3 2
___________________________________________
2
4
5
2
4
3
6
3
5
5
© Enslow Publishers, Inc. Based on the book Percents and Ratios by Lucille Caron and Philip M. St. Jacques,
ISBN 0-7660-1435-5, pages 18–19.
7
Name _____________________________________________
Date ___________________
Ratios and Decimals
Expressing Decimals as Whole Number Ratios
Example:
1. Write 5.2 to 2.6 as a ratio of whole numbers.
5.2 one decimal place, so multiply by 10
2.6 one decimal place, so multiply by 10
52 2 or 2 to 1
,
26 1
2. Write 0.0028 to 0.00014 as a ratio of whole numbers.
(When there is a difference in the decimal places, multiply by the greater number of
decimals.)
00.0028 100,000 280
20 , or 20 to 1
0.00014 100,000 14
1
Write these decimal ratios as whole number ratios.
7.5
a. 5.0
___________________________________________
0.016
b. 0.008
___________________________________________
6.4
c. 1.6
___________________________________________
0.00003
d. 0.002
___________________________________________
5.5
e. 1.1
___________________________________________
0.0042
f. 0.00021
___________________________________________
2.70
g. 1.35
___________________________________________
0.026
h. 0.0016
___________________________________________
16.4
i. 3.28
___________________________________________
0.0008
j. 0.00001
___________________________________________
© Enslow Publishers, Inc. Based on the book Percents and Ratios by Lucille Caron and Philip M. St. Jacques,
ISBN 0-7660-1435-5, pages 20–21.
8
Name _____________________________________________
Date ___________________
Unit Pricing
Finding the Better Buy
Example:
$4.98
4
What is the better buy: 4 Ping-Pong balls for $4.98 or 7 for $8.50?
1.245 or $1.25
4冄4
苶.9
苶8
苶0
苶
4
9
8
18
16
20
20
0
$850
7
1.214 or $1.21
7冄8
苶.5
苶0
苶0
苶
7
15
1 4
10
7
30
28
2
The better buy is 7 balls for $8.50 because one ball costs $1.21 at that rate.
Circle the better buy for each of the following. What is the difference in price for one?
Difference in price
a. 3 cans of juice for $5.00 or 5 cans of juice for $8.00
_______________
b. 10 ounces of popcorn for $2.50 or 35 ounces or popcorn for $8.40
_______________
c. 5 notebooks for $6.25 or 9 notebooks for $11.00
_______________
d. 4 pounds of candy for $2.24 or 6 pounds of candy for $3.12
_______________
e. 5 pounds of bananas for $3.45 or 2 pounds of bananas for $1.30
_______________
f. 7 cantaloupes for $9.55 or 12 cantaloupes for $16.30
_______________
© Enslow Publishers, Inc. Based on the book Percents and Ratios by Lucille Caron and Philip M. St. Jacques,
ISBN 0-7660-1435-5, pages 22–23.
9
Name _____________________________________________
Date ___________________
Ratio and Proportion
A proportion is an equation that shows two ratios.
Example:
4
16
and 2
8
To see if the ratios are equal, multiply the diagonals of the proportion.
4 8 32
2 16 32
4
16
2
8
Therefore,
Cross multiply to find if these proportions are equal. Place an or sign on the line.
30
10
a. ____ 12
4
16
4
b. ____ 20
5
18
15
c. ____ 6
45
4
20
d. ____ 11
55
1
22
e. ____ 8
96
5
15
f. ____ 3
10
4
7
g. ____ 12
42
4
8
h. ____ 5
10
2
18
i. ____ 3
21
8
24
j. ____ 3
9
21
10
k. ____ 14
6
5
25
l. ____ 6
30
Finding an Unknown Term
Example:
8
n
2
3
Cross multiply.
Divide by 2.
832n
24 2n
n
12
24
2n
n 12
2
2
1
1
Solve for the unknown number (n) by cross multiplying.
2
n
a. 3
18
7
n
b. 10
100
3
n
c. 8
64
n
13
d. 8
26
4
n
e. 9
36
n
30
f. 10
100
9
n
g. 15
35
9
12
h. n
36
4
n
i. 12
24
3
15
j. n
50
4
n
k. 5
20
1
n
l. 8
96
© Enslow Publishers, Inc. Based on the book Percents and Ratios by Lucille Caron and Philip M. St. Jacques,
ISBN 0-7660-1435-5, pages 24–25.
10
Name _____________________________________________
Date ___________________
Finding a Number When a Ratio Is Known
Example:
chairs
8
desks
3
In a class, the ratio of the number of chairs to the number of desks is
8 to 3. If there are 15 desks in the class, how many chairs are there?
x
chairs
15
desks
x
8
15
3
3x 120
3x
120
3
3
x 40
There are 40 chairs.
Solve the following problems by first setting up the proper ratio and then solving for x,
the unknown.
4
a. The ratio of a son’s age to his father’s age is . If the son is 16 years old, how old is
10
the father?
16
b. Joan misspelled 4 words on her test. This was of the total words on the test. How
60
many words were on the test?
c. Jack earns $12 each day for 3 hours of work. How much does he earn in 15 hours?
d. If 6 ounces of oil are mixed with 3 ounces of vinegar, how many ounces of oil will be
mixed with 10 ounces of vinegar?
e. The cost to enlarge 4 pictures is $4.25. At this rate, how much would enlarging 36
pictures cost?
f. The bicycle shop sold 24 bicycles in 10 days. At that rate, how many bicycles will be
sold in 15 days?
© Enslow Publishers, Inc. Based on the book Percents and Ratios by Lucille Caron and Philip M. St. Jacques,
ISBN 0-7660-1435-5, pages 26–27.
11
Name _____________________________________________
Date ___________________
Scale Drawings
Reduction
The scale on a map reads 1 inch 8 miles. To the nearest mile,
what is the distance between two cities that are 5 inches apart?
Example:
inches
miles
1
5 inches
8
x miles
1x 40
x 40 miles
The two cities are 40 miles apart.
Find the distance between the following cities. Use the scale 1 inch 8 miles.
a. 2 cities 8 inches apart
b. 2 cities 3 1 inches apart
2
c. 2 cities 6 3 inches apart
4
Enlargement
Example:
An illustrator uses a scale of 1 inch in the drawing 1 millimeter (mm).
2
He draws an ant that is 3 inches long. What is the actual length of the ant?
inch
mm
0.5
3 inches
1
x mm
0.5
3
1
x
0.5x 3
0.5x
3
3
3
x6
The ant is 6 mm long.
Find the size of the following illustration measurements. Use the scale 1 inch 1 mm.
2
a. an illustration of a plant that is 6 inches tall
b. an illustration of a watch battery that is 2 1 inches wide
2
© Enslow Publishers, Inc. Based on the book Percents and Ratios by Lucille Caron and Philip M. St. Jacques,
ISBN 0-7660-1435-5, pages 28–29.
12
Name _____________________________________________
Date ___________________
Probability
number of ways an event can occur
Probability (Event) number of all possible outcomes
Example:
If you flip a penny, what is the probability of getting a tail?
number of ways a tail can occur
total outcomes (heads + tails)
1
2
1
The probability of getting a tail is one in two ().
2
Find the probability of the following. Reduce the ratio to lowest terms.
You are going to roll a cube that has 2 white faces, 1 gray face, and 3 black faces. Find the
probability that each color will end up on top.
a. white
b. gray
c. black
A jar contains 6 green marbles, 4 striped marbles, and 8 yellow marbles. Without looking,
you are going to reach into the jar and choose a marble. Find the probability of selecting
each of the following:
d. green marble
e. striped marble
f. yellow marble
g. green or striped marble
h. green or yellow marble
© Enslow Publishers, Inc. Based on the book Percents and Ratios by Lucille Caron and Philip M. St. Jacques,
ISBN 0-7660-1435-5, pages 32–33.
13
Name _____________________________________________
Date ___________________
Percents and Ratios
Changing a Ratio to a Percent When the Second Term Is 100
Example:
75 of the 100 books in the library are science books.
75
This can be stated as 75 out of 100, or , or 75%.
100
Express each of the following ratios as percents.
71
a. 100 ______________
16
b. 1 00 ______________
1
c. 1 00 ______________
99
d. 100 ______________
50
e. 100 ______________
45
f. 100 ______________
Changing a Percent to a Ratio
Example:
Write 20% as a ratio. This can be done three different ways:
20
20:100
20 out of 100
100
Express each of the following percents as ratios. Use the second way, a fraction, and
reduce your answer.
g. 27% _____________
h. 50% ____________
i. 40% ____________
j. 30% _____________
k. 45% ____________
l. 63% ____________
m. 75% _____________
n. 10% ____________
o. 20% ____________
p. 16% _____________
q. 3% ____________
r. 97% ____________
© Enslow Publishers, Inc. Based on the book Percents and Ratios by Lucille Caron and Philip M. St. Jacques,
ISBN 0-7660-1435-5, pages 36–37.
14
Name _____________________________________________
Date ___________________
Decimal Equivalents
Changing a Percent to a Decimal
To change a percent to a decimal, move the decimal point two places to the left and drop
the percent sign. Add zeros when necessary.
Example:
35% 35.%
9% 9.%
35.
09.
0.35
0.09
Express the following percents as decimals.
a. 18% _______________________
b. 38% _______________________
c. 5% _______________________
d. 11.5% _______________________
e. 0.7% _______________________
f. 0.016% _______________________
Changing a Decimal or Mixed Decimal to a Percent
To change a decimal to a percent, move the decimal point two places to the right and add
a percent sign.
Example:
0.069 0.069 6.9%
6.2 6.20 620%
4 4. 4.00 400%
Express the following decimals or mixed decimals as percents.
g. 0.25 _____________
h. 0.076 ____________
i. 0.05 ____________
j. 0.003 _____________
k. 0.6 ____________
l. 0.00042 ____________
m. 1.03 _____________
n. 7 ____________
o. 3.5 ____________
p. 4.1 _____________
q. 16 ____________
r. 1.99 ____________
© Enslow Publishers, Inc. Based on the book Percents and Ratios by Lucille Caron and Philip M. St. Jacques,
ISBN 0-7660-1435-5, pages 38–39.
15
Name _____________________________________________
Date ___________________
Fraction Equivalents
Changing a Percent to a Fraction
Example:
20
2
1
20% 100
10
5
Express the following percents as fractions.
a. 50% ________________________
b. 75% ________________________
c. 40% ________________________
d. 30% ________________________
e. 60% ________________________
f. 7% ________________________
Changing a Fraction Percent to a Decimal
Example:
1
% 0.5% 0.005
2
2冄1
苶.0
苶
10
0
1
% 0.005
2
Express the following fraction percents as decimals.
1
g. %
5 _______________
1
h. %
8 _______________
3
i. %
4 _______________
9
j. %
10 _______________
3
k. %
5 _______________
1
l. %
4 _______________
© Enslow Publishers, Inc. Based on the book Percents and Ratios by Lucille Caron and Philip M. St. Jacques,
ISBN 0-7660-1435-5, pages 40–41.
16
Name _____________________________________________
Date ___________________
More Fraction Equivalents
Changing a Fraction to a Percent
1
Example: Write as a percent. 4
Step 1:
1
100%
100%
4
1
4
Step 2:
25
25%
4冄1
苶0
苶0
苶
8
20
20
0
Express the following fractions as percents.
4
a. 5 _________________________
3
b. 10 _________________________
6
c. 50 _________________________
14
d. 25 _________________________
12
e. 1 00 _________________________
7
f. 10 _________________________
Changing an Improper Fraction to a Percent
11
Example: Write 4
as a percent.
Step 1:
11
100%
1100%
4
1
4
Express the following improper fractions as percents.
Step 2:
275%
4冄1
苶1
苶0
苶0
苶
8
30
28
20
20
0
9
g. 2 _______________
16
h. 4 _______________
11
i. 1 0 _______________
29
j. 20 _______________
© Enslow Publishers, Inc. Based on the book Percents and Ratios by Lucille Caron and Philip M. St. Jacques,
ISBN 0-7660-1435-5, pages 40–41.
17
Name _____________________________________________
Date ___________________
Mixed Numerals
Changing a Mixed Decimal Percent to a Decimal
Example:
Write 32.5% as a decimal.
Move the decimal two places to the left and drop the percent sign.
32.5% 0.325
Write these mixed decimal percents as decimals.
a. 18.2% ________________________
b. 26.245% ________________________
c. 11.9% ________________________
d. 8.6% ________________________
e. 33.8% ________________________
f. 16.3% ________________________
Changing a Decimal to a Mixed Decimal Percent
Example:
Write 0.345 as a percent.
Move the decimal two places to the right and add the percent sign.
0.345 34.5%
Write these decimals as mixed decimal percents.
g. 0.126 _____________
h. 0.751 ____________
i. 0.627 ____________
j. 0.981 _____________
k. 0.437 _____________
l. 0.855 ____________
Changing a Mixed Numeral Percent to a Fraction
Example:
Write 83 1% as a fraction.
3
Change the mixed number to an improper fraction and divide by 100.
250
100
250
1
5
83 1% ÷ 3
3
1
3
100
6
Write these percents as fractions. Be sure to reduce your answer to lowest terms.
m. 87 1% __________________________________________________________
2
n. 62 1% ___________________________________________________________
2
© Enslow Publishers, Inc. Based on the book Percents and Ratios by Lucille Caron and Philip M. St. Jacques,
ISBN 0-7660-1435-5, pages 42–43.
18
Name _____________________________________________
Date ___________________
Finding the Percent of a Number
Example:
What is 35% of $30?
Change the percent to a decimal. Then multiply.
35% 0.35
0.35
So, 35% of $30 is $10.50.
$30
$10.50
Example:
What is 7 2% of 300?
3
Change the percent to a mixed number and divide by 100. Then multiply.
3
3
3
7 2% 2
÷ 100 2
1 2
3
3
23
300 23
300
3
100
300
2
So, 7 of 300 23
3
Solve each problem.
a. 6% of $42
b. 12 1% of 96
c. 78% of 1,500
d. 8 1% of 600
e. 62% of 275
f. 7 1% of 400
g. 50% of 1,000
h. 6 2% of 75
2
3
2
3
© Enslow Publishers, Inc. Based on the book Percents and Ratios by Lucille Caron and Philip M. St. Jacques,
ISBN 0-7660-1435-5, pages 44–45.
19
Name _____________________________________________
Date ___________________
Applying Percent: Part and Whole
Example:
What percent of 48 is 36?
36
3
1. Divide the part by the whole and reduce to lowest terms. 48
4
25
3
100%
2. Change the fraction to a percent. 75%
4
1
You can also use ratio and proportion to solve the same problem.
6
1. Divide the part by the whole and reduce to lowest terms. 3
3
48
2. Let x equal the percentage.
3
x
4
100
3. Cross multiply.
4x 300
4. Divide by 4.
x 75%
4
Use either of the above methods to find percentage.
a. 16 is what percent of 80?
b. 15 is what percent of 60?
c. 8 is what percent of 25?
d. 34 is what percent of 102?
e. 100 is what percent of 250?
f. 30 is what percent of 40?
© Enslow Publishers, Inc. Based on the book Percents and Ratios by Lucille Caron and Philip M. St. Jacques,
ISBN 0-7660-1435-5, pages 46–47.
20
Name _____________________________________________
Date ___________________
Finding the Total Number
Finding the Whole When the Part and Percent Are Given
Example:
450 is 15% of what number?
1. Identify the part.
450
2. Identify the percent and write it as a fraction.
5
15% 1
3. Let x equal the whole. Place the part over the whole.
4. Cross multiply. Divide both sides by 15.
450
x
100
450
15
x
100
5
1
100
15x 45,000
x 3,000
So, 450 is 15% of 3,000.
Solve each of the following.
a. 70 is 50% of what number?
b. 120 is 60% of what number?
c. 54 is 18% of what number?
d. 90 is 40% of what number?
e. 8 is 80% of what number?
f. 300 is 75% of what number?
g. 75 is 150% of what number?
h. 15 is 10% of what number?
© Enslow Publishers, Inc. Based on the book Percents and Ratios by Lucille Caron and Philip M. St. Jacques,
ISBN 0-7660-1435-5, pages 48–49.
21
Name _____________________________________________
Date ___________________
Percent Increase and Decrease
Percent Increase
Example:
The price of a video game increased from $20 to $25.
What percent increase is this?
1. Find the difference between the two prices. $25 $20 $5
$5
2. Place the difference ($5) over the original price. $
20
3. Multiply this fraction by 100%.
5
$5
100%
25%
$20
1
So, the percent increase is 25%.
Find the percent increase for the following problems.
a. From 50 to 75
b. From 400 to 500
c. From 6 to 10
d. From 20 to 35
e. From 60 to 80
f. From 70 to 140
Percent Decrease
Example:
What is the percent decrease from 100 to 90?
10
1. Write the difference over the original number. 100
1
10
2. Multiply by 100%. 100% 10%
100
Find the percent decrease for the following problems.
g. From 150 to 125
h. From 50 to 40
i. From 12 to 9
j. From 30 to 27
© Enslow Publishers, Inc. Based on the book Percents and Ratios by Lucille Caron and Philip M. St. Jacques,
ISBN 0-7660-1435-5, pages 50–51.
22
Name _____________________________________________
Date ___________________
Discount and Sale Price
Discount
Example:
Regular price: $150
Discount rate: 5%
What is the discount?
1. Change the discount rate percent to a decimal. 5% 0.05
2. Multiply the regular price by the discount rate. $150 0.05 $7.50
So, the discount is $7.50.
Find the discount on the following amounts.
a. 10% off $200
b. 6% off $1.50
c. 15% off $5.00
d. 5% off $45
Sale Price
Example:
Regular price: $55
Discount rate: 20%
What is the sale price?
1. Find the discount (as above).
$55 0.2 $11 discount
2. Subtract the discount from the regular price.
$55 $11 $44
So, the sale price is $44.
Find the sale price of the following.
e. 15% off $100
f. 25% off $250
g. 20% off $75
h. 10% off $35
© Enslow Publishers, Inc. Based on the book Percents and Ratios by Lucille Caron and Philip M. St. Jacques,
ISBN 0-7660-1435-5, pages 52–53.
23
Name _____________________________________________
Date ___________________
Percents Larger than 100%
Expressing Percents Larger than 100% as Decimals
Example:
Write 143% as a decimal.
Place the decimal point to the right of the ones place.
Divide by 100% (Move decimal point two places to the
left and drop % symbol)
143.%
1.43
Express these percents as decimals.
a. 200% _______________________
b. 365% _______________________
c. 121% _______________________
d. 199% _______________________
e. 212% _______________________
f. 152% _______________________
Expressing Decimals as Percents
Example:
Write 3.62 as a decimal.
Multiply the decimal by 100% by moving the decimal point two
places to the right. Add the percent (%) symbol.
3.62 362%
Express these decimals as percents.
g. 1.25 _______________________
h. 4.52 _______________________
i. 2.29 _______________________
j. 8.01 _______________________
Expressing Percents Larger than 100% as Fractions
Example:
150%
15
3
Divide by 100%. 100%
10
2
Write 150% as a fraction.
Express these percents as fractions.
k. 250% _______________________
l. 125% _______________________
m. 420% _______________________
n. 140% _______________________
o. 350% _______________________
p. 550% _______________________
© Enslow Publishers, Inc. Based on the book Percents and Ratios by Lucille Caron and Philip M. St. Jacques,
ISBN 0-7660-1435-5, pages 54–55.
24
Name _____________________________________________
Date ___________________
Commission and Income
Commission
Example:
With a rate of commission of 5% and total sales of $148,
how much commission would you earn?
1. Change the commission rate to a decimal. 5% 0.05
2. Multiply the commission rate by the total sales. 0.05 $148 $7.40
So, you would earn a commission of $7.40.
Find the amount of commission for the following.
a. 6% on $200 of sales
b. 15% on $500 of sales
c. 5% on $268 of sales
d. 12% on $440 of sales
Income
Gross income is the total amount earned before deductions (taxes).
Net income is the amount left after deductions.
Example:
What is the net income on $500 if 6% was taken out for taxes?
1. Change the percent to a decimal. Multiply. $500 0.06 $30
2. Find the difference between the gross income and deductions.
$500 – $30 $470.
So, net income is $470.
Find the net income for the following.
e. Gross: $650; deduction 8%
f. Gross: $400; deduction 5%
g. Gross: $1,000; deduction 10%
h. Gross: $325; deduction 3%
© Enslow Publishers, Inc. Based on the book Percents and Ratios by Lucille Caron and Philip M. St. Jacques,
ISBN 0-7660-1435-5, pages 56–57.
25
Name _____________________________________________
Date ___________________
Simple Interest
The equation for simple interest is I PRT
P Principal (money placed in bank)
R Rate of interest
Example:
T Time (in years)
Find the simple interest on $700 for 2 years at 8% interest rate.
Interest $700 8% 2 years
Change the percent to a decimal. 8% 0.08
Interest $700 0.08 2 $112.00
Find the simple interest on the following principals.
a. $800 for 3 years at 5%
b. $900 for 2 years at 8%
There are different terms used for time when finding interest.
Annually means every 1 year.
6
Semiannually means every 6 months 0.5 year.
12
3
Quarterly means every 3 months 0.25 year.
12
1
Monthly means every 1 month year.
12
1
Daily means every 1 day year.
365
Example:
Find the semiannual interest on $800 at 9%.
Interest P R T
$800 0.09 0.5 year $36.00
Find the simple interest on the following principals.
c. $120, semiannually at 4%
d. $400, quarterly at 8%
e. $840, annually at 10%
f. $1,000, quarterly at 5%
© Enslow Publishers, Inc. Based on the book Percents and Ratios by Lucille Caron and Philip M. St. Jacques,
ISBN 0-7660-1435-5, pages 58–59.
26
Name _____________________________________________
Date ___________________
Compound Interest
Example:
Find the compound interest earned on $900 invested for 1 year
at 7%, compounded twice a year (semiannually).
I PRT
Interest $900 7% 6 months
Interest $900 0.07 0.5 $31.50
$31.50 is the interest for first 6 months.
Add the interest from the first 6 months to the principal.
$900 $31.50 $931.50
$931.50 is the new principal.
Find the interest for the next 6 months using the new principal.
I PRT
Interest $931.50 0.07 0.5 $32.6025, rounded to $32.60
Add the two interests.
$31.50 $32.60 $64.10 Compound interest after one year
is $64.10.
Find the compound interest after one year on the following principals.
a. $200 at 5% compounded semiannually
b. $650 at 4% compounded quarterly
c. $500 at 6% compounded semiannually
d. $800 at 8% compounded quarterly
e. $1,000 at 7% compounded semiannually
© Enslow Publishers, Inc. Based on the book Percents and Ratios by Lucille Caron and Philip M. St. Jacques,
ISBN 0-7660-1435-5, pages 60–61.
27
Percents and Ratios Answers
Reducing Ratios, page 2
9
2
2
20
8
a. 9 to 1, , 9:1; b. 2 to 1, , 2:1; c. 2 to 5, , 2:5; d. 20 to 3, , 20:3; e. 8 to 1, ,
1
1
5
3
1
16
3
5
4
8:1; f. 16 to 5, , 16:5; g. 3 to 1, , 3:1; h. 5 to 3, , 5:3; i. 4 to 1, , 4:1; j. 5 to 1,
5
1
3
1
5
3
, 5:1; k. 3 to 1, , 3:1
1
1
Ratios and Percents, page 3
first term less than 100: a. 3 to 5; b. 3 to 4; c. 3 to 10; d. 1 to 4; e. 17 to 20; f. 2 to 5
first term greater than 100: a. 11 to 2; b. 6 to 1; c. 3 to 2; d. 21 to 20; e. 5 to 4; f. 7 to 4;
g. 2 to 1; h. 9 to 1; i. 17 to 2
Equivalent Ratios, page 4
higher terms: a. 40 to 20; b. 18 to 10; c. 6 to 4; d. 30 to 20; e. 16 to 12; f. 100 to 8;
g. 70 to 22; h. 20 to 6
lowest terms: a. 3 to 1; b. 9 to 5; c. 4 to 1; d. 2 to 1; e. 10 to 3; f. 7 to 1; g. 3 to 1; h. 3 to 1
Rates, page 5
writing rates as fractions: a. $4.00 per 12 bagels; b. 5 miles per hour;
c. 16 feet per minute
56 houses
$3.00
75 miles
writing rates using words: a. ; b. ;
c.
2 pounds of tomatoes
2 city blocks
hour
40 miles
2 cars
reducing rates to lowest terms: a. ; b. ; c. $13.00 per CD;
hour
household
d. 10 feet per second
Units of Measure, page 6
money: a. 4 to 1; b. 6 to 1; c. 8 to 1; d. 5 to 3; e. 3 to 1; f. 25 to 8
time: a. 2 to 7; b. 14 to 5; c. 8 to 1; d. 4 to 1; e. 2 to 7; f. 9 to 1
Ratios and Fractions, page 7
fractions: a. 9 to 4; b. 20 to 9; c. 10 to 3; d. 3 to 2; e. 3 to 2
mixed numbers: a. 9 to 16; b. 27 to 22; c. 33 to 40; d. 45 to 24; e. 25 to 68
Ratios and Decimals, page 8
a. 3 to 2; b. 2 to 1; c. 4 to 1; d. 3 to 200; e. 5 to 1; f. 20 to 1; g. 2 to 1; h. 65 to 4;
i. 5 to 1; j. 80 to 1
Unit Pricing, page 9
a. 5 cans of juice for $8.00; b. 35 ounces of popcorn for $8.40; c. 9 notebooks for
$11.00; d. 6 pounds of candy for $3.12; e. 2 pounds of bananas for $1.30; f. 12
cantaloupes for $16.30
28
Ratio and Proportion, page 10
cross multiply: a. ; b. ; c. ; d. ; e. ; f. ; g. ; h. ; i. ; j. ; k. ; l. finding unknown term: a. 12; b. 70; c. 24; d. 4; e. 16; f. 3; g. 21; h. 27; i. 8; j. 10;
k. 16; l. 12
Finding a Number When a Ratio Is Known, page 11
a. 40 years; b. 15 words; c. $60; d. 20 ounces; e. $38.25; f. 36 bikes
Scale Drawings, page 12
reduction: a. 64 miles; b. 28 miles; c. 54 miles
enlargement: a. 12 mm; b. 5 mm
Probability, page 13
a. 1 in 3; b. 1 in 6; c. 1 in 2; d. 1 in 3; e. 2 in 9; f. 4 in 9; g. 5 in 9; h. 7 in 9
Percents and Ratios, page 14
27
1
2
3
9
a. 71%; b. 16%; c. 1%; d. 99%; e. 50%; f. 45%; g. ; h. ; i. ; j. ; k. ;
100
2
5
10
20
63
3
1
1
4
3
97
l. ; m. ; n. ; o. ; p. ; q. ; r. 100
4
10
5
25
100
100
Decimal Equivalents, page 15
a. 0.18; b. 0.38; c. 0.05; d. 0.115; e. 0.007; f. 0.00016; g. 25%; h. 7.6%; i. 5%; j. 0.3%;
k. 60%; l. 0.042%; m. 103%; n. 700%; o. 350%; p. 410%; q. 1,600%; r. 199%
Fraction Equivalents, page 16
1
3
2
3
3
7
a. ; b. ; c. ; d. ; e. ; f. ; g. 0.002; h. 0.00125; i. 0.0075; j. 0.009; k. 0.006;
4
5
10
5
100
2
l. 0.0025
More Fraction Equivalents, page 17
a. 80%; b. 30%; c. 12%; d. 56%; e. 12%; f. 70%; g. 450%; h. 400%; i. 110%; j. 145%
Mixed Numerals, page 18
a. 0.182; b. 0.26245; c. 0.119; d. 0.086; e. 0.338; f. 0.163; g. 12.6%; h. 75.1%;
7
5
i. 62.7%; j. 98.1%; k. 43.7%; l. 85.5%; m. ; n. 8
8
Finding the Percent of a Number, page 19
a. $2.52; b. 12; c. 1,170; d. 50; e. 170.5; f. 30; g. 500; h. 5
Applying Percent: Part and Whole, page 20
a. 20%; b. 25%; c. 32%; d. 33 1%; e. 40%; f. 75%
3
Finding the Total Number, page 21
a. 140; b. 200; c. 300; d. 225; e. 10; f. 400; g. 50; h. 150
29
Percent Increase and Decrease, page 22
a. 50%; b. 25%; c. 66 2%; d. 75%; e. 33 1%; f. 100%; g. 16 2%; h. 20%;
3
3
3
i. 25%; j. 10%
Discount and Sale Price, page 23
a. $20; b. $0.09; c. $0.75; d. $2.25; e. $85; f. $187.50; g. $60; h. $31.50
Percents Larger than 100%, page 24
a. 2; b. 3.65; c. 1.21; d. 1.99; e. 2.12; f. 1.52; g. 125%; h. 452%; i. 229%; j. 801%;
5
5
21
7
7
11
k. ; l. ; m. ; n. ; o. ; p. 4
5
5
2
2
2
Commission and Income, page 25
a. $12; b. $75; c. $13.40; d. $52.80; e. $598; f. $380; g. $900; h. $315.25
Simple Interest, page 26
a. $120; b. $144; c. $2.40; d. $8.00; e. $84; f. $12.50
Compound Interest, page 27
a. $10.13; b. $26.40; c. $30.45; d. $65.95; e. $71.23
30