Ratio Workbook
Efta
Tape/Bar Diagrams
Name: ___________________________________ HR: ________ Date: ________________________
Tape Diagrams Practice Class Work
Problem #1
The ratio of boys to girls at a party is 2 to 3. If there are 10 boys then how
many girls are there?
boys
girls
a. What’s wrong with this tape diagram? How can it be fixed?
_____________________________________________________________________
_____________________________________________________________________
b. Circle the correct tape diagram. Put an “X” through the wrong tape diagrams.
c. Fill in the correct tape diagram and solve the problem.
Don’t forget this part.
MA_Ratios_Lesson03_Classwork_mod.doc
How many girls are there? ___________ girls
Intro to Tape Diagrams
2. In a zoo there are 9 monkeys. The ratio of monkeys to zebras is 3 to 1. How many
zebras are there?
a. Put the numbers into the tape diagram
below.
b. Solve the problem.
Answer: _______ zebras
Complete the tape diagrams. Put numbers in the boxes and for the length of each tape.
3. In a basket, there are 24 sweet oranges
and the rest are sour oranges. The ratio of
sweet oranges to the sour oranges is 4:1.
Find the number of sour oranges.
Answer: ________________________
4. The ratio of blue marbles to red marbles in a box is 3 to
2. If there are 12 blue marbles in the box then how many
red marbles are there?
Answer: ________________________
Try these:
5. Children at recess are either playing or
sitting down resting. The ratio of kids
playing to resting is 3:1. If there are 8
children resting, then how many children
are playing?
Answer: ________________________
MA_Ratios_Lesson03_Classwork_mod.doc
6. A fruit basket is made with apples and
oranges. The ratio of apples to oranges in
a fruit basket is 2 to 3. If there are 15
oranges in the basket, then how many
apples are there?
Answer: ________________________
Intro to Tape Diagrams
Name: _______________________________________________ HR: _____________ Date: ______________________________________________________
Introduction to Tape Diagrams Homework
Directions
1. Draw a line to match the tape diagram with the story problem that it represents.
2. For each tape diagram, write numbers in each box so the tape diagrams are complete.
3. Solve each problem on the line below the story. Label each answer.
(1)
(2)
(3)
(4)
A
The ratio of girls to boys
in a class is 1:3. If there
are 12 boys, how many
girls are there?
B
The ratio of boys to girls
in a class is 1:2. If there
are 12 boys, how many
girls are there?
C
The ratio of girls to boys
in a class is 3:1. If there
are 12 boys, how many
girls are there?
D
The ratio of boys to girls
in a class is 2:1. If there
are 12 boys, how many
girls are there?
_____________________________
_____________________________
_____________________________
_____________________________
MA_Ratios_Lesson03_Homework.doc
Intro to Tape Diagrams
Directions
Solve each problem and write the answer on the line below the story.
Fill in the missing information for each tape diagram. Then solve the problem.
(5) The ratio of cats to dogs in the Crazy Cat
Lady’s house is 3:1. If there are 30 cats,
then how many dogs does she have?
Answer: _______________________________
(7) Lem and his sister Ada are selling juice
for a fundraiser. For every 3 cups Lem sells
Ada sells 2. If Lem sold 27 cups of juice,
how many cups did Ada sell?
Answer: _______________________________
MA_Ratios_Lesson03_Homework.doc
(6) Charlene has 14 pens in her pencil box.
She always keeps a ratio of 2 pens to every
3 pencils in her pencil box. How many pencils
does she have?
Answer: _______________________________
(8) The ratio of dancing monkeys to dancing bears
in a circus is 4:1. If there are 7 bears, how many monkeys
are there?
Answer: _______________________________
Intro to Tape Diagrams
Ratio Tables
Double Line Graphs
Rates and
Unit Rates
NAME ________________________________________ DATE _____________ PERIOD _____
Homework Practice
Rates
Write each rate as a unit rate.
1. 3 inches of rain in 6 hours
2. $46 for 5 toys
3. 70 miles in 2 hours
4. 64 ounces in 8 cups
5. CLASSES A school has 825 students and 55 teachers. How many students
are there per teacher?
6. CELL PHONE Tiffany pays $40 for 160 minutes of talk time on her cell
phone. How many minutes of talk time does she get per dollar?
7. HAMBURGERS Mrs. Farley made 72 ounces of hamburger into 24 meat
patties. How many ounces of hamburger are in each meat patty?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
For Exercises 8 and 9, refer to the table showing
the statistics of women’s baseball teams.
8. For each team, find the unit rate games per loss.
9. Which team has the best record? Explain how you
know.
The Flamingo League Stats
Team
Jules’
Rules
Pink
Sox
GoGirls
High5s
Games
Losses
36
12
68
17
52
13
72
8
10. BREAKFAST Franco is making breakfast. He uses 36 eggs for 12 orders.
How many eggs does he use per order?
11. TRAINS A train travels 558 miles in 3 hours. At this rate, how far does
the train travel per hour?
12. SCHEDULES A bus makes 28 stops every 2 hours. How many stops does
it make in 3 hours? in 4 hours?
Get ConnectED
For more practice, go to www.connected.mcgraw-hill.com.
Course 1 • Ratios and Rates
MAT1L0
Name _______________________
Instructions: For each question, calculate the unit rate for each option and determine
which one is the BEST buy. Write your final choice in the last column.
! The first one is done as an example for you to follow
! Round all answers to TWO decimal places if necessary
Option 1
Option 2
Unit Rate 1
Unit Rate 2
BEST BUY
Question #1
3 batteries
for $4.80
12 batteries for
$14.76
$4.80 / 3
= $1.60
$14.76 / 12
= $1.23
OPTION # 2
(cheaper)
Question #2
22 staplers
for $330
4 staplers for
$80
Question # 3
5 calculators
for $105
24 calculators
for $552
Question # 4
18 pens for
$6.84
30 pens for
$8.40
Question # 5
18 ounces for 27 ounces for
$7.38
$15.39
Question # 6
11 books for
$99
Question # 7
$15.98 for 34 $4.68 for 12
litres of gas
litres of gas
Question # 8
$160 for 10
calendars
29 books for
$203
$114 for 6
calendars
Question # 9
16 pounds
for $31.68
28 pounds for
$49.56
$800 for 33
Question # 10 $625 for 25
pairs of shoes pairs of shoes
10 litres of pop
Question # 11 3 litres of
pop for $1.89 for $6.90
Question # 12 $407 for 37
pairs of jeans
$570 for 48
pairs of jeans
Question # 13 12 chocolate
bars for $22
20 chocolate
bars for $33
Question # 14 24 grams of
turkey for
$10.08
9 grams of
turkey for
$4.77
Equivalent Ratio
and Proportions
Proportions Word Problems
1.
If 3 apples cost $6, how much would 12 apples cost?
2.
3 pounds cost $15. How many pounds can you buy for
$45?
3.
Three tea bags are needed to make a gallon of iced tea.
How many tea bags are needed to make four gallons?
4.
If 5 pencils cost 20 cents, how much would 15 pencils
cost?
5.
If 3 twinkies cost $1, how much is it for 15 twinkies?
6.
You can buy 2 hot dogs for $3. How much would it be
for 4 hot dogs?
7.
The ratio of teachers to students needs to be 1:30. If
there were 120 students, how many teachers would be
needed?
8.
The ratio of seventh graders to eighth graders
participating in the science fair is 4:3. There are 18
eight graders participating in the science fair. How
many 7th graders are there?
9.
To make lemonade, you need 6 lemons and 8 cups of
water. How many lemons do you need if you have 24
cups of water?
10.
Darrell drove 187 miles in 3 hours. What was
Darrell’s average rate of speed in miles per hour?
11.
If three bakers can prepare 15 cakes in 60 minutes, how
long will it take six bakers working at the same rate to
prepare 20 cakes?
12.
At Discount Copy, 12 copies cost $0.66. Melissa needs
56 copies. How much should they cost?
13.
Two 100-W light bulbs used a total of 400 Wh of
energy. For how many hours did the light bulbs use
power?
14.
An amusement park line is moving about 4 feet every
15 minutes. At this rate, approximately how long will
it take for a person at the back of the 50- foot line to
reach the front of the line?
15.
For every left-handed person, there are about 4 righthanded people. If there are 30 students in a class, write
and solve a proportion to predict the number of students
who are right-handed.
16.
A diagram measuring 20 cm long is reduced on a copy
machine to 15 cm long. If the width of the original
copy is 16 cm, what is the width of the reduced copy?
17.
You estimate that you can do 12 math problems in 45
min. How long should it take you to do 20 math
problems?
18.
Evarado paid $1.12 for a dozen eggs. Write and solve a
proportion to determine the cost of the 3 eggs Evarado
needs for a recipe.
19.
The ratio of an object’s weight on Earth to its weight on
the Moon is 6:1. The first person to walk on the Moon
was Neil Armstrong. He weighed 165 pounds on Earth.
How much did he weigh on the moon?
20.
The ratio of the length of the actual height of a person
to the length of their shadow cast is 1:3. At the same
time, a lighthouse casts a shadow that is 600 meters
long. How tall is the lighthouse?
21.
Three posters cost $9.60. At that rate, how many
posters can you buy for $48?
22.
At the Copy Shoppe, 18 copies cost $1.08. At that rate,
how much will 40 copies cost?
23.
A 20-gigabyte digital music player sells for $249. A
similar 30-gigabyte player sells for $349. Which player
offers the better price per gigabyte of storage?
24.
Which costs more per issue, an 18-issue subscription
for $40.50 or a 12-issue subscription for $33.60?
25.
For every person who actually has the flu, there are 6
people who have flu-like symptoms resulting from a
cold. If a doctor sees 40 patients, write and solve a
proportion to determine how many of these you would
expect to have a cold.
26.
An 8-ounce box of Crispy Crackers costs $1.59
and a 2-pound box costs $6.79. Which box is the
better buy?
27.
Lee is reading a 374-page novel. It takes her 6 days to
read the first 132 pages. At this rate, how many more
days will it take her to finish the novel?
28.
Jaron is downloading a file. The size of the file is 3,200
KB. It takes 3 minutes to download the first 1,200 KB
of the file. If the file continues downloading at the same
rate, how many more minutes will it take to finish
downloading?
29.
Ana is using a photocopier to make 315 copies of a
poster. It takes 3 minutes to print the first 63 posters. If
the photocopier continues to print at the same rate, how
many more minutes will it take to complete the job?
30.
A 5-pound bag of grass seed covers 2,000 square feet.
An opened bag has 3 pounds of seed remaining in it.
Will this be enough to seed a 14-yard by 8-yard piece
of land? (Answer YES or NO)
31.
It takes 20 minutes to cut a log into
5 equal-size pieces. How long will it take to
cut a similar log into 3 equal-size pieces?
32.
A 50-pound bag of Glossy Coat Horse Fee costs
$23.50. A 25-pound bag costs $15.50. How much
money per pound would you save by buying the bag
with the lower unit price?
33.
Patrice and Tatiana share baby-sitting duties. The ratio
comparing the amount of time each one works is 6:5.
They earn a total of $77. If Patrice works longer, how
much should each receive?
34.
Jacob is selling T-shirts at a music festival. Yesterday,
he sold 51 shirts and earned $191.25. How many shirts
must Jacob sell today and tomorrow to earn a total of
$536.25 for all 3 days?
6
9
5
10
35
24
62
75
12
0.15
0.28
200
5
3
8
12
42
24
40
12
11
0.60
27.5
1.59
4
2
20
12
92
18
24
15
≈ 34
3.08
2.40
249
Proportion Word Problems
1. Carol spends 17 hours in a 2-week period practicing her culinary skills. How many hours does she
practice in 5 weeks?
2. In the typing world, 80 words per minute is considered acceptable. How many words per 30 minutes is
this?
3. In the year 2000, there were 8.7 deaths per 1000 residents in the United States. If there were 281,421,906
residents in the U.S. during 2000, how many people died that year?
4. In a shipment of 400 parts, 14 are found to be defective. How many defective parts should be expected in
a shipment of 1000?
5. Joseph drives 125 miles in 2
1
hours. At the same rate, how far will he be able to travel in 6 hours?
2
6. A piece of cable 8.5 cm long weighs 52 grams. What will a 10-cm length of the same cable weigh?
7. A rainstorm produced a rainfall of 2 inches per hour. How many hours would it take to get a rainfall
amount of one foot?
8. A snowstorm dumped 18 inches of snow in a 12-hour period. How many inches were falling per hour?
9. Mary can read 22 pages in 30 minutes. How long would it take her to read a 100 page book? Write your
answer in hours and minutes and round to the nearest minute, if needed.
10. It takes about me 25 minutes to make out a test for a mathematics class. How long will it take to make
out tests for all five of my classes?
11. The chance of a woman getting breast cancer in her lifetime is 1 out of 8. At this rate, how many
women in a classroom of 32 women would be expected to come down with breast cancer in her lifetime?
12. If 15.9 out of every 100 pregnant women in Georgia deliver their babies by C-Section, how many
pregnant women out of 25,250 would be expected to deliver by C-Section?
13. A company’s quality control department found and average of 5 defective models for every 1000
models that were checked. If the company produced 60,000 models in a year, how many of them would be
expected to be defective?
14. To determine the number of deer in a forest, a forest ranger tags 280 and releases them back into the
forest. Later, 405 deer are caught, out of which 45 of them are tagged. Estimate how many deer are in the
forest.
15. An employee working at an electronics store earned $3582 for working 3 months during the summer.
What did the employee earn for the first two months?
16. A worker can complete the assembly of 15 tape players in 6 hours. At this rate, how many can the
worker complete in a 40-hour work week?
17. The ratio of men to women at a class is 6 to 5. How many women students are there if there are 3600
men?
18. If 3 pounds of apples costs $0.90, how much will 10 pounds cost?
19. You find that your watch gains 2 minutes in 6 hours. How much will it gain in 3 days?
20. Sirloin steak costs $2.99 per pound. How much will 3.4 pounds cost?
21. A yard of fabric costs $12.99. How much will 2 feet cost?
22. Hurricane Katrina dropped about 14 inches of rain over a 48 hour period. How much rain is this per
hour? (Round your answer to the nearest tenth.)
23. It takes about 20 minutes to grade a student’s paper. How long, in hours, does it take to grade papers
for a class of 25 people?
24. A doctor sees each of her patients for 25 minutes during a typical appointment. How many patients can
1
she see in a typical 7 hour day?
2
25. If a trip between work and home takes 15 minutes each way, how much time will be spent in a 5-day
work week traveling back and forth to work? (Assume that at no point does the employee have to go home
and come back within the same day.)