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Name___________________________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
Explain, in your own words, the least common multiple of two numbers.
Tell what you would do if you added the fraction parts of mixed numbers and the result
was greater than 1.
A student is asked to perform the following division: 6 ÷ 21
2. He starts by writing 6 ÷ 21
2=
(6 ÷ 2) + (6 ÷1
2). Do you think this method will give the correct answer? If not, how should
the student have proceeded?
Explain why, when rewriting a fraction with a different denominator, the fraction can be
multiplied by another fraction whose numerator and denominator are the same.
A student added two mixed numbers in the following way:
54
9+ 37
9= 811
9
Explain in your own words what is wrong with the answer and give the correct answer.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve. Write a mixed numeral for the answer.
An attorney drove 141
3 miles from his home to a client’s home and another 122
5 miles to get to his
office. How far did he drive in total?
Solve. Write a mixed numeral for the answer.
Derek spent 23
4 hours studying for his math exam and another 25
12 hours doing his math
homework. How long did he spend on math in total?
Add. Write a mixed numeral for the answer.
Convert to fraction notation.
Solve. Write a mixed numeral for the answer.
The floor of a rectangular room is to be tiled with 1
3 foot square tiles along a 107
8 foot wall. How
many tiles will be needed along the wall?
Convert to a mixed numeral.
Multiply. Write a mixed numeral for the answer.
Add. Write a mixed numeral for the answer.
Estimate the value as a whole number or as a mixed numeral where the fractional part is 1
2.
Convert to a mixed numeral.
Add. Write a mixed numeral for the answer.
Multiply. Write a mixed numeral for the answer.
Convert to fraction notation.
Find the LCM of the set of numbers.
Solve. Write a mixed numeral for the answer.
A laminated lab bench has 11
4 inches of plywood, 11
3 inches of pressed board, and 2
5 inch of
formica. What is the thickness of the lab bench?
Subtract. Write a mixed numeral for the answer.
Solve. Write a mixed numeral for the answer.
The population of Anna’s grandmother’s country is 21
4 times the population of Anna’s country.
The population of Anna’s country is 212 million. What is the population of Anna‘s grandmother’s
country?
Stock in a company is selling for $221
2 per share. If someone purchases $1395 worth of stock in this
company, how many shares did they get?
Solve. Write a mixed numeral for the answer.
Peter must practice the piano 81
4 hours per week. He has already practiced 33
4 hours. How many
more hours does he need to practice?
Add. Write a mixed numeral for the answer.
Lorrie bought 1
3 lb of basil and 1
7 lb of oregano. How many pounds of herbs did she buy in total?
Find the LCM of the set of numbers.
Add. Write a mixed numeral for the answer.
Estimate the fraction as 0, 1
2, or 1.
Solve. Write a mixed numeral for the answer.
The front cover of a book measures 81
2 inches by 93
5 inches. What is the total distance around (the
perimeter of) the front cover of the book?
Find the LCM of the set of numbers.
Robert has built a mechanical model solar system with three balls representing planets at the ends
of rods attached to the center representing the sun. The planets are aligned when he turns on the
motor. The innermost planet makes a revolution in 12 seconds, the middle planet makes a
revolution in 30 seconds, and the outermost planet makes a revolution in 42 seconds. After how
many seconds will the planets be aligned again?
Add. Write a mixed numeral for the answer.
Divide. Write a mixed numeral for the answer.
Provide an appropriate response.
Let x represent a whole number which is not equal to 6. If the LCM for x and 6 is equal to x, what
can you conclude about x?
i: x is greater than 6
ii: x is smaller than 6
iii: x is a multiple of 6
iv: x is a factor of 6
Convert to a mixed numeral.
Find the LCM of the set of numbers.
The earth, Jupiter, Saturn, and Neptune all revolve around the sun. The earth takes 1 year, Jupiter
approximately 12 years, Saturn approximately 30 years, and Neptune approximately 165 years to
make a complete revolution. How often will Jupiter and Neptune appear in the same direction in
the night sky as seen from earth?
[Hint: Find the LCM of 12 and 165]
Estimate the value as a whole number or as a mixed numeral where the fractional part is 1
2.
54 2
18 ÷217
18 +31
10 ·516
18
Find the LCM of the set of numbers.
A layer of paint on a piece of wood has a thickness of 1
21 inch. The thickness of the piece of wood is
6
7 inch. What is the total thickness of the wood and the paint?
Solve. Write a mixed numeral for the answer.
The dimensions of a rectangular mural on the wall of Amy’s bedroom are 21
4 feet by 33
5 feet. What
is the area of the mural?
Estimate the fraction as 0, 1
2, or 1.
Solve. Write a mixed numeral for the answer.
While shopping for a party, June bought 11
2 pounds of hamburger, 31
3 pounds of chicken, and 41
4
pounds of ham. How much meat did she buy?
Estimate the value as a whole number or as a mixed numeral where the fractional part is 1
2.
Refer to the following recipe to answer the question. Give your answer as a mixed numeral.
Grandma‘s Fork Cookies
11
2 cup brown sugar
11
2 cup white sugar
11
4 cup shortening
1 pinch salt
3 eggs
21
2 tsp soda
21
4 tsp cream of tartar
11
2 tsp vanilla
Cream sugars and shortening. Beat in remaining ingredients. Add flour to stiffen like regular cookie dough. Roll into
balls, then flatten with a fork. Cook until brown.
If the recipe is tripled, how much soda will be needed?
The earth, Jupiter, Saturn, and Neptune all revolve around the sun. The earth takes 1 year, Jupiter
approximately 12 years, Saturn approximately 30 years, and Neptune approximately 165 years to
make a complete revolution. How often will Jupiter, Saturn, and Neptune appear in the same
direction in the night sky as seen from earth?
[Hint: Find the LCM of 12, 30, and 165]
Solve. Write a mixed numeral for the answer.
Denise’s triplets weighed 35
8 lb, 4 3
16 lb, and 41
4 lb at birth. Find their average birth weight.
Find the average of the set of numbers.
Convert to a mixed numeral.
Subtract. Write a mixed numeral for the answer.
Estimate the fraction as 0, 1
2, or 1.
Bill has 24
36 yards of canvas from which he is cutting strips. He has cut 9
36 yards already. How
much of the canvas is left?
Find the average of the set of numbers.
Solve. Write a mixed numeral for the answer.
To obtain a certain shade of paint, Peter mixed 25
7 gallons of white paint with 7 gallons of brown
paint and 12
3 gallons of blue paint. How much paint did he have?
Find the length of the section represented by x in the figure.
a=271
4
b=13
16
c=163
4
Refer to the following recipe to answer the question. Give your answer as a mixed numeral.
Grandma‘s Fork Cookies
11
2 cup brown sugar
11
2 cup white sugar
11
4 cup shortening
1 pinch salt
3 eggs
21
2 tsp soda
21
4 tsp cream of tartar
11
2 tsp vanilla
Cream sugars and shortening. Beat in remaining ingredients. Add flour to stiffen like regular cookie dough. Roll into
balls, then flatten with a fork. Cook until brown.
Find the amount of cream of tartar needed if you take 11
2 times the recipe.
Estimate the value as a whole number or as a mixed numeral where the fractional part is 1
2.
Solve. Write a mixed numeral for the answer.
June wants to work for 111
4 hours at her part–time job this week. She has already worked 71
2
hours. How many more hours does she need to work?
Convert to fraction notation.
Solve. Write a mixed numeral for the answer.
A painter used 85
6 gallons of paint to paint the front of a house and another 55
9 gallons to paint the
back. How much paint did he use in total?
To make a batch of juice, 22
3 cups of concentrate are required. How many batches of juice can be
made from 32 cups of concentrate?
Brian was training to run a marathon. During the three–day period before the race he decided that
he would train for a total of 10 hours. If he trained for 14
5 hours on the first day and 37
10 hours on
the second day, how many hours would he need to train on the third day?
Refer to the following recipe to answer the question. Give your answer as a mixed numeral.
Grandma‘s Fork Cookies
11
2 cup brown sugar
11
2 cup white sugar
11
4 cup shortening
1 pinch salt
3 eggs
21
2 tsp soda
21
4 tsp cream of tartar
11
2 tsp vanilla
Cream sugars and shortening. Beat in remaining ingredients. Add flour to stiffen like regular cookie dough. Roll into
balls, then flatten with a fork. Cook until brown.
Find the amount of white sugar needed if you take 21
2 times the recipe.
Divide. Write a mixed numeral for the answer.
Linda walked 3
10 mi to the park and then another 1
15 mi to the cafe. How far did she walk in
total?
Divide. Write a mixed numeral for the answer.
Provide an appropriate response.
Arrange the following numbers in order from smallest to largest.
14
914
11 14
914
11
14
11, 14
9, 1 4
11, 14
9
14
11, 14
9, 1 4
11, 14
9
14
9, 14
9, 14
11, 1 4
11
14
11, 1 4
11, 14
9, 14
9
Find the LCM of the set of numbers.
A snail is moving at 23
4 feet per minute. How far will it move in 31
3 minutes?
Use < or > for to write a true sentence.
Find the LCM of the set of numbers.
Divide. Write a mixed numeral for the answer.
Convert to fraction notation.
Estimate the value as a whole number or as a mixed numeral where the fractional part is 1
2.
Saji swims 1
3 mi every day. One day he had already swum 1
8 mi. How much further should he
swim?
Convert to a mixed numeral.
Subtract. Write a mixed numeral for the answer.
A lawyer stacks three case files on top of each other. The thicknesses of the files are 4
8, 1
12 , and 7
15
inches. What is the total height of the stack of files?
Use < or > for to write a true sentence.
Find the average of the set of numbers.
Multiply. Write a mixed numeral for the answer.
Estimate the value as a whole number or as a mixed numeral where the fractional part is 1
2.
Use < or > for to write a true sentence.
Add. Write a mixed numeral for the answer.
Use < or > for to write a true sentence.
Divide. Write a mixed numeral for the answer.
Convert to a mixed numeral.
Tom and Larry are food inspectors at a cookie making company. Tom tests every 8th batch of
dough for fat percentage. Larry tests every 28th batch of dough for carbohydrate percentage. If they
both start working at the same time, which batch will be the first that they both test?
Solve. Write a mixed numeral for the answer.
A nail 34
5 inches long is driven into a board 21
2 inches thick. How much of the nail protrudes from
the other side of the board?
Find the LCM of the set of numbers.
Estimate the fraction as 0, 1
2, or 1.
Multiply. Write a mixed numeral for the answer.
Divide. Write a mixed numeral for the answer.
Solve. Write a mixed numeral for the answer.
A courier distributes packages along two routes. The northern route can be completed in 73
8
minutes, whereas the southern route takes 25
8 minutes. Find the total time it takes to complete the
deliveries for one month if the northern route is taken 56 times and the southern route 47 times.
Add. Write a mixed numeral for the answer.
Convert to a mixed numeral.
Estimate the value as a whole number or as a mixed numeral where the fractional part is 1
2.
3210
21 + 20 8
15 · 14 1
18
Divide. Write a mixed numeral for the answer.
Use < or > for to write a true sentence.
Convert to a mixed numeral.
Convert to fraction notation.
Solve. Write a mixed numeral for the answer.
A small company sells stock for 83
8 dollars per share. How much will 72 shares cost?
A square piece of paper has a side length of s = 75
8 inches. A square of side length 1
2· s is cut from
one corner of the piece of paper. Find the area of the piece of paper that remains.
A recipe calls for 11
4 cups of water. How much water would be needed for 1
2 the recipe?
Divide. Write a mixed numeral for the answer.
Convert to fraction notation.
Estimate the value as a whole number or as a mixed numeral where the fractional part is 1
2.
Find the LCM of the set of numbers.
Solve. Write a mixed numeral for the answer.
A rectangular lot measures 2861
3 feet by 2201
2 feet. A building with dimensions of 120 feet by 353
4
feet is built on the lot. How much area is left over?
Use < or > for to write a true sentence.
Solve. Write a mixed numeral for the answer.
The population of the country where Ken lives is 22
5 times the population of the country where he
was born. The population of the country where he lives is approximately 12,000,000. What is the
approximate population of the country where he was born?
The weight of a substance is 23
4 g per cubic centimeter. What is the weight of 31
3 cubic centimeters
of the substance?
The earth, Jupiter, Saturn, and Neptune all revolve around the sun. The earth takes 1 year, Jupiter
approximately 12 years, Saturn approximately 30 years, and Neptune approximately 165 years to
make a complete revolution. How often will Saturn and Neptune appear in the same direction in
the night sky as seen from earth?
[Hint: Find the LCM of 30 and 165]
A cereal manufacturer uses three large overhead bins to hold the three ingredients in one of its
cereal mixes. Bin A delivers a premeasured quantity of dried fruit every 55 minutes, bin B delivers
raisins every 25 minutes, and bin C delivers flakes every 35 minutes. If they start the morning shift
at the same time, how long before they deliver their ingredients at the same time again?
Solve. Write a mixed numeral for the answer.
A book cover measures 101
2 inches by 121
4 inches. What is the perimeter of the front cover of the
book?
101
2 in.
121
4 in.
John bought 1
5 lb of thyme, 7
5 lb of rosemary, and 1
15 lb of dill. How many pounds of herbs did he
buy in total?
Subtract. Write a mixed numeral for the answer.
Divide. Write a mixed numeral for the answer.
Multiply. Write a mixed numeral for the answer.
Add. Write a mixed numeral for the answer.
A car traveled 447 miles on 165
9 gallons of gas. How many miles per gallon did it get?
Daniel is 701
6 in. tall and his brother Tyler is 67 7
12 in. tall. How much taller is Daniel?
In one city , the average adult consumes 23
4 ounces of chocolate per week. How much chocolate do
28 average adults consume per week?
At a track and field event, an athlete recorded the following heights at the high jump: 841
4 in., 833
4
in., 831
2 in., and 85 in. Find the average of the four jumps.
Add. Write a mixed numeral for the answer.
Add. Write a mixed numeral for the answer.
The second tallest child in a class is 342
3 inches tall. The tallest child is 45
6 inches taller. How tall is
the tallest child in the class?
Convert to fraction notation.
Solve. Write a mixed numeral for the answer.
Ellen is knitting a scarf with one 5–inch blue stripe, one 4–inch green stripe, and one 22
9–inch
white stripe. How wide is the scarf?
At a national computer show, two software companies continuously run videos showing their
products. Company A’s video repeats every 15 minutes, while Company B’s video repeats every 33
minutes. If both companies begin the videos at 1:00 P.M. when the show opens, how many minutes
will elapse before they are in sync again?
Multiply. Write a mixed numeral for the answer.
Karl Mason sold 1
3 gross of data disks on Monday, 3
12 gross on Tuesday, and 2
6 gross on
Wednesday. What was the total amount of data disks sold?
Find the LCM of the set of numbers.
Solve. Write a mixed numeral for the answer.
Find the perimeter (distance around) of the polygon below. Each side of the polygon has the same
length.
side length =61
3 yd
Divide. Write a mixed numeral for the answer.
Use < or > for to write a true sentence.
Add. Write a mixed numeral for the answer.
Three partners share the ownership of a sailboat on Lake Michigan. One partner owns 9
16 of the
boat and the second owns 1
8. How much of the boat does the third partner own?
A recipe calls for 1
11 L of water and 5
11 L of milk. If the recipe is doubled, how much liquid will be
needed?
Solve. Write a mixed numeral for the answer.
Mr. Meredith is building a table. The top will have a piece of marble 101
2 inches by 18 inches,
bordered by 23
4 inches of wood on all four sides. Give the overall dimensions of the table top.
Convert to fraction notation.
Add. Write a mixed numeral for the answer.
Subtract. Write a mixed numeral for the answer.
Johnny’s Bakery cuts their blueberry pies into 6 slices and their pizzas into 12 slices. On a busy
Saturday, they sold 37 slices of blueberry pie, or 37
6 pies, and 121 slices of pizza, or 121
12 pizzas.
Convert 37
6 and 121
12 to mixed numerals.
Divide. Write a mixed numeral for the answer.
Find the LCM of the set of numbers.
Find the average of the set of numbers.
Find the LCM of the set of numbers.
Solve. Write a mixed numeral for the answer.
A technician has readings that take 12
3 minutes each to read and record. How many readings can
be completed in 90 minutes?
Subtract. Write a mixed numeral for the answer.
Find the LCM of the set of numbers.
Add. Write a mixed numeral for the answer.
Divide. Write a mixed numeral for the answer.
Estimate the value as a whole number or as a mixed numeral where the fractional part is 1
2.
Multiply. Write a mixed numeral for the answer.
Convert to a mixed numeral.
Solve. Write a mixed numeral for the answer.
The weight of a certain gas is 21
5 kg per cubic meter. How many cubic meters would be occupied
by 132 kg of the gas?
From a 21
20 –lb wheel of cheese, a 2
5–lb piece was served. How much cheese remained on the
wheel?
Use < or > for to write a true sentence.
Estimate the value as a whole number or as a mixed numeral where the fractional part is 1
2.
Divide. Write a mixed numeral for the answer.
Solve. Write a mixed numeral for the answer.
A Boeing 767 flew 920 mi on a nonstop flight. On the return flight, it landed after having flown 530
7
9 mi. How far was the plane from its original point of departure?
Stained Glass Solutions sells a framed stained glass window as shown below. Its dimensions are
293
4 inches wide by 347
8 inches high. What is the perimeter of the framed stained glass window?
347
8 in.
293
4 in.
Multiply. Write a mixed numeral for the answer.
Find the LCM of the set of numbers.
Estimate the value as a whole number or as a mixed numeral where the fractional part is 1
2.
Find the LCM of the set of numbers.
Find the average of the set of numbers.
Cory and Melissa are racing electronic cars around a circular track. They begin at the same time
going in the same direction. Cory’s car completes a revolution in 55 seconds, while Melissa’s car
completes a revolution in 50 seconds. How long will it take them before both cars reach the starting
point again simultaneously?
Estimate the fraction as 0, 1
2, or 1.
Solve. Write a mixed numeral for the answer.
There were 211
8 yards of wire on a spool. After a customer bought 67
8 yards of wire from the spool,
how many yards were left?
Multiply. Write a mixed numeral for the answer.
Convert to fraction notation.
Alan walked 4
7 mi to the store and then another 4
3 mi to his friend’s house. How far did he walk?
Find the average of the set of numbers.
Use < or > for to write a true sentence.
Solve. Write a mixed numeral for the answer.
Annie must send two packages. One of the packages weighs 62
5 lb and the other weighs 51
4 lb.
What is the total weight of the two packages?
Divide. Write a mixed numeral for the answer.
Estimate the value as a whole number or as a mixed numeral where the fractional part is 1
2.
Divide. Write a mixed numeral for the answer.
Find the average of the set of numbers.
Erika spent 3
4 hr on her computer visiting the history channel and the discovery channel websites.
She spent 1
3 hr at the history channel website. How many hours did she spend at the discovery
channel website?
Refer to the following recipe to answer the question. Give your answer as a mixed numeral.
Grandma‘s Fork Cookies
11
2 cup brown sugar
11
2 cup white sugar
11
4 cup shortening
1 pinch salt
3 eggs
21
2 tsp soda
21
4 tsp cream of tartar
11
2 tsp vanilla
Cream sugars and shortening. Beat in remaining ingredients. Add flour to stiffen like regular cookie dough. Roll into
balls, then flatten with a fork. Cook until brown.
Find the amount of vanilla needed if the recipe is halved.
Solve. Write a mixed numeral for the answer.
A test of five light bulbs showed that they burned for the following lengths of time (in days): 172
3,
191
4, 201
2, 21, and 18 3
4 . For how many days, on average did the light bulbs burns?
From a 7
8–lb package of ground beef, a 1
4–lb hamburger was made. How much ground beef is
left in the package?
Solve. Write a mixed numeral for the answer.
Fahrenheit temperatures can be obtained from Celsius (centigrade) by multiplying by 14
5 and
adding 32°. What Fahrenheit temperature corresponds to a Celsius temperature of 69°?
Convert to fraction notation.
Estimate the value as a whole number or as a mixed numeral where the fractional part is 1
2.
Solve. Write a mixed numeral for the answer.
A serving of filleted fish is generally considered to be 1
3 lb. How many servings can be prepared
from 91
4 lb of flounder fillet?
Subtract. Write a mixed numeral for the answer.
Solve. Write a mixed numeral for the answer.
Find the length of the section represented by x in the figure.
a=27
12
b=12 1
12
Subtract. Write a mixed numeral for the answer.
Solve. Write a mixed numeral for the answer.
A road acceleration test measures the time in seconds required to go from 0 mph to 60 mph. The
results for five cars were as follows: 6 3
10 sec, 72
5 sec, 8 1
10 sec, 64
5 sec, and 71
2 sec. What was the
average time?
Provide an appropriate response.
Let x represent a whole number. If the LCM for x and 5 is equal to the product of 5 and x, what can
you conclude about x?
i: x is greater than 5
ii: x is smaller than 5
iii: 5 is not a factor of x
iv: 5 is a factor of x
Solve. Write a mixed numeral for the answer.
Amy decided to bake bread and a cake. For the bread she needed 31
2 cups of flour. For the cake she
needed 12
3 cups of flour. She had 63
5 cups of flour. How much flour did she have left over?
Answer:
C
Explanation:
A)
B)
C)
D)
Multiply. Write a mixed numeral for the answer.
A recipe calls for 1
11 L of water and 8
11 L of milk. If the recipe is halved, how much liquid will be
needed?
Solve. Write a mixed numeral for the answer.
A photograph measuring 71
2 in. by 10 in. is put in a frame measuring 8 in. by 101
2 in. What is the
area of the border around the photo?
Add. Write a mixed numeral for the answer.
Estimate the value as a whole number or as a mixed numeral where the fractional part is 1
2.
Johanna has a 3
4–lb mixture of cashews and peanuts that includes 1
20 lb of cashews. How many
pounds of peanuts are in the mixture?
Estimate the fraction as 0, 1
2, or 1.
Estimate the value as a whole number or as a mixed numeral where the fractional part is 1
2.
Annie is packing for her trip to Hawaii. Her suitcase measures 262
3 in. ×171
4 in. ×91
5 in. Convert
262
3,171
4, and 91
5 to fraction notation.