Prime Factorization
Find the prime Factorization of the following:
1. 21
3x7
2. 130 2 x 5 x 13
3. 84
2x2x3x7
The Combination for the lock on Jacoby’s
suitcase is based on the prime factorization of
315. What is the combination?
a. 5 x 7 x 9
b. 3 x 7 x 15
c. 3 x 3 x 5 x 7
d. 2 x 3 x 3 x 5 x 7
c. 3 x 3 x 5 x 7
Chris left out one prime factor when he wrote
this prime factorization for 168.
2x2x2x3x
What is the missing prime factor?
a.
b.
c.
d.
2
3
5
7
7
Logan left out one prime factor when she
wrote this prime factorization for 1092.
2 x 2 x x 7 x 13
What is the missing prime factor?
a.
b.
c.
d.
2
3
7
13
3
The combination lock is a 3-digit number. The
digits are the prime factors of 42 listed from
greatest to least. What is the combination for
the lock?
7-3-2
What are the first 10 multiples for 4?
4,8,12,16,20,24,28,32,36,40
What are the first 10 multiples for 10?
10,20,30,40,50,60,70,80,90,100
What numbers appear in both lists?
What is the Least Common Mutliple?
20
20 and 40
Find the Least Common Multiple for each set of
numbers:
1. 5 and 20
2. 6 and 15
20
30
3. 12 and 30 60
Mark purchases materials to make watches for a
jewelry show. There were 6 watch faces in a pack
and 9 watch bands in a pack. What is the least
number of watches Mark can make without having
any supplies left over?
Kaley purchases materials to make dog collars for a
pet show. There are 6 buckles in a pack and 8
straps in a pack. What is the least number of dog
collars Kaley can make without having any supplies
left over?
Penc ils are sold in packages of 10, and erasers are
sold in packages of 6. What is the least number of
pencils and erasers you can buy so that there is one
pencil for each eraser with none left over?
Greatest Common Factor
• Find the Greatest Common Factor for each
pair of numbers:
1. 18 and 45 9
2. 33 and 66
33
3. 72 and 96
24
Distributive Property
• Use the GCF and Distributive property to
express the sum as a product.
6(3 + 4)
1. 18 +24
2. 15 +75
15 x (1 + 5)
3. 36 + 54
18 x (2 +3)
Trystan has 56 roses and 42 daises to use in floral
centerpieces for a party. Each centerpiece will have
the same number of flowers and will contain only
roses or only daisies. What is the greatest number
of flowers that Trystan can use in each centerpiece?
There are 24 sixth graders and 40 seventh graders.
Mr. Evans wants to divide both grades into groups of
equal size, with the greatest possible number of
students in each group. How many students should
be in each group?
Jacob is putting 18 nonfiction and 30 fiction books
on the bookshelves. Each shelf will have only fiction
or only nonfiction, and every shelf will have the
same number of books. What is the greatest
number of books for each shelf, and how many
shelves will be there for each type of book.
Decimals
Find the sum or the difference.
1. 62.38 + 26.92
2. 48.28 – 9.41
3. 81.04 + 52 + 16.44
4. 27.29 – 19.39
5. 743.5 – 462.87
6. 98.01 + 52.003
7. 74.9 – 16.227
8. (235.152 + 77.12) – 46.326
Find the product
1) 8.6 x 4.1
2) 12.8 x 2.21
3) $8.65 x 9.2
4) Maria works 24.5 hours each week at a
bookstore. She earns $8.76 per hour. How much
does Maria earn each week?
5) A camera costs 115 Canadian dollars. If the
Canadian dollar is worth 0.952 U.S. dollars, how
much will the camera cost in U.S. dollars?
Find the quotient.
1)
2)
3)
4)
5)
3.78 ÷ 6 =
92.8 ÷ 16 =
1.725 ÷ 5 =
135.3 ÷ 11=
O’Darion’s kitchen sink has leaked
36.054 liters of water during the past 6
months. What is the average amount of
water leaked each month?
Find the quotient.
1) 9.176 ÷ 0.62=
2) 21.05 ÷ 0.2 =
3) 145.7 ÷ 2.71 =
4) 18.62 ÷ 0.02 =
5) Adrian wants to buy a new MP3 player that
cost $76.50. If he saves $8.50 each week, how
many weeks will it take Adrian to save enough
money to buy the MP3 player?
Ratios
Write the ratio of triangles to squares.
Make a model of the ratio 5:1.
Complete the table.
1 table for every 5 students
Students
Tables
5
1
15
2
4
There are four quarts in 1 gallon. How
many quarts are in 3 gallons?
12
At Fabric World, ribbon is sold at a rate
of $2 for 1 Yard. What would 8 yards of
fabric cost?
$16
Andre purchased 1 quart of lemonade from a
concession stand for $1.50. Which shows the rate
for 6 quarts of lemonade?
$0.25
𝑎.
6 𝑞𝑢𝑎𝑟𝑡𝑠
$1.50
𝑏.
1 𝑞𝑢𝑎𝑟𝑡
$7.50
𝑐.
1 𝑞𝑢𝑎𝑟𝑡
$9.00
𝑑.
6 𝑞𝑢𝑎𝑟𝑡𝑠
Cameron can buy 20 pens for $1.60 or 25
pens for $2.25. Find the unit rate for each
and decide which is the better buy.
David used the grocery store ads to list apple
prices at 4 stores.
Gordon’s 4 pounds for $3.32
Greenwise: 2 pounds for $1.62
PJ’s: 3 pounds for $2.37
Tosko: 5 pounds for$4.50
Which stores charges the least amount per
pound?
Write 2 ratios equivalent to
5
.
9
Sharon takes a 6-minute break after every 24
minutes of study. Ben takes an 8 minute break
after every 32 minutes of study. Are their ratios
of study time to break time equivalent?
Find the unknown value.
4
?
1. =
2.
5
24
27
20
?
=
9
3. Sophie can make 3 loaves of bread with 7 cups
of flour. How many loaves of bread can be she
make with 21 cups of flour?
4. Honeybees produce 7 pounds of honey for
every 1 pound of beeswax they produce. Use
equivalent ratios to find how many pounds of
honey are produced when 25 pounds of
beeswax are produced.
Joseph takes a trip on a train that travels at a
rate of 95 miles per hour. Which set of ordered
pairs represents the trains distance over time?
A.
B.
C.
D.
(1,95); (2,96); (3,97); (4,98)
(1,95); (1,190); (1, 285); (1,380)
(1,95); (2,95); (3,95); (4,95)
(1,95); (2,190); (3,285); (4,380)
To stay properly hydrated a person should drink
32 fluid ounces of water for every 60 minutes of
exercise. How much water should Damon drink
if he rides his bike for 135 minutes ?
Percents
How can you model 19%?
What ratio represents the shaded part?
What decimal represents the shaded part?
Write each percent as a decimal and as a fraction in
simplest terms.
1) 75%
2) 38%
3) 0.9%
4) 234%
Write the decimal or fraction as a percent.
1) .45
2) 0.6
3)
7
8
4) 0.03
5)
51
10
Find the percent of the quantity.
1) Find 8% of 90.
2) Find 0.25% of 120.
3) Find 155% of 30.
4) In a crate of 1,500 light bulbs, it is estimated that 4% are
defective. How many of the 1,500 light bulbs in the
crate are likely defective?
5) The recommended daily amount of vitamin C for
children 9 to 13 years old is 45 mg. A serving of juice
contains 60 % of the recommended amount. How
At a deli, 56 sandwiches were sold during lunchtime. 25%
of the sandwiches sold were tuna salad sandwiches. How
many of the sandwiches sold were not tuna salad?
Jaqueline has 80 books in her collection. If 60% of the
books are fiction, how many of the books are non fiction?
Find the unknown value.
1) 12 is 40% of __________.
2) 36 is 90% of __________.
3) Michaela is hiking on a weekend camping trip. She has
walked 6 miles so far. This is 30 % of the total distance.
What is the total number of miles she will walk?
Conversions
1. Convert 4.5 miles to yards.
2. Convert 48 inches to feet.
3. 0.8 hectometers = _________millimeters
4. 45 centimeters = ______________ dekameters
1. Convert 0.72 kiloliters to deciliters.
2. 52 liters = _____________ hectoliters
3. 78 quarts= ____________ gal =___________ qt
4. 5 pints = ____________ cups =_____________ oz
1. 43.2 dg = _______________ hg
2. 3.5 grams = _____________ milligrams
3. 4,500 pounds = _____________ Tons
4. 3 pounds = _____________ ounces
5. Maggie bought 52 ounces of swordfish selling for
$6.92 per pound. What was the total cost?
1. Green grapes are on sale for $2.50 a pound. How
much will 9 pounds cost?
2. A car travels 32 miles for each gallon of gas. How
many gallons of gas does it need to travel 192
miles?
3. Sammy is riding a raft down a stream that is
moving at a rate of 75 feet per minute. How far
down stream does she travel in 5 minutes?
1
142
2
4. Anaelle drove
miles at a rate of 57 miles per
hour. For how long was Anaelle driving?
Draw the model to find the quotient:
Take the shaded part and split it into 2 equal parts.
Each part is now
1
.
8
1
4
÷ 2.
Draw the model to find the quotient:
Take the shaded part and split it into 4 equal parts.
Each part is now
1
.
6
2
3
÷ 4.
Draw the model to find the quotient:
Start with
1
3
2
1
÷ .
6
1
3 .
2
We need 𝑤ℎ𝑒𝑟𝑒 6 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒𝑠 𝑒𝑞𝑢𝑎𝑙 1 ℎ𝑒𝑥𝑎𝑔𝑜𝑛.
Now count the number of triangles you have.
21
Find the quotient.
1.
3
4
2.
1
4
2
÷
1
1
2
÷
3
1
4
3. 24÷
2
2
3
4.
7
3
8
÷4
A branch measuring
7
8 𝑓𝑒𝑒𝑡 𝑤𝑎𝑠 𝑐𝑢𝑡 𝑓𝑟𝑜𝑚 𝑎 𝑡𝑟𝑒𝑒. 𝐴𝑛𝑛𝑖𝑒 𝑚𝑎𝑑𝑒
8
3
2
𝑤𝑎𝑙𝑘𝑖𝑛𝑔 𝑠𝑡𝑖𝑐𝑘𝑠 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑏𝑟𝑎𝑛𝑐ℎ.
16
1
𝑆ℎ𝑒 𝑑𝑖𝑠𝑐𝑎𝑟𝑑𝑒𝑑 𝑓𝑜𝑜𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑏𝑟𝑎𝑛𝑐ℎ.
8
𝐻𝑜𝑤 𝑚𝑎𝑛𝑦 𝑤𝑎𝑙𝑘𝑖𝑛𝑔 𝑠𝑡𝑖𝑐𝑘𝑠 𝑑𝑖𝑑 𝑠ℎ𝑒 𝑚𝑎𝑘𝑒
𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑏𝑟𝑎𝑛𝑐ℎ?
Multiplying Fractions
Find the Product.
1)
2)
3
1
𝑥
4
5
4
5
=
1
+
3
𝑥
5
9
=
3) Mr. Carly had a gas can with
1
4
1
4
4
gallons of
gasoline in it. He used of the amount in the
can to mow his lawn. How many gallons did Mr.
Carly use to mow his lawn?
3
1
4) 4 𝑥 1 =
5
8
Exponents
Write as an expression using equal factors. Then find the
value.
34
53
85
107
5. John is making a patio in his yard. He needs a total of 15
squared concrete blocks to cover the area. How many
blocks does John need?
1.
2.
3.
4.
Order of Operations
Evaluate each expression.
1)82 − 72 + 1
2) 5 − 22 + 12 ÷ 4
3) (80-15÷3)÷52
4) 8 x (16 - 24 )
Algebraic Expressions
Write an algebraic expression for the word
expression.
1. b divided by 9
2. d decreased by 29
3. 8 times g
4. 2 less than the quotient of d and 16
5. Let h represent Jake’s height in inches. Heather
is 7 inches shorter than Jake. Write an algebraic
expression that represents Heather’s height.
Evaluate the expression for x =3,2,1, and 0
1) 13 + 6x
2) 2x + 3 + 𝑥 2
Evaluate the expression for the given value of the
variables.
1) 7x + y + 16 for x=2, y=3
2) 12b – 2c + 3 for b=5, c=10
3) The formula P= 2l + 2w gives the perimeter(p) of a
rectangular room with length (l) and width (w). A
rectangular living room is 26 feet long and 21 feet
wide. What is the perimeter of the room?
Combining like Terms
Tereza sells produce in boxes at a Farmer’s market.
She put 6 ears of corn and 9 tomatoes in each box.
The expression 6b +9b represents the total pieces of
produce in b boxes. Simplify this expression by
combining the like terms.
Jackets cost $15 and a set of decorative buttons cost
$5. The delivery fee is $5 per order. The expression
15n +5n + 5 gives the cost in dollars, of buying
jackets with buttons for n people. Which is another
way to write this expression?
Simplify:
1) 7x + 2x + 5x
2) 9c – 6 + c
3) 3(m + 7)
4) 8(4n -2n)
Are the two expressions equivalent:
5) 6(p + q) and 6p + q
6) 7y – 15 + 2y and 9y - 15
Determine if the statement is true.
1) m ≥ 4 if m = 2
2) Y ≤ 3 if y = 6
False
false
3) Give two solutions for this inequality: v ≥ 9.
4) In the town of Big Hill, there is an average of 16
sunny days each month. Write an expression to
represent the number of sunny days for any
number of months. Then identify what the
16s where “s”
variable represents.
equals the number
of months
Write the equation for each word sentence.
1) 18 more than a number is 29
2) The product of a number and 6 is 138.
3) Four fifths of a number is 11
4) An ostrich egg weighs 2.9 pounds. The
difference between the weight of this egg and
the weight of an emu egg is 1.6 pounds.
Write an equation that could be used to find
the weight w, in pounds, of an emu egg.
Solve and check.
1) X + 13 = 27
2) 38 = d – 22
3) w -
3
2
5
=
4) 4x = 12
5)
𝑑
4
=5
2
4
5
Solve and check.
6)
4
𝑘
5
= 12
7) 1.5w = 12
8) Haley runs 6 laps on a track. She runs a total
of 1 mile or 5,280 feet. Write and solve an
equation to find the distance, in feet, she runs
each lap.
Solve and check.
9)
3
Alyssa’s cat weighs 12 pounds, which is of
8
3
the weight of her dog. Use the equation 𝑑
8
=
12 to find the weight of Alyssa’s dog.
10) Jana paid $12 for a shirt that was on sale.
1
The sale price of the shirt was of the original
1
𝑝
3
3
price p. The equation
= 12 can be used to
find the original price of the shirt. What is the
original price of the shirt?
An IPOD can store less than 240 songs. Which inequality
represents the possible number of songs s the IPOD can
store?
a. S ≥ 240
b. S ≤ 240
c. S > 240
d. S < 240
A ship can carry no more than 6 tons of cargo. Which
inequality represents the number of tons t that the ship
can carry?
a. t< 6
b. t> 6
c. t ≤ 6
d. t ≥ 6
Graph the inequality.
1) k< 8
2) r ≥ 6
Write the inequality shown by
each graph.
-5
-4
-4
-3
-3
-2
-3
-1
0
-2
1
2
-1
3
4
5
0
6
7
1
8
9
23