Prime Factorization

Prime Factorization

Find the prime Factorization of the following:

1. 21

2. 130

3. 84

3 x 7

2 x 5 x 13

2 x 2 x 3 x 7

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.

2 x 2 x 2 x 3 x What is the missing prime factor?

a. 2b. 3c. 5d. 7

7

Logan left out one prime factor when she wrote this prime factorization for 1092.

2 x 2 x x 7 x 13What is the missing prime factor?

a. 2b. 3c. 7d. 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? 20 and 40

What is the Least Common Mutliple?

20

Find the Least Common Multiple for each set of numbers:

1. 5 and 20

2. 6 and 15

3. 12 and 30

20

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

2. 33 and 66

3. 72 and 96

9

33

24

Distributive Property

• Use the GCF and Distributive property to express the sum as a product.

1. 18 +24

2. 15 +75

3. 36 + 54

6(3 + 4)

15 x (1 + 5)

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) 3.78 ÷ 6 =2) 92.8 ÷ 16 =3) 1.725 ÷ 5 =4) 135.3 ÷ 11=5) 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 5 15Tables 1 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?

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 $3.32Greenwise: 2 pounds for $1.62PJ’s: 3 pounds for $2.37Tosko: 5 pounds for$4.50

Which stores charges the least amount per pound?

Write 2 ratios equivalent to

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.

1. 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?

2. 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. (1,95); (2,96); (3,97); (4,98)B. (1,95); (1,190); (1, 285); (1,380)C. (1,95); (2,95); (3,95); (4,95)D. (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) 0.03

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 much vitamin C does the juice drink have?

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?

4. Anaelle drove 142 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

Draw the model to find the quotient:

Take the shaded part and split it into 4 equal parts.

Each part is now

Draw the model to find the quotient:

Start with

W

N

2

Find the quotient.

1. 4

2. 24

3. 3

A branch measuring

Multiplying Fractions

Find the Product.

1) Mr. Carly had a gas can with 4gallons 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?

2) =

Exponents

Write as an expression using equal factors. Then find the value.

1. 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?

Order of Operations

Evaluate each expression.

1)

2) (80-15÷3)÷

3) 8 x (16 -

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 +

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 + q6) 7y – 15 + 2y and 9y - 15

Determine if the statement is true.

1) m ≥ 4 if m = 2

2) Y ≤ 3 if y = 6

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 variable represents. 16s where “s”

equals the number of months

False

false

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 - 2

4) 4x = 12

Solve and check.

6) 1.5w = 12

7) 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) Alyssa’s cat weighs 12 pounds, which is of the weight of her dog. Use the equation to find the weight of Alyssa’s dog.

10) Jana paid $12 for a shirt that was on sale. The sale price of the shirt was of the original price p. The equation 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 ≥ 240b. S ≤ 240c. S > 240d. 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< 6b. t> 6c. t ≤ 6d. t ≥ 6

Graph the inequality.

1) k< 8

2) r ≥ 6

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

-4 -3 -3 -2 -1 0 1 23

Write the inequality shown by each graph.