Study Guide
Unit 3: Multiplication and Division
Chapter 1  Examples of test questions:

Fill in the blank with +, , x, or division (%)
 9 __ 8 = 1
 9 __ 8 = 72
 9 __ 8 = 17
 72 __ 9 = 8

Fill in the blank with the missing number
 9 x ___ = 72
 72 % 9 = ____

Word problems

Sam bought 7 cars for $100 each. He spent ____ altogether. (7 x $100 = $700)
 Be able to show your answer in repeated addition form: $100 + $100 + $100 + $100 + $100 + $100 + $100 = $700
 Sam counted 20 wheels on his cars. How many cars were there? (20 % 4 = 5 cars)
 There were 20 wheels on 5 of Sam’s cars. How many wheels were on each car? (20 % 5 = 4 wheels)

Sam bought 7 cars for $100 each. He spent ____ altogether. (7 x $100 = $700)

Write multiplication sentences for pictures

If ten cars were shown (five in each row):
 2 x 5 = 10
 5 x 2 = 10

If five cars were shown with four wheels each:
 Multiplication: 5 x 4 = 20 wheels
 Repeated addition: 4 + 4 + 4 + 4 + 4 = 20

If ten cars were shown (five in each row):
Chapter 2  Examples of test questions:

How many are there if:
 18 carrots are shared between 9 children. (18 % 9 = 2 carrots)
 Some carrots were shared between 9 children. Each received 2 carrots. (9 x 2 = 18 carrots)
 5 cakes. 5 candles on each cake. (5 x 5 = 25 candles)
 16 bicycle wheels were fixed. (16 % 2 = 8 bicycles)
 8 people paid for the bicycles to be fixed. Each person paid $9. What was the total cost? (8 x $9 = $72)
 Ellie and Mandy ate 7 cookies each. Sam ate 21 cookies. How many cookies were eaten altogether? (7 + 7 + 21 = 35 cookies)

Ellie ate 5 cookies. Mandy had 2 times as many as Ellie. Sam had 4 times as many as Mandy. How many did Sam eat?
 Step 1 – 2 x 5 = 10 cookies
 Step 2 – 4 x 10 = 40 cookies

Mandy ate 15 cookies. Ellie ate 9 fewer cookies than Mandy. Ellie ate 2 times as many cookies as Art. How many cookies did Art eat?
 Step 1 – 15 – 9 = 6 cookies
 Step 2 – 6 % 2 = 3 cookies

At the park there were 4 children. There were 4 times as many adults as children. How many more adults than children are there?
 Step 1 – 4 x 4 = 16 adults
 Step 2 – 16 – 4 = 12 more adults

There are 16 pillows on the couch. There are 3 times as many crocheted pillows as store bought. The mom brings home 4 more store bought pillows. How many store bought pillows are there now?
 Step 1 – 16 % 4 = 4 store bought pillows
 Step 2 – 4 + 4 = 8 store bought pillows

A block of swiss cheese weighed 3 lbs. A block of mozzarella cheese weighed 8 lbs. The cheddar cheese weighed twice the weight of both the swiss and mozzarella cheese. How much did the cheddar cheese weigh?
 Step 1 – 3 + 8 = 11 lbs.
 Step 2 – 2 x 11 lbs. = 22 lbs.

Sally was going to the amusement park 8 days in a row. She had $40 to spend.
 How much could she spend each day? ($40 % 8 = $5)
 One morning she spent $4. How much did she have left for the day? ($5  $4 = $1)
Chapter 3  Examples of test questions:

Multiply in various ways:
 Multiply 42 by 4
 What is 56 x 1
 Find the product of 4,512 and 3

Word problems:
 There are 7 hours in a school day. How many hours in 5 days?
 26 students each had 5 pencils. How many pencils are there in all?
 There are 4,523 pencils in one basket. How many pencils in 3 baskets?

Alex receives 24 baseball cards each week. Frank receives 5 more than Alex each week. How many does Frank have in 4 weeks?
 Step 1 – 24 + 5 = 29 baseball cards
 Step 2 – 4 x 29 = 116 baseball cards

Alex receives 224 baseball cards each week. Frank receives 25 less than Alex each week. How many baseball cards does Frank receive in 2 weeks?
 Step 1 – 224 – 25 = 199 baseball cards
 Step 2 – 2 x 199 = 398 baseball cards

Frank received 199 baseball cards. He received 25 less than Alex. Alex received the same number of baseball cards for 4 weeks. How many baseball cards did Alex receive altogether?
 Step 1 – 199 + 25 = 224 baseball cards
 Step 2 – 4 x 224 = 896 baseball cards

Sally sold 162 glasses of lemonade the first day. The second day she sold 7 times as many. On the third day she sold 934 fewer glasses than the second week. How many glasses did she sell in the third week?
 Step 1 – 7 x 162 = 1,134 glasses of lemonade
 Step 2 – 1,134 – 934 = 200 glasses of lemonade
 2,483
x 4
9,932
 Round 2,483 to the nearest hundred to check if the answer is reasonable. (2,500 x 4 = 10,000)
 Is the answer reasonable? (yes)
Chapter 4  Examples of test questions:

Quotient – the result of division
 6 % 3 = 2
 the quotient is 2

Remainder – whatever is “left over” in a division problem
 9 % 2 = 4 R 1
 the remainder is 1

Divide 80 by 6
 The quotient is ___ (13)
 The remainder is ___ (2)

How would you check if the answer was correct?
 Step 1  6 x 13 = 78
 Step 2  78 + 2 = 80

True or False:
 When 27 is divided by 9 the quotient is 3. (True)
 28 % 9 = 3 + 1 (False)
 For 28 % 9, the remainder is an odd number (True)

Be able to group items:

Draw 28 pencils in 9 boxes.
 How many pencils are in each box? (3 pencils)
 How many pencils are left? (1 pencil)

Divide 28 by 9
 Quotient = ______ (3)
 Remainder = ______ (1)

My mom has 23 flowers. She places 7 flowers in each vase. How many vases does she have?
 23 % 7 = 3 R 2 (She has 3 vases)

My mom has 23 flowers. She places them equally in three vases. She gives the remainder to me. How many flowers do I get?
 23 % 3 = 7 R 2 (I receive 2 flowers)

Is there a remainder when you divide 27 by 9?
 No
 Show your work (draw 9 groups of 3 items)

Draw 28 pencils in 9 boxes.

How would you check if the answer to the following problem is correct?
 28 % 9 = 3 R 1

Show your work:
 Step 1 – 9 x 3 = 27
 Step 2 – 27 + 1 = 28

Wanda has 65 ft. of material. She uses 9 ft. to make a blanket.

How many blankets can she make?
 65 % 9 = 7 R 2 (7 blankets)
 How much material will she have left? (2 ft.)

How many blankets can she make?

Wanda was paid $108 for 3 hours of sewing. She was given an equal amount for each hour of work and an extra $9 for a god job. How much did she get paid an hour?
 Step 1 – $108  $9 = $99
 Step 2  $99 % 3 = $33 an hour
Chapter 5  Examples of test questions:

Long division asked in various ways
 860 % 2 = ___

Divide 860 by 2
 Quotient = ____
 Remainder = ____
 What is the Quotient when 860 is divided by 2?

860 % 2 = 430

Show how you would check this answer using multiplication
 2 x 430 = 860
 Is the quotient correct? ____ (yes)

Show how you would check this answer using multiplication

Word problems
 860 people were in a building. There were 4 rooms. How many people were in each room? (215 people)
 There were 4 pencils in each box. There were 860 pencils. How many boxes are needed if all the pencils have to be put into boxes? (215 boxes)

There were 860 pencils. 6 pencils were put in each box. How many boxes were filled and how many pencils were left over?

860 % 6 = 143 R 2
 ___ boxes were filled (143)
 ___ pencils were left over (2)

860 % 6 = 143 R 2

860 pencils were put in 6 boxes. How many pencils are needed to that there will be an equal number of pencils in each box?
 Step 1  860 % 6 = 143 R 2
 Step 2 – 860 – 2 = 858 pencils are needed

There were 234 pens. There were 45 more pencils than pens. The pencils were put into 6 groups. How many groups of pencils were there?
 Step 1 – 234 + 45 = 279 pencils
 Step 2 – 279 % 6 = 46 R 3 (There were 46 groups of pencils)

Arnold has 234 pens. He has 34 more pens than Ester. Ester has twice as much as Zane. How many pens does Zane have?
 Step 1 – 234 – 34 = 200 pens
 Step 2 – 200 % 2 = 100 pens
Units 13 Cumulative Test: Review all of Units 1  3