Study Guide
Unit 3: Multiplication and Division
Chapter 1 - Examples of test questions:
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Fill in the blank with +, -, x, or division (%)
- 9 __ 8 = 1
- 9 __ 8 = 72
- 9 __ 8 = 17
- 72 __ 9 = 8
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Fill in the blank with the missing number
- 9 x ___ = 72
- 72 % 9 = ____
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Word problems
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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)
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Sam bought 7 cars for $100 each. He spent ____ altogether. (7 x $100 = $700)
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Write multiplication sentences for pictures
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If ten cars were shown (five in each row):
- 2 x 5 = 10
- 5 x 2 = 10
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If five cars were shown with four wheels each:
- Multiplication: 5 x 4 = 20 wheels
- Repeated addition: 4 + 4 + 4 + 4 + 4 = 20
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If ten cars were shown (five in each row):
Chapter 2 - Examples of test questions:
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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)
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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
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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
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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
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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
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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.
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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:
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Multiply in various ways:
- Multiply 42 by 4
- What is 56 x 1
- Find the product of 4,512 and 3
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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?
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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
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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
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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
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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:
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Quotient – the result of division
- 6 % 3 = 2
- the quotient is 2
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Remainder – whatever is “left over” in a division problem
- 9 % 2 = 4 R 1
- the remainder is 1
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Divide 80 by 6
- The quotient is ___ (13)
- The remainder is ___ (2)
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How would you check if the answer was correct?
- Step 1 - 6 x 13 = 78
- Step 2 - 78 + 2 = 80
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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)
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Be able to group items:
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Draw 28 pencils in 9 boxes.
- How many pencils are in each box? (3 pencils)
- How many pencils are left? (1 pencil)
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Divide 28 by 9
- Quotient = ______ (3)
- Remainder = ______ (1)
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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)
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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)
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Is there a remainder when you divide 27 by 9?
- No
- Show your work (draw 9 groups of 3 items)
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Draw 28 pencils in 9 boxes.
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How would you check if the answer to the following problem is correct?
- 28 % 9 = 3 R 1
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Show your work:
- Step 1 – 9 x 3 = 27
- Step 2 – 27 + 1 = 28
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Wanda has 65 ft. of material. She uses 9 ft. to make a blanket.
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How many blankets can she make?
- 65 % 9 = 7 R 2 (7 blankets)
- How much material will she have left? (2 ft.)
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How many blankets can she make?
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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:
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Long division asked in various ways
- 860 % 2 = ___
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Divide 860 by 2
- Quotient = ____
- Remainder = ____
- What is the Quotient when 860 is divided by 2?
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860 % 2 = 430
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Show how you would check this answer using multiplication
- 2 x 430 = 860
- Is the quotient correct? ____ (yes)
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Show how you would check this answer using multiplication
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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)
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There were 860 pencils. 6 pencils were put in each box. How many boxes were filled and how many pencils were left over?
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860 % 6 = 143 R 2
- ___ boxes were filled (143)
- ___ pencils were left over (2)
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860 % 6 = 143 R 2
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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
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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)
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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 1-3 Cumulative Test: Review all of Units 1 - 3