 # Math Unit 3

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)
• 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

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)
• How would you check if the answer to the following problem is correct?
• 28 % 9 = 3 R 1
• 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.)
• 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)
• 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 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 1-3 Cumulative Test: Review all of Units 1 - 3