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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
    • 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.)
  • 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

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