Study Guide
Unit 4: Multiplying Tables of 6, 7, 8, and 9
Chapter 1 Examples of test questions:
 Have all 6, 7, 8, and 9 multiplication (and division) problems memorized.

Be able to answer multiplication and division problems in various ways:
 ___ x 9 = 54
 What is 8 x 6?
 63 % 9 =
 Divide 49 by 7.

Write two multiplication sentences for a picture. For example, if there were 20 objects, example sentences would be:
 2x10=20
 10x2=20
 1x20=20
 20x1=20
 4x4=20
 5x4=20
 4x9 = 40__ = ___ (if four times nine is 36, the final blank is 36; 404 is equal to 36 so the second blank is 4)
 7x7 is ___ more than 7x4 (7x7 is 49 and 7x4 is 28; 4928 is 21, so the blank is 21)
 There are 63 eggs put equally in 7 bowls. How many eggs are there in each bowl?
 Multiply 437 by 8.
 What is 527 x 9? (4,743) Also be able to use estimation to see if an answer is reasonable. (500x10 = 5,000)
 Be able to do long division with remainders.
 What is the remainder when you divide 741 by 7?
 How would you check if the following is correct? 357 % 7 = 51 (you would show your work by multiplying 51x7)

Two step word problems:
 Alex has $4,876. He gives $31 to each of his 9 family members. How much does he have left? ($31x9 = $279) ($4,876279=$4,597)
 There are 357 apples and oranges altogether. There are 6 times as many apples as oranges. How many oranges are there? (If there are 6 times as many apples as oranges, you need 7 equal groups. Divide the total number by 7 to find out how many oranges there are: 357 % 7 = 51 oranges)
Chapter 2  Examples of test questions:
 Patterns: 6, 12, 18, ___, 30, ___, 42, 48, 54, ____

See examples in Chapter 1:
 Write two multiplication sentences for a picture
 Be able to answer multiplication and division problems in various ways
 How would you check if a division problem was correct?
 How many days are there in 9 weeks?
 The store sold 584 items each day. How many items were sold in a week?

Two step problems:
 7,358 carrots were placed in bags of 9. How many bags were needed? How many carrots were left?
 There are 18 balloons in 3 bags. Each balloon cost $7. How much does a bag of balloons cost? (18%3=6 balloons in each bag) (6x$7=$42 a bag)
 9 boxes cost $558. How much do 6 such boxes cost? ($558%9 = $62) ($62x6 = $372)
 There are 558 people in the store. There are 8 times as many women as men. How many men are there? (If there are 8 times as many women as men, you need 9 equal groups. Divide the total number by 9 to find out how many men there are)
Chapter 3  Examples of test questions:

Patterns: be able to use variable – instead of having blanks to fill in, there will be letters of the alphabet.
 2, 4, 6, A, 8, 10, 12, 14
 6, 12, 18, 24, 30, B, 42, 48, 54,
 A is ____
 B is ____

There will be a picture of objects broken into groups. Be able to write both multiplication and division sentences. If there were 72 objects in 8 groups:
 8x9=72
 72%8=9
 Write 8x9 as a repeated addition sentence. (8+8+8+8+8+8+8+8+8=72)
 Long division problems with remainders.

<, >, =
 558 % 9 ___ 6x8 (558%9 is 62) (6x8 is 48) (62 > 48)
 Sherry ate 4 strawberries in a day. She ate the same number of strawberries each day for 9 days. How many strawberries did she eat in all?
 Find an answer and use estimation to check if an answer is reasonable. 42x7=____ (294) (Estimation: 40x10=400)

How would you check if a division problem was correct? (multiply the two smaller numbers to see if it equals the larger number)
 6,712 % 7 = _______ (the answer is 958 R6; to check the problem, multiply 958 by 7 and add the remainder)
 Each week Eric has $62 left over after he paid his bills. How much will he have after 9 weeks?

Two Step Problems:
 Marsha purchased 52 baskets for $9 a piece. She paid $600. How much does she have left? (52x$9 = $468) ($600468 = $132)
 504 liters of soda were being poured into 6 smaller containers. Sally asked for her container to have only 77 liters. How many liters were left in Sally’s container? (504 % 6 = 84 liters in each smaller container) (8477 = 7 liters)
 Alice asked for 4,074 yards of cloth. 7 yards cost $6. How much did she pay? (4,074%7 yards = 582 yards) (582 x $6 = $3,492)
 The cloth cost $3,492. Alice paid $401 every month for 6 months. How much more will she have to pay after 6 months? ($401x6 = $2,406) ($3,492  $2,406 = $1,086)
Chapter 4  Examples of test questions:

See examples in Chapter 1:
 Write multiplication sentences for a picture
 Estimate the value of multiplication problems

Be able to answer multiplication and division problems in various ways

Fill in missing numbers
 6x7 = 84  ___ = _____
 6x__ = 84
 84%6 = ___

Fill in missing numbers
 How would you check if a division problem was correct?
 Find the missing number. (the center number multiplied by the number next to it equals the number on the outside: 7x1=7, 7x3=21, 7x6=42, 7x5=?) (the answer would be 35)
?
5
42 6 7 1 7
3
21

When dividing know the difference between quotient and remainder.
 6,712 % 7 = _______ (the quotient is 958) (the remainder is 6)

Multistep problems:
 There are 7 baskets. In each basket are 12 chocolates and 3 more fruit than chocolates. How many items altogether? (Fruit: 12+3=15) (Items in the basket: 12+15=27) (27x7=189 items altogether)
 In the basket are 12 chocolates and 15 fruit. Each chocolate costs $5 and a piece of fruit costs $4. How much does the basket cost? (12x$5 = $60) (15x4 = $60) ($60+$60=$120)
 Art painted 432 portraits and 390 landscapes. He sold each painting for 7 cents each. How much did he get if he sold all the paintings? (432+390=822 paintings) (822x7cents = 5,754 cents)
 A ticket to Valley Fair costs 9 times as much as a meal. The meal costs 4 times as much as the beverage. If a ticket to Valley Fair costs $72, how much does the beverage cost? ($72%9 = $8) ($8%4 = $2 for a beverage)

When dividing a word problem, you many need to take into account a remainder:
 The ride at Valley Fair could hold 8 people, and there were 692 people in line. How many trips would the ride have to take so that all the people could have a turn? (692%8 = 86 R5) (It would need to take 87 trips even though the last trip would have only 5 people)
Chapter 5  Examples of test questions:

Write a multiplication sentences for a picture:
 There are 5 groups. In each group are 4 rows of 6 items. ___ x ___ x ___ = ___ (4 rows x 6 items equals 24) (24 items x 5 groups = 120) (4 x 6 x 5 = 120)

Fill in the blanks:
 12 x 8 x 2 = ____ x 2 = _____ (12x8 = 96) (96x2 = 192) (the first blank would be 96 and the second blank 192)

When multiplying multiple numbers, a mathematical rule is to go left to right.
 45 x 6 x 3 = ___ (start with 45x6=270) (then multiply with the next number 270x3=810)
 If 45 x 6 x 3 = 810, what is 3 x 45 x 6? ____ (3x45=135) (135x6=810)

Division problems asked in various ways:
 20,000 % 4 = ______
 20 hundreds divided by 5 ____

Estimate the value of 507 % 6.
 ____ % 6 = _____ (507 rounds to 500) (on the first blank write 500) (500%6=83R2) (on the second blank write 83 R2)
 507%6 is about ___. (on the blank write 83: the remainder would round down)
 When given three division problems and an estimated problem, be able to circle the problem that was estimated.

Multistep problems:
 There are 53 small marbles and 6 times as many large marbles. How many marbles in all?
 9 TVs were selling for $54,918. Estimate the cost of each TV. How many TVs could be purchased for $12,742? (Divide 54,918 by 9 and get 6,102 and round that to $6,000) (If each TV costs approximately $12,742, then 2 TVs could be purchased)

There are 120 swings. There are 3 times as many children as swings. How many children are there? (120x3 = 360 children)
 The children were put into groups of 7. Estimate the number of groups formed. (360%7=51 R3) (Estimate: 50 groups)
Unit 4 Cumulative Test:
 Review all of Units 1  4