Math Unit 4

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; 40-4 is equal to 36 so the second blank is 4)
- 7x7 is ___ more than 7x4 (7x7 is 49 and 7x4 is 28; 49-28 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) ($4,876-279=$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) ($600-468 = $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) (84-77 = 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 = ___
- 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)

42 6 7 1 7

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