Download Copyright © 2014 Edmentum -- All rights reser. Properties of

Copyright © 2014 Edmentum -- All rights reser.
Properties of Multiplication and Division
1.
5×?=
35
Use the multiplication sentence above to solve the division sentence below.
35 ÷ 5
=?
A. 5
B. 35
C. 7
D. 12
2.
?×2=
4
Use the multiplication sentence above to solve the division sentence below.
4÷2=
?
A. 4
B. 2
C. 3
D. 1
3. The picture below shows three rows of five hearts.
Which of the following shows the same number of hearts as the picture above?
W.
A. X
B. Y
C. Z
D. W
X.
Y.
Z.
4. Kelly bought two boxes of roasted walnuts. Each box had six bags tied with a ribbon in it, and within each bag
was eight roasted walnuts. Kelly and Sam tried to quickly determine how many walnuts Kelly bought.
Sam solved the problem using (2 × 6) × 8. Kelly found the same answer as Sam, but set it up differently.
Which expression below could be Kelly's expression?A. 2 × (6 + 8)
B. (2 + 6) + 8
C. (2 + 6) × 8
D. 2 × (6 × 8)
5. Directions: Write the correct answer in each box. Use numerals instead of words.
Use properties of multiplication to find the missing numbers below.
16 × 12 = 192
12 × 16 =
× 13 = 221
13 × 17 = 221
24 × 15 = 360
18 × 19 = 342
15 ×
= 360
19 × 18 =
6. Directions: Select all the correct answers.
Which expressions below are equal to each other?
(3 + 4) + 2
3 + (4 × 2)
(3 × 4) + 2
3 × (4 + 2)
(3 × 4) × 2
3 × (4 × 2)
7. Directions: Write the correct answer in each box. Use numerals instead of words.
Find the missing numbers in the multiplication and division sentences below.
6×
= 42
× 4 = 36
42 ÷ 6 =
36 ÷ 4 =
8.
Use the fact family triangle above to determine the number that makes all of the number sentences below true.
9 × 3=
÷ 9= 3
A. 9
B. 30
C. 27
D. 24
9.
(4 × 1) × 5 = ?
A. 4 × (1 × 5)
B. 4 × (5 × 5)
C. (4 × 4) × 5
D. (5 × 1) × 5
3 × 9=
÷ 3= 9
Answers
1. C
2. B
3. B
4. D
5. ---6. ---7. ---8. C
9. A
Explanations
5×3=?
1. Find the number that makes 35 when multiplied by 5.
5 × ? = 35
?=7
Multiplication and division are opposite operations. The multiplication sentence, 5 × 7 = 35, can be used to solve
the division sentence below.
35 ÷ 5 = 7
2. Find the number that makes 4 when multiplied by 2.
?×2=4
?=2
Multiplication and division are opposite operations. The multiplication sentence, 2 × 2 = 4, can be used to solve the
division sentence below.
4÷2=2
3. The commutative property says that the order in which two numbers are multiplied does not matter. This means
that three rows of five hearts are equal to five rows of three hearts.
=
three rows of five
3 × 5 = 15
five rows of three
5 × 3 = 15
The correct answer is Y.
4. The associative property of multiplication says that numbers can be grouped and multiplied in any way without
changing the answer.
Sam solved the problem using (2 × 6) × 8. Since Kelly set up her expression differently from Sam, but she found
the same answer, Kelly's expression could be 2 × (6 × 8).
5.
The commutative property of multiplication says that you can change the order of the numbers without changing
the answer.
6.
The associative property of multiplication says that numbers can be grouped to multiply in any way without
changing the answer.
3 × (4 × 2) = (3 × 4) × 2
7.
Multiplication and division are opposite operations. These number sentences are parts of fact families.
Since multiplication and division are opposite operations, the number sentence 6 × 7 = 42 can be used to solve
42 ÷ 6 = 7, and 9 × 4 = 36 can be used to solve 36 ÷ 4 = 9.
8. A fact family triangle shows the relationships between multiplication and division. The fact family triangle below
shows how the numbers 3, 9, and 27 are related.
9 × 3 = 27
3 × 9 = 27
27 ÷ 9 = 3
27 ÷ 3 = 9
The number 27 makes all of the number sentences true.
9. The associative property of multiplication says that numbers can be grouped in any way without changing the
answer.
So, (4 × 1) × 5 = 4 × (1 × 5).
10. The commutative property of multiplication says that you can change the order of the numbers involved without
changing the answer.
So, 5 × 3 = 3 × 5.