PROPERTIES OF ADDITION AND MULTIPLICATION WORKSHEET

Simplify each expression. 

Problem 1 : 

35 + 43 + 65

Problem 2 : 

4 ⋅ 7 ⋅ 25

Problem 3 : 

15⅓ + 4 + 1⅔

Problem 4 : 

8 ⋅ 5 ⋅ 3/2

Problem 5 : 

410 + 58 + 90 + 2

Problem 6 : 

2.5 ⋅ 3 ⋅ 4 ⋅ 6

Problem 7 : 

7/3 + 4/5 + 2/3

Problem 8 : 

5/6 ⋅ 2/7 ⋅ 9/10 ⋅ 21/8

Detailed Answer Key

Problem 1 : 

35 + 43 + 65

Solution : 

=  35 + 43 + 65

Use the Commutative Property of Addition.

=  (35 + 65) + 43

Use the Associative Property of Addition to make groups of compatible numbers.

=  100 + 43

=  143

Problem 2 : 

4 ⋅ 7 ⋅ 25

Solution : 

=  4 ⋅ 7 ⋅ 25

Use the Commutative Property of Multiplication.

=  7 ⋅ 4 ⋅ 25

Use the Associative Property of Multiplication to make groups of compatible numbers.

=  7 ⋅ (4 ⋅ 25)

=  7 ⋅ 100

=  700

Problem 3 : 

15⅓ + 4 + 1⅔

Solution : 

=  15⅓ + 4 + 1⅔

Use the Commutative Property of Addition.

=  15⅓ + 1⅔ + 4

Use the Associative Property of Addition to make groups of compatible numbers.

=  (15⅓ + 1⅔) + 4

=  (46/3 + 5/3) + 4

=  51/3 + 4

=  17 + 4

=  21

Problem 4 : 

8 ⋅ 5 ⋅ 3/2

Solution : 

=   8 ⋅ 5 ⋅ 3/2

Use the Commutative Property of Multiplication.

=  5 ⋅ 8 ⋅ 3/2

Use the Associative Property of Multiplication to make groups of compatible numbers.

=  5 ⋅ (8 ⋅ 3/2)

Simplify 8 and 2 using 2 times table. 

=  5 ⋅ (4 ⋅ 3/1)

=  5 ⋅ 12

=  60

Problem 5 : 

410 + 58 + 90 + 2

Solution : 

=   410 + 58 + 90 + 2

Use the Commutative Property of Addition.

=  410 + 90 + 58 + 2

Use the Associative Property of Addition to make groups of compatible numbers.

=  (410 + 90) + (58 + 2)

=  500 + 60

=  560

Problem 6 : 

2.5 ⋅ 3 ⋅ 4 ⋅ 6

Solution : 

=   2.5 ⋅ 3 ⋅ 4 ⋅ 6

Use the Commutative Property of Multiplication.

=   2.5 ⋅ 4 ⋅ 3 ⋅ 6

Use the Associative Property of Multiplication to make groups of compatible numbers.

=  (2.5 ⋅ 4) ⋅ (3 ⋅ 6)

 =  10 + 18

=  28

Problem 7 : 

7/3 + 4/5 + 2/3

Solution : 

=  7/3 + 4/5 + 2/3

Use the Commutative Property of Addition.

=  7/3 + 2/3 + 4/5

Use the Associative Property of Addition to make groups of compatible numbers.

=  (7/3 + 2/3) + 4/5

=  (7 + 2)/3 + 4/5

=  9/3 + 4/5

Least common multiple of (3, 5) = 15.

=  45/15 + 12/15

=  (45 + 12)/15

=  57/15

=  19/5

=  3⅘

Problem 8 : 

5/6 ⋅ 2/7 ⋅ 9/10 ⋅ 21/8

Solution : 

=  5/6 ⋅ 2/7 ⋅ 9/10 ⋅ 21/8

Use the Commutative Property of Addition.

=  5/6 ⋅ 9/10 ⋅ 2/7 ⋅ 21/8

Use the Associative Property of Addition to make groups of compatible numbers.

=  (5/6 ⋅ 9/10) ⋅ (2/7 ⋅ 21/8)

Simplify using times table. 

=  (1/2 ⋅ 3/2) ⋅ (1/1 ⋅ 3/4)

=  3/4 ⋅ 3/4

=  (3 ⋅ 3) / (4 ⋅ 4)

=  9/16

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