Properties of Multiplication
Properties of Multiplication
You can use the properties of multiplication to evaluate expressions.
Commutative Property
Changing the order of factors does not change their product.
Example:
a x b = b x a
4 x 20 = 20 x 4
Associative Property
Changing the grouping of factors does not change their product.
Example:
a x (b x c) = (a x b) x c
4 x (5 x 8) = (4 x 5) x 8
Identity Property
The product of any number and 1 is that number.
Example:
z x 1 = z and 1 x z = z
35 x 1 = 35 and 1 x 35 = 35
Zero Property
The product of any number and 0 is 0.
Example:
r x 0 = 0 and 0 x r = 0
12 x 0 = 0 and 0 x 12 = 0
Distributive Property
The product of a factor and a sum (or difference) equals the sum (or difference) of the product.
Example:
a x (b + c) = (a x b) + (a x c)
8 x (20 + 4) = (8 x 20) + (8 x 4)
TIP
Use the Distributive Property to make problems easier to solve:
(5 x 6) + (5 x 4) =
5 x (6 + 4) =
5 x 10 = 50
Guided Practice (Ask your tutor for help.)
Fill in the blank in each multiplication problem, and identify its property on the line below.
1. 45 x ____ = 45
_______________ Property
2. 6 x 65 x ____ = 6 x 3 x 65
_______________ Property
3. (72 x 12) + (72 x 57) = 72(12 + ____)
_______________ Property
4. 8 x (34 x 1) = 8 x ____
_______________ Property
5. Evaluate the expression, given u = 12 and v = 20.
(0 x u) x v
6. Evaluate the expression, given v = 20.
(v x 1) ÷ 5
7. Evaluate the expression, given u = 12.
(u x 5) - (u x 2)
8. Evaluate the expression, given t = 4.5 and v = 20.
(t + 15.5) / v
9. Compare. Fill in the blanks with >, <, or =.
1.3(f + c) ____ 1.3f + 1.3c
10. Compare. Fill in the blanks with >, < or =.
29 x 1 ____ 29
Answer Key
1. 45 x 1 = 45 Identity Property
2. 6 x 65 x 3 = 6 x 3 x 65 Commutative Property
3. (72 x 12) + (72 x 57) = 72(12 + 57) Distributive Property
4. 8 x (34 x 1) = 8 x 34 Identity Property
5. 0
6. 4
7. 36
8. 1
9. 1.3(f + c) = 1.3f + 1.3c
10. 29 x 1 = 29