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