Properties of Multiplication

GRE Resources

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 + 57Distributive 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