Basic Mathematics for College Students

Whenever we multiply a whole number by 0, the product is 0. For example,
, , and
Whenever we multiply a whole number by 1, the number remains the same. For
example,

, , and

These examples illustrate the multiplication properties of 0 and 1.

3  1  3 7  1  7 1  9  9

0  5  0 0  8  0 9  0  0

1.4 Multiplying Whole Numbers 45

Multiplication Properties of 0 and 1

The product of any whole number and 0 is 0.

The product of any whole number and 1 is that whole number.

Success Tip If one (or more) of the factors in a multiplication is 0, the

product will be 0. For example,

16(27)(0) 0 and 109  53  0  2  0

To multiply three numbers, we first multiply two of them and then multiply that
result by the third number. In the following examples, we multiply in two ways.
The parentheses show us which multiplication to perform first. The steps of the
solutions are written in horizontal form.

3  2  4

The Language of Mathematics In the following example, read (3 2) 4 as

“The quantityof 3 times 2,” pause slightly, and then say “times 4.” We read

3 (2 4) as “3 times the quantityof 2 times 4.” The word quantity alerts the

reader to the parentheses that are used as grouping symbols.

Method 1: Group 3  2

Multiply 3 and 2 to

get 6.

Multiply 6 and 4 to

get 24.

 24

( 3  2 ) 4  6  4

Method 2: Group 2  4

Then multiply 2 and 4

to get 8.

Then multiply 3 and 8

to get 24.

 24

3 ( 2  4 ) 3  8

 

Same result

Either way, the answer is 24. This example illustrates that changing the grouping when
multiplying numbers doesn’t affect the result. This property is called the associative
property of multiplication.

Associative Property of Multiplication

The way in which whole numbers are grouped does not change their product.

For example,

(23) 5  2 (35)

Sometimes, an application of the associative property can simplify a calculation.