Basic Mathematics for College Students

44 Chapter 1 Whole Numbers

The Language of Mathematics In Example 4, the numbers

1,308and 8,720are called partial products.We added the

partial products to get the answer, 10,028. The word partial

means only a part, as in a partialeclipse of the moon.

4 3 6

 2 3

1 3 0 8

8 7 2 0

1 0, 0 2 8

When a factor in a multiplication contains one or more zeros, we must be careful

to enter the correct number of zeros when writing the partial products.

EXAMPLE (^5) Multiply: a. b.
Strategy We will think of 406 as 6 400 and 3,009 as 9 3,000.
WHY Thinking of the multipliers (406 and 3,009) in this way is helpful when
determining the correct number of zeros to enter in the partial products.
Solution
We will use vertical form to perform each multiplication.
a.Since , we will multiply 253 by 6 and by 400, and add those
partial products.
The product is 102,718.
b.Since , we will multiply 2,007 by 9 and by 3,000, and add
those partial products.
The product is 6,039,063.
d 9  2,007
d3,000 2,007. Think of 3,000 as 3 1,000 and simply multiply
2,007 by 3 and attach three zeros (shown in blue) to the result.

2,007

3,009

18 063

6 021 000

6,039,063

3,009 9 3,000

d 6  253

d 400 253. Think of 400 as 4 100 and simply multiply 253 by 4

and attach two zeros (shown in blue) to the result.

253

 406

1 518

101 2 00

102,718

406  6  400

406  253 3,009(2,007)

Self Check 5

Multiply:

a.706(351)

b.4,004(2,008)

Now TryProblem 41

4 Use properties of multiplication to multiply whole numbers.

Have you ever noticed that two whole numbers can be multiplied in either order

because the result is the same? For example,

and

This example illustrates the commutative property of multiplication.

4  6  24 6  4  24

Commutative Property of Multiplication

The order in which whole numbers are multiplied does not change their

product.

For example,

7  5  5  7