Basic Mathematics for College Students

1.5 Dividing Whole Numbers 55

EXAMPLE (^1) Write the related multiplication statement for each division.
a. b. c.
Strategy We will identify the quotient, the divisor, and the dividend in each
division statement.
WHY A related multiplication statement has the following form:
Quotient divisor dividend.
Solution
a.
b. because. 4 is the quotient, 6 is the divisor, and 24 is the dividend.
c. because 7  3  21. 7 is the quotient, 3 is the divisor, and 21 is the dividend.

21

3

 7

4  6  24

4

6  24

Divisor

Quotient

 

10  5  2 because 2  5 10.

Dividend



21

3

 7

4

10  5  2 6 ^24

Self Check 1

Write the related multiplication

statement for each division.

a.

b.

c.

Now TryProblems 19 and 23

36

4

 9

8

7  56

8  2  4

The Language of Mathematics To describe the special relationship between

multiplication and division, we say that they are inverse operations.

2 Use properties of division to divide whole numbers.

Recall from Section 1.4 that the product of any whole number and 1 is that whole
number.We can use that fact to establish two important properties of division.
Consider the following examples where a whole number is divided by 1:

because.

because.

because.

These examples illustrate that any whole number divided by 1 is equal to the number
itself.
Consider the following examples where a whole number is divided by itself:
because.

because.

because.

These examples illustrate that any nonzero whole number divided by itself is equal to 1.

1  35  35

35

35

 1

1  9  9

1

(^9)  9

6  6  1 1  6  6

20  1  20

20

1

 20

4  1  4

4

(^1)  4

8  1  8 8  1  8

Properties of Division

Any whole number divided by 1 is equal to that number. For example,.

Any nonzero whole number divided by itself is equal to 1. For example,^1414  1.

14

1 ^14