Basic Mathematics for College Students

54 Chapter 1 Whole Numbers

SECTION 1.5

Dividing Whole Numbers

Division of whole numbers is used by everyone. For example, to find how many

6-ounce servings a chef can get from a 48-ounce roast, he divides 48 by 6. To split a

$36,000 inheritance equally, a brother and sister divide the amount by 2. A professor

divides the 35 students in her class into groups of 5 for discussion.

1 Write the related multiplication statement for a division.

To divide whole numbers, think of separating a quantity into equal-sized groups. For

example, if we start with a set of 12 stars and divide them into groups of 4 stars, we will

obtain 3 groups.

We can write this division problem using a division symbol ,a long division symbol

, or a fraction bar. We call the number being divided the dividend and the

number that we are dividing by is called the divisor.The answer is called the quotient.





There are 3 groups of 4 stars.

A set of 12 stars.

Recall from Section 1.4 that multiplication is repeated addition. Likewise,

division is repeated subtraction. To divide 12 by 4, we ask, “How many 4’s can be

subtracted from 12?”

Since exactly three 4’s can be subtracted from 12 to get 0, we know that

.

Another way to answer a division problem is to think in terms of multiplication.

For example, the division asks the question, “What must I multiply 4 by to get

12?” Since the answer is 3, we know that

because

We call the related multiplication statementfor the division

In general, to write the related multiplication statement for a division, we use:

Quotient divisor dividend

3  4  12 12  4 3.

12  4  3 3  4  12

12  4

12  4  3

Subtract 4 one time.

Subtract 4 a second time.

Subtract 4 a third time.

12

 4

8

 4

4

 4

0

Objectives

1 Write the related multiplication

statement for a division.

2 Use properties of division to

divide whole numbers.

3 Perform long division (no

remainder).

4 Perform long division (with a

remainder).

5 Use tests for divisibility.

6 Divide whole numbers that end

with zeros.

7 Estimate quotients of whole

numbers.

8 Solve application problems by

dividing whole numbers.

Division symbol

12  4  3

Dividend Divisor Quotient

  

Long division symbol

Quotient

Divisor Dividend

 

3

(^4)  12

Fraction bar
Dividend Quotient
Divisor


12

4

 3





We read each form as “12 divided by 4 equals (or is) 3.”