Basic Mathematics for College Students



The extra zeros (shown in the steps highlighted in red and blue) are often omitted.

We can use long division to perform divisions when the divisor has more than one

digit. The estimation step is often made easier if we approximate the divisor.

4 1 9

6  2 5 1 4

 2 4 0 0

1 1 4

 6 0

5 4

 5 4

0

58 Chapter 1 Whole Numbers

HundredsTensOnes

Here, we are really subtracting 400 6, which is 2,400, from 2,514. That is

why the 4 is written in the hundreds column of the quotient

Here, we are really subtracting 10 6, which is 60, from 114. That is why the

1 is written in the tens column of the quotient.

Here, we are subtracting 96, which is 54, from 54. That is why the 9 is

written in the ones column of the quotient.

EXAMPLE (^3) Divide using long division:
Strategy We will follow a four-step process:estimate, multiply, subtract,and
bring down.
WHY This is how long division is performed.
Solution
To help you understand the process, each step of this division is explained
separately. Your solution need only look like the laststep.
Since 48 will not divide 3, nor will it divide 33, we divide 338 by 48.
Ask: “How many times will 48 divide 338?” Since 48 is almost 50, we can
the answer to that question by thinking is about 6, and
we write the 6 in the hundreds column of the quotient.

705

48  33888

 336

28

 0

288

 240

48

70

(^48)  33888
 336
28
 0
28

7

48  33888

 336

2

6

48  33888

 288

50

estimate 33  5

6

(^48)  33888
(^48) 33,888
Self Check 3
Divide using long division:
Now TryProblem 35
(^57) 45,885
6 and 48, and their product, 288, from 338 to get

50. Since 50 is greater than the divisor, 48, the estimate of 6 for the
    hundreds column of the quotient is too small. We will erase the 6 and
    increase the estimate of the quotient by 1 and try again.

Multiply subtract

Change the from 6 to 7 in the hundreds column of the quotient.

7 and 48, and their product, 336, from 338 to get 2.

Since 2 is less than the divisor, we can proceed with the long division.

Multiply subtract

estimate

the 8 from the tens column of the dividend. Ask: “How many

times will 48 divide 28?” Since 28 cannot be divided by 48, write a 0 in the

tens column of the quotient. 0 and 48, and their

product, 0, from 28 to get 28.

Multiply subtract

Bring down

the 8 from the ones column of the dividend. Ask: “How many

times will 48 divide 288?” We can estimate the answer to that question by

thinking 28 5 is about 5, and we write the 5 in the ones column of the

quotient. 5 and 48, and their product, 240, from

288 to get 48. Since 48 is equal to the divisor, the estimate of 5 for the

ones column of the quotient is too small. We will erase the 5 and increase

the estimate of the quotient by 1 and try again.

Multiply subtract

Bring down