Basic Mathematics for College Students

60 Chapter 1 Whole Numbers

Change the from 4 to 3 in the tens column of the quotient.

3 and 23, and their product, 69, from 83, to get 14.

the 2 from the ones column of the dividend.

Ask: “How many times will 23 divide 142?” We can the answer to

that question by thinking is 7, and we write the 7 in the ones column

of the quotient. 7 and 23, and write their product, 161, under 142.

Because 161 is greater than 142, the estimate of 7 for the ones column of

the quotient is too large.We will erase the 7 and decrease the estimate of

the quotient by 1 and try again.

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

6 and 23, and their product, 138, from 142, to get 4.

The remainder

The quotient is 36, and the remainder is 4. We can write this result as 36 R 4.

To check the result, we multiply the divisor by the quotient and then add the

remainder. The result should be the dividend.

Check: Quotient Divisor Remainder

Dividend

Since 832 is the dividend, the answer 36 R 4 is correct.

 832 

(36  23)  4  828  4

  

Multiply subtract

estimate

36

23  832

 69

142

 138

4

Multiply

14  2

estimate

37

(^23)  832
 69
142
 161
Bring down

3

(^23)  832
 69
142
Multiply subtract
estimate

3

23  832

 69

14

EXAMPLE 5

Divide:

StrategyWe will write the problem in long-division form and follow a four-step

process:estimate, multiply, subtract,and bring down.

WHYThis is how long division is performed.

Solution

We write the division in the form: Since 518 will not divide 1, nor 13,

nor 130, we divide 1,301 by 518.

Ask: “How many times will 518 divide 1,301?” Since 518 is about 500,

we can the answer to that question by thinking is

about 2, and we write the 2 in the tens column of the quotient.

2 and 518, and their product, 1,036, from 1,301, to

get 265.

Multiply subtract

estimate 13  5

2

518  13011

 1036

265

(^518)  13011.

13,011

518

Self Check 5

Divide:

Now TryProblem 43

28,992

629