Basic Mathematics for College Students

1.5 Dividing Whole Numbers 57

Next, we 4 and 6, and their product, 24, from 25, to get 1.

Now we the next digit in the dividend, the 1, and again estimate,

multiply, and subtract.

To complete the process, we the last digit in the dividend, the 4, and

, , and one final time.

To check the result, we see if the product of the quotient and the divisor equals the
dividend.

The check confirms that 2,514 6  419.

6  (^2514) 
Quotient
Divisor
Dividend




4

1

1

5

9

 6

2 , 5 1 4

419

(^6)  2514
 24
11
 6
54
 54
0
estimate multiply subtract
bring down

41

6  2514

 24

11

 6

5

bring down

4

(^6)  2514
 24
1
multiply subtract
Ask: “How many times will 6 divide 11?” We that 11 6 is about 1,
and write the 1 in the tens column above the long division symbol. 1
and 6, and subtracttheir product, 6, from 11, to get 5.
Multiply
estimate
419
6  2514
 24
11
 6
54
 54
0
Your solution
should look
like this:
Ask: “How many times will 6 divide 54?” We
that 54 6 is 9, and we write the
9 in the ones column above the long division
symbol. 9 and 6, and
their product, 54, from 54, to get 0.
Multiply subtract
estimate
The Language of Mathematics In Example 2, the long division process ended
with a 0. In such cases, we say that the divisor divides the dividend exactly.
We can see how the long division process works if we write the names of the place-
value columns above the quotient. The solution for Example 2 is shown in more detail
on the next page.