Page 85 - Basic College Mathematics with Early Integers

62 C HAPTE R 1 I THE WHOLE NUMBERS

3
d. If = a number, then the number times 0 = 3. Recall from Section 1.6 that any
0
3
number multiplied by 0 is 0 and not 3.We say, then, that is undefined.
0
Work Practice 3
Example 3 illustrates important division properties of 0.

Division Properties of 0
The quotient of 0 and any number (except 0) is 0. For example,

0 0
0 , 9 = 0 = 0
5 140
The quotient of any number and 0 is not a number.We say that
3
, 03, and 3 , 0
0
are undefined.

Objective Performing Long Division

When dividends are larger, the quotient can be found by a process called long
division. For example, let’s divide 2541 by 3.
divisor S 32541
c
dividend
We can’t divide 3 into 2, so we try dividing 3 into the first two digits.
8 25 , 3 = 8 with 1 left, so our best estimate is 8.We place 8 over
the 5 in 25.
32541
Next, multiply 8 and 3 and subtract this product from 25. Make sure that this differ-
ence is less than the divisor.
8

32541

-24 8(3) = 24
1 25 - 24 = 1, and 1 is less than the divisor 3.
Bring down the next digit and go through the process again.

84 14 , 3 = 4 with 2 left
32541
–24
14
– 12 4(3) = 12
2 14 - 12 = 2

Once more, bring down the next digit and go through the process.
847
21 , 3 = 7
32541

– 24
14
– 12 Copyright 2012 Pearson Education, Inc.
21
– 21 7(3) = 21
0 21 - 21 = 0
The quotient is 847.To check, see that 847 * 3 = 2541.