Recall from Section 1.4 that the product of any whole number and 0 is 0.We can
use that fact to establish another property of division. Consider the following
examples where 0 is divided by a whole number:
because.because.because.These examples illustrate that 0 divided by any nonzero whole number is equal to 0.
We cannot divide a whole number by 0. To illustrate why, we will attempt to find
the quotient when 2 is divided by 0 using the related multiplication statement shown
below.
Division statement Related multiplication statementThere is no number that gives
2 when multiplied by 0.
Since does not have a quotient, we say that division of 2 by 0 is undefined.Our
observations about division of 0 and division by 0 are listed below.2
0? 0 2
2
0
?
0 42 0
0
42
0
0 7 0
0
7 0
0 2 0 0 2 0
56 Chapter 1 Whole Numbers
Division with Zero1.Zero divided by any nonzero number is equal to 0. For example,.
2.Division by 0 is undefined. For example,^170 is undefined.0
17 ^03 Perform long division (no remainder).
A process called long division can be used to divide larger whole numbers.EXAMPLE (^2) Divide using long division:. Check the result.
Strategy We will write the problem in long-division form and follow a four-step
process:estimate, multiply, subtract,and bring down.
WHY The repeated subtraction process would take too long to perform and the
related multiplication statement (?6 = 2,514) is too difficult to solve.
Solution
To help you understand the process, each step of this division is explained
separately. Your solution need only look like the laststep.
We write the problem in the form. The quotient will appear above the
long division symbol. Since 6 will not divide 2,
we divide 25 by 6.
Ask: “How many times will 6 divide 25?” We that 25 6 is about 4,
and write the 4 in the hundreds column above the long division symbol.
estimate
4
(^6) 2514
6 2514
6 2514
2,514 6
Self Check 2
Divide using long division:. Check the result.
Now TryProblem 31