You can always divide an integer by another integer, except when the divisor is 0. Then you
get a fraction. A fraction might not be an integer, but it’s still a number.“Messy” Quotients
Figure 6-1 shows how you move around on the number line when you divide 3 by −2. First,
you take the additive inverse of 3, because you’re dividing by a negative quantity. That puts
you at the point corresponding to −3. Then you reduce your distance from 0 by a factor equal
to the absolute value of the divisor. That absolute value is 2, so you must move halfway from
−3 to 0. That puts you at a point between −1 and −2.Remainders
In the situation of Fig. 6-1, the finishing point is midway between the point for −1 and the
point for −2. When you divide 3 by −2, you get −1 with a remainder 1. In this context, the
word “remainder” means “portion left over.”
The divisor in this situation is −2, so you have a remainder of 1/(−2), which has the same
numerical value as −1/2. The remainder is always added to the whole-number part of the
quotient to get the final version of the quotient. Here, the arithmetic works out like this:3/(−2)=− 1 + (−1/2)
=−(1+ 1/2)
=−1-1/2The last quantity above is read “negative one and a half.” The whole-number part is separated
from the fractional part by a dash. This dash is not a minus sign! (The minus sign is much
longer.) Some writers leave a space between the whole-number part and the fractional part of
an expression like this. But that can also be confusing, because it could make the above result
look like −11/2. That would mean −5-1/2, not −1-1/2.83CHAPTER6 Fractions Built of Integers
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