Algebra Know-It-ALL

84 Fractions Built of Integers

Improper or proper?

In a fraction, the dividend is called the numerator, and the divisor is called the denominator. In

the situation shown by Fig. 6-1, the numerator you start out with is 3, and the denominator

is−2. You can change this so the numerator is −3 with a denominator of 2. That’s easier to

understand. You can always take the additive inverse of both the numerator and denominator

in a fraction, and you’ll still have the same numerical value.

When the absolute value of the numerator in a fraction is larger than, or equal to, the

absolute value of the denominator, some people call it an improper fraction. There’s nothing

really inappropriate about this type of fraction, but in everyday usage, such a fraction can seem

bizarre. No one ever says anything like, “It’s 7/3 times as far to Happyville as it is to Blues-

dale.” Instead they would say, “It’s 2-1/3 times as far to Happyville as it is to Bluesdale.”

When the numerator in a fraction is an exact integer multiple of the denominator, the

fraction divides out to a plain integer. Otherwise, an improper fraction can always be changed

to an integer plus or minus a fraction. You divide the numerator by the denominator, get-

ting the whole-integer part. Then you divide the remainder by the denominator to get the

fractional part.

When the absolute value of the numerator in a fraction is less than the absolute value

of the denominator, you have a proper fraction. In this context, the word “proper” does not

imply anything more technically acceptable than “improper.” It means that the fraction can’t

be changed into an integer plus or minus a fraction. A proper fraction can also be called a

simple fraction.

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3

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Start here

First, take additive

inverse

Finish here

Not at integer point

Next, cut distance

from 0 in half

Figure 6-1 When you divide 3 by −2 and follow the process on

the number line, you end up at a point that doesn’t

correspond to an integer.