Technical Mathematics, Sixth Edition

11.5. Simplifying Fractions

From factoring, we move on to our study of fractions and fractional equations. As usual we start with a reminder of some definitions.

A fraction has a numerator, a denominator, and a fraction line, or bar.

This fraction can also be written on a single line as a/b. A fraction is a way of indicating a quotient of two quantities. Thus the fraction a/b can be read as "a divided by b." Another way of indicating this same division is a ÷ b. The quotient of two quantities is also spoken of as the ratio of those quantities. Thus a/b is the ratio of a to b.

Recall that the bar or fraction line is a symbol of grouping. The quantities in the numerator must be treated as a whole, and the quantities in the denominator must be treated as a whole.

Example 29: In the fraction the numerator x + 4 must be treated as a whole. The 4 in the numerator, for example, cannot be divided by the 2 in the denominator, without also dividing the x by 2.

11.5.1. Division by Zero

Since division by zero is not permitted, it should be understood in our work with fractions that the denominator cannot be zero.

Example 30: What values of x are not permitted in the following fraction