Technical Mathematics, Sixth Edition

2.9. Dividing a Monomial by a Monomial

Our last basic operation with algebraic expressions is division. As always, we will start with the simplest kind, dividing a monomial by a monomial, and then progress to more difficult types.

2.9.1. Symbols for Division

Division may be indicated by any of the following symbols:

The names of the parts are

The quantity is also called a fraction. The horizontal line is the fraction bar. It is a symbol of grouping for multiple terms in the numerator or in the denominator.

2.9.2. Reciprocals

As we saw earlier, the reciprocal of a number is 1 divided by that number. The reciprocal of n is 1/n. We can use the idea of a reciprocal to show how division is related to multiplication. We may write the quotient of x ÷ y as

We see that to divide by a number is the same thing as to multiply by its reciprocal. This fact will be especially useful for dividing by a fraction.

2.9.3. Division by Zero

Division by zero is not a permissible operation.

Example 75: In the fraction x cannot equal 2, or the illegal operation of division by zero will result.

If division ...