Multiplying and Dividing Terms

## Multiplying and Dividing Terms

Terms can be multiplied and divided, together with their coefficients (the numbers at the front of a letter).

4b xx 3e is the same as 4 xx 3 xx b xx e = 12be.

The calculation b xx c is the same as c xx b (order in a multiplication does not matter). Therefore bc = cb, although it is normal to put the letters in alphabetical order.

When dividing a term by a number, consider only the number parts. For 12x ÷ 3, divide 12 by 3 giving 4 and leave the x as it is to give an answer of 4x.

A number divided by itself is 1; similarly a ÷ a = 1. And 5x ÷ x = 5.

If one term is being divided by another term where both have the same variable, then calculate the number parts and the letter parts separately. frac(15x)(3x) = frac(15)(3) \times frac(x)(x) = 5 \times 1 = 5.

The rules for multiplying and diving with negative numbers still apply: -2x times -y = +2xy.

## Example 1

Simplify 5 xx -a.

The a is negative: as it is a positive times a negative, the answer is negative.

Answer:  -5a

## Example 2

Simplify 3 xx b xx 4 xx c

3 x 4 = 12; then the remaining letters are put together without the times sign.

Answer: 12bc