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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`