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Interpreting algebraic notation

Interpreting algebraic notation

Algebraic notation consists of letters and numbers. A letter is an unknown value. Each letter may be multiplied by a number; for example `3x` means three lots of `x`. The number is always put before the letter.

When an unknown is multiplied by a number, the times sign is left out, so that `3 xx a` is the same as `3a`. This avoids mixing up the times sign x with the unknown value `x`.

One unknown can multiply another unknown. If the number of boxes of pencils is unknown (call that `b`), and the number of pencils in each box is unknown (call that `p`), then the total number of pencils in all the boxes is `bp`, or `b` x `p`. Note that the times sign is not written, and that the letters are placed in alphabetical order (this is a convention, as `bp` is actually the same as `pb`).

Algebra follows the same BIDMAS rules as arithmetic. Brackets are often used to control the sequence of operations in algebra.

Example 1

A small convoy is moving animals from one zoo to another. There are three vans each carrying the same number of marmosets, and two vans each carrying the same number of rattlesnakes. Write down how many animals are being transported, using `m` for marmosets and `r` for rattlesnakes.

3 vans x `m` marmosets in each van

2 vans x `r` rattlesnakes

`3 xx m + 2 xx r`

Dropping the times sign gives `3m + 2r`

Answer: 3m + 2r

Example 2

There are four boxes of pens. Each box contains the same number of pens. There are seven boxes of crayons. Each box of crayons contains the same number of crayons.

Write the number of pens and crayons algebraically.

4 boxes with p pens in each box = 4 x p = 4p

7 boxes of crayons, with c crayons in each box = 7 x c = 7c

The crayons and the pens cannot be added together, because the value of p and the value of c could be different.

Answer: 4p + 7c

See also Priority of Operations