Expressions: cheat sheet

Algebra Foundations · The words and methods from the lessons, with an example of each.

A rule that gives one quantity from others, written with letters. This one gives the perimeter of a rectangle.

P = 2l + 2w

"5 more than n" is $n + 5$ . "5 less than n" is $n - 5$ : you start from $n$ and take 5 away, so $n$ comes first.

n + 5 \qquad n - 5

With $x = 4$ , $2x$ is 8, not 24.

2x = 2 \times x

Replace each letter with its value, write in the × signs, then work it out: brackets, then × and ÷, then + and −.

\begin{aligned} P &= 2l + 2w \\ &= 2 \times 5 + 2 \times 3 \\ &= 16 \end{aligned}

A letter for a quantity that can change. Each rectangle has its own $l$ , $w$ and $P$ .

P, \; l, \; w

A number that stays the same, such as a 20 dollar call-out fee. $\pi$ is a constant too.

C = 5h + \mathbf{20}

In an equation, a letter can stand for one particular number: here only $x = 4$ works.

3x + 2 = 14

Brackets keep a part together so it is worked out first. "Add 3, then double the result" is $2(n + 3)$ ; "double, then add 3" is $2n + 3$ .

2(n + 3) \ne 2n + 3

Say what the letter stands for (a number that changes), multiply it by the amount for each one, then add anything paid once.

\begin{aligned} &\text{Let } g = \text{number of guests} \\ &C = 5g + 60 \end{aligned}

Substitute what you know, then solve the equation that is left by undoing. Check by substituting back.

\begin{aligned} 20 &= 2 \times 6 + 2w \\ 8 &= 2w \\ w &= 4 \end{aligned}