---
title: "Expressions: cheat sheet"
subtitle: "Algebra Foundations"
---

# Expressions

> The words and methods from this unit, with an example of each.

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

$$P = 2l + 2w$$

_l = 5 and w = 3 give P = 16_

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

$$P, \; l, \; w$$

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

$$C = 5h + \mathbf{20}$$

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

$$3x + 2 = 14$$

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**more than, less than**: "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.

$$n + 5 \qquad n - 5$$

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**brackets**: 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 $2n + 3$.

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

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**2x means 2 times x**: With $x = 4$, $2x$ is 8, not 24.

$$2x = 2 \times x$$

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

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

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

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

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**find an unknown in a formula**: Substitute what you know, then solve the equation that is left by undoing. Check by substituting back.

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

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