# Simple formulae

## In a nutshell

Formulae are rules or facts that are written in a mathematical way. They are used to help you work out missing numbers by using other connected quantities.

## Understanding and using formulae

When a formula is written out you will see letters or sentences used instead of numbers. These are then replaced by numbers to solve the problem.

### Using sentences in formulae

In some cases word problems can be turned into formulae made from sentences.

##### Example 1*The time needed to cook a cake is forty minutes plus twenty minutes for every egg used.*
*Written as a formula:*
*Cooking time $= 40$ minutes $+ \ (20\ \times$ number of eggs used)*
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### Using letters in formulae

In other cases letters might be used to represent quantities. To work out volume, the formula used is:

volume $=$ length $\times$ width $\times$ height.

This can also be written as:

volume $=lwh$

*Note: **In maths, letters and numbers written next to each other means they are multiplied.*

##### Example 2
*What is the volume of this cuboid?*
*Write down the formula:*
*volume** *$=lwh$* *
*length*$=5cm$*, **width*$=2cm$* **and height*$=3cm$* *
$l=5cm, w=2cm, h=3cm$*, *
*Substituting into the formula.*
*volume* $= 5cm \times 2cm \times 3cm = \underline{30cm}$
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