Units in an Algebraic Context
# Units in an Algebraic Context

GCSE(F), GCSE(H),

When using units with algebra, ensure that:

• the units used are consistent throughout, and

• that the units are manipulated along with the calculation.

For example, `x` cm x `y` mm should be changed to 10`x` mm x ``mm, which is equal to `10xytext( cm)^2`.

## Examples

1. What is the volume of a cuboid that is `5x` cm long, `3x` cm wide and `2x` cm high?

Answer: `30x^3text( cm)^3`

Multiply the numbers together: 5 x 3 x 2 = 30

Multiply the `x` values together for `x^3`

The measurements are also multiplied together; cm x cm x cm = cm^{3}

2. The area of a rectangle is 115.2 cm^{2}. The length of the rectangle is `x` cm, and the width of the rectangle is `8x` mm. What is `x`?

Answer: `x = 12`

Note that the width is in millimetres. Convert mm to cm: width is `0.8x` cm

`115.2 = x text( cm) times 0.8x text( mm)`

`115.2 = 0.8x^2`

`144 = x^2`

`x = 12`

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