Units in an Algebraic Context

## Units in an Algebraic Context

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 10x mm x mm, which is equal to 10xytext( cm)^2.

## Example 1

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

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 = cm3

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

## Example 2

The area of a rectangle is 115.2 cm2. The length of the rectangle is x cm, and the width of the rectangle is 8x mm. What is x?

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

Answer: x = 12