成人快手

Simplifying more difficult ratios

Ratios with decimals

To simplify a ratio with a decimal:

  1. multiply the numbers to make them all
  2. divide both numbers by the

Example

Simplify \(6:1.5\).

Multiply both numbers by 2.

\(6:1.5 \times 2 = 12:3\)

Divide both numbers by 3.

\(12:3 \div 3 = 4:1\)

Ratios with fractions

To simplify a ratio with fractions:

  1. convert the fractions so they have a
  2. multiply both fractions by the common denominator
  3. simplify by dividing by the highest common factor

Example

Simplify \(\frac{1}{2}:\frac{3}{4}\).

Convert so the fractions have a common denominator.

\(\frac{1}{2}:\frac{3}{4} \rightarrow \frac{2}{4}:\frac{3}{4}\)

Multiply by 4.

\(\frac{2}{4}:\frac{3}{4} \times 4 = 2:3\)

The highest common factor is 1 so this is the simplest form.

Ratios in different units

To simplify ratios that are in different units:

  1. convert the larger unit to the smaller unit
  2. simplify the ratio as normal

Example

Simplify \(25 \:\text{mm}:5 \:\text{cm}\).

Convert centimetres into millimetres by multiplying by 10.

\(5 \times 10 = 50\) \(5 \:\text{cm} = 50 \:\text{mm}\)

Simplify by dividing by 25.

\(25:50 \div 25 = 1:2\)

Ratios as fractions

Ratios can be used to show fractions and of amounts.

Example

A room has to be painted blue and yellow in the ratio \(2:3\). Express the proportion of the room that has to be painted in each colour as a fraction.

There are five parts in this ratio: \(2 \:\text{blue} + 3 \:\text{yellow} = 5 \:\text{total}\)

Row of 5 blocks. 2 blue and 2 yellow

The fraction painted blue is \(\frac{2}{5}\) and the fraction painted yellow is \(\frac{3}{5}\).