Simplifying more difficult ratios
Ratios with decimals
To simplify a ratio with a decimal:
- multiply the numbers to make them all Any number which does not need a decimal point. Also known as an integer.
- divide both numbers by the The highest common factor (HCF) of two numbers is the largest number which will divide exactly into both of them, for example, the highest common factor of 24 and 36 is 12.
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:
- convert the fractions so they have a A common denominator exists when the denominator (the number at the bottom of a fraction) of two or more fractions is the same. Common denominators help to compare or add/subtract two or more fractions. Common denominators are made by using equivalent fractions, eg a common denominator for 1/4 and 1/3 would be twelfths.
- multiply both fractions by the common denominator
- 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:
- convert the larger unit to the smaller unit
- simplify the ratio as normal
Example
Simplify \(25 \:\text{mm}:5 \:\text{cm}\).
Convert centimetres into millimetres by multiplying by 10:
\(5 \:\text{cm} \times 10 = 50 \:\text{mm}\)
Simplify by dividing both numbers by 25:
\(25 \div 25 : 50 \div 25 = 1 : 2\)
Ratios as fractions
Ratios can be used to show fractions and Proportion is used to show how quantities and amounts are related to each other. The amount that one quantity changes in relation to another quantity is governed by proportion rules. 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: \(2 \:\text{blue} + 3 \:\text{yellow} = 5 \:\text{total}\)
The fraction painted blue is \(\frac{2}{5}\) and the fraction painted yellow is \(\frac{3}{5}\).