Manipulating Ratios
Maths: Edexcel IGCSE Higher, topic 1.7.1
Simplifying Ratios
A ratio a : b means that for each 'a' of one thing there are 'b' of another. For example if the ratio of boys to girls in a class is 3 : 4 that means that for every 3 boys there are 4 girls.
Reducing a ratio
- To reduce a ratio to a simpler form divide all parts by the same number.
- It is in its simplest form if all parts are whole numbers and there are no more common factors left to divide by.
Fractions and decimals
- If a ratio contains decimals or fractions, multiply to get rid of them before simplifying the ratio.
- If a ratio has mixed units convert both to the smaller unit and simplify.
- Then remove the units from the ratio.
Ratio Notation & Reduction
A ratio a : b means that for each "a" of one thing there are "b" of another. For example if the ratio of boys to girls in a class is 3 : 4 that means that for every 3 boys there are 4 girls.
Reducing a ratio
- To reduce a ratio to a simpler form divide all parts by the same number.
- It is in its simplest form if all parts are whole numbers and there are no more common factors left to divide by.
Decimals and fractions in ratios
- If a ratio contains decimals or fractions multiply to get rid of them before simplifying the ratio.
- 2.5 : 3 is the same as 5 : 6 (multiplied both sides by 2)
Mixed unit ratios
- If a ratio has mixed units convert both to the smaller unit and simplify.
- Once both are using the same unit you can remove the units from the ratio.
- 4.6kg : 2300g is the same as 4600g : 2300g
- We can remove the unit and simplify to get 2:1
Part : Part Ratio
If three people (Amy, Bob and Cara) divide up £5400 in the ratio 2 : 3 : 4, how much money does each of them get?
Find number of parts
- If three people (Amy, Bob and Cara) divide up £5400 in the ratio 2 : 3 : 4 then there are 9 parts in total.
- 2 + 3 + 4 = 9
Find value of each part and multiply
- Each part is worth £5400 ÷ 9 = £600:
- Amy gets 2 × £600 = £1200
- Bob gets 3 × £600 = £1800
- Cara gets 4 × £600 = £2400
Checking
- Check the result by adding these quantities and checking it is the same as the original.
Test yourself on Manipulating Ratios
Which ratio is equivalent to 25:100?
What is the simplest form of the ratio 0.1 : 7?
What is the simplest form of the ratio 4.5 : 3?