Ratio & Proportion — Year 8 Revision Notes
These notes cover simplifying ratios, dividing a quantity in a ratio, and solving direct and inverse proportion problems — all at Year 8 (Stage 8) level.
Simplifying ratios
Simplify a ratio by dividing all its parts by their highest common factor, just like a fraction. 12 : 18 simplifies to 2 : 3. If the quantities have units, change them to the same unit first — 1 m : 50 cm becomes 100 cm : 50 cm = 2 : 1.
Key Facts & Formulas
- 12 : 18 = 2 : 3
- 1 m : 50 cm = 2 : 1
Tips
- Convert to the same units before simplifying.
- Divide every part by the same number.
Sharing in a ratio
To divide a quantity in a ratio, add the parts to get the total number of parts, find the value of one part, then multiply. To share 30 sweets in the ratio 2 : 3, there are 5 parts, one part is 30 ÷ 5 = 6, so the shares are 12 and 18.
Key Facts & Formulas
- Total parts = sum of ratio numbers
- One part = amount ÷ total parts
Tips
- Check your shares add back up to the original amount.
- Find the value of one part first.
Direct and inverse proportion
In direct proportion, two quantities increase together at the same rate; use the unitary method by finding the value of one unit first. In inverse proportion, one quantity increases as the other decreases, so their product stays constant — for example, twice as many workers take half the time.
Key Facts & Formulas
- Direct: find the value of 1 unit, then scale
- Inverse: quantity × other quantity = constant
Tips
- For direct proportion, find one unit first.
- For inverse proportion, more of one means less of the other.
Revision Checklist
- I can simplify ratios, including with units
- I can divide a quantity into a given ratio
- I can solve direct proportion problems with the unitary method
- I can recognise and solve simple inverse proportion problems
Frequently Asked Questions
What is the unitary method?
It means finding the value of one unit first, then scaling up to the amount you need. If 5 pens cost $2, one pen costs $0.40, so 8 pens cost 8 × $0.40 = $3.20.
Build strong foundations in Ratio & Proportion
A free trial class with Teacher Rig helps your Year 8 child master Ratio & Proportion now — so IGCSE Maths feels familiar, not frightening, later.
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