Ratio & Proportion — Year 7 Revision Notes
These notes cover writing and simplifying ratios, dividing a quantity in a given ratio, and solving direct proportion problems using the unitary method.
Writing and simplifying ratios
A ratio compares quantities in a fixed order, such as 2:3. Simplify a ratio by dividing every part by their highest common factor, just like a fraction. So 4:6 simplifies to 2:3.
Key Facts & Formulas
- divide every part by the HCF to simplify
Tips
- Keep the quantities in the order given in the question.
- Make sure both parts are in the same units before simplifying.
Sharing in a given ratio
To share an amount in a ratio, add the parts to find the total number of parts, find the value of one part by dividing, then multiply for each share. To share RM40 in the ratio 2:3, there are 5 parts, so one part is RM8, giving RM16 and RM24.
Key Facts & Formulas
- one part = total ÷ (sum of parts)
Tips
- Check your shares add back up to the original total.
- The first quantity is 2/5 of the total in a 2:3 ratio, not 2/3.
Direct proportion
In direct proportion, quantities increase at the same rate. Use the unitary method: find the value of one item, then scale up. If 3 books cost RM18, one book costs RM6, so 5 books cost RM30.
Key Facts & Formulas
- value of one = total ÷ number
Tips
- Find the cost or amount for one first — it makes scaling easy.
- Best-buy questions: compare the price for the same amount, e.g. per 100 g.
Revision Checklist
- I can write and simplify a ratio
- I can share a quantity in a given ratio
- I can use the unitary method for direct proportion
- I understand the difference between a ratio and a fraction of the whole
Frequently Asked Questions
In the ratio 2:3, what fraction is the first part?
The total is 2 + 3 = 5 parts, so the first part is 2/5 of the whole, not 2/3.
Build strong foundations in Ratio & Proportion
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