Ratios Using Arithmetic
A ratio compares two or more quantities of the same type. Arithmetic is at the heart of every ratio calculation.
Writing and Simplifying Ratios
12 : 8 → divide both by HCF (4) → 3 : 2
Sharing in a Ratio
- Add the parts of the ratio to find the total number of shares.
- Divide the total quantity by the number of shares to find one share.
- Multiply to find each part.
Share £60 in the ratio 2 : 3
Total parts = 2 + 3 = 5. One share = £60 ÷ 5 = £12. First part = 2 × £12 = £24. Second part = 3 × £12 = £36.
Three-Part Ratio
Share 90 sweets in the ratio 1 : 2 : 3. Total = 6 parts. One part = 15. Shares: 15, 30, 45
Equivalent Ratios
2 : 3 = 4 : 6 = 6 : 9 = 10 : 15 (multiply or divide both parts by same number)
Ratios and Fractions
In ratio 3 : 5, the first quantity is 3/8 of the total; the second is 5/8.
Key Takeaways
- Simplify ratios by dividing by the HCF.
- Sharing: find one part, then multiply.
- Ratios and fractions are closely related.
- Equivalent ratios are found by multiplying or dividing both parts by the same value.
Practice Questions
- Simplify 18 : 24.
- Share £80 in the ratio 3 : 5.
- Share 120 in the ratio 1 : 3 : 2.
- In a class of 30 students the ratio of boys to girls is 2 : 3. How many of each?
- Two lengths are in the ratio 5 : 7 and together measure 60 cm. Find each length.