- Define and explain Simplifying Ratios in your own words
- Use key terms such as Proportion accurately
- Apply what you have learned to new examples and questions
- Avoid the common mistakes learners make with this topic
Ratios compare quantities and proportion keeps them in step — from mixing paint to reading maps, they describe how things scale together.
This lesson focuses on Simplifying Ratios: reduce ratios to their simplest form like fractions.
Reduce ratios to their simplest form like fractions.
Key ideas
Simplifying ratios
Divide every part by the same number, just like cancelling fractions: 10:15 simplifies to 2:3. A ratio in simplest form is easiest to read.
Sharing in a ratio
Add the parts to find the total number of shares, then divide the amount by that total. For £30 in the ratio 2:3, there are 5 shares of £6.
Key term — Proportion: A statement that two ratios are equal, such as 1:2 = 2:4.
Are the ratios 4:6 and 10:15 equivalent?
Yes — both simplify to 2:3.
Answer: Yes — both simplify to 2:3.
- Simplifying only one part of a ratio Every part must be divided by the same number, or the comparison changes.
- Adding instead of multiplying when scaling Doubling a recipe means multiply by 2, not add 2 — scaling is always multiplication.
Practice
£24 and £16 — 5 shares of £8 each.
100 ml — 500 ÷ 5 = 100.
2:3 — both divide by 6.
£12 — one notebook costs £1.50, and 8 × £1.50 = £12.
Quick check
Which of these best defines "Proportion"?
A map scale is 1:50,000. A road measures 6 cm on the map. What is its real length in km?
- Simplifying Ratios: reduce ratios to their simplest form like fractions.
- Simplifying ratios: Divide every part by the same number, just like cancelling fractions: 10:15 simplifies to 2:3.
- Scale factor: The number you multiply by to enlarge or reduce a shape, recipe or map.
- Watch out for: simplifying only one part of a ratio