1. Simplify 6:9.
- 3:2
- 6:3
- 2:3
Check the answer and reasoning
2:3
Divide both parts by their common factor 3.
MATH / Foundations
Ratio, proportion and percentages
A ratio compares quantities using equal units. Scaling every part by the same factor preserves the comparison; a percentage expresses a fraction out of one hundred.
Learning objectives
- Explain ratio, proportion and percentages using a concrete example.
- Apply the worked method and justify each step.
- Recognise the limitation described in the final check.
The big idea
A ratio compares quantities using equal units. Scaling every part by the same factor preserves the comparison; a percentage expresses a fraction out of one hundred.
For a percentage change, identify the original quantity. Repeated changes multiply scale factors rather than adding percentage points.
Equations and relationships
new value = original × (1 + r)
Use r as a decimal increase; use a negative r for a decrease.
Worked example
A £40 item rises by 15%. Find the new price.
Follow the solution
15% of £40 is £6; £40 + £6 = £46.
Investigate and explain
Predict the worked result before calculating. Change one input, record the new result, and explain which assumptions still hold.
Related interactive model. Compare its assumptions with the explanation; it is not a complete syllabus lesson.
Check your understanding
2. A £40 item rises by 15%. Find the new price.
- £46
- £55
- £34
Check the answer and reasoning
£46
15% of £40 is £6; £40 + £6 = £46.
3. An increase of 20% followed by a decrease of 20% gives what multiplier?
- 1
- 0.96
- 0.8
Check the answer and reasoning
0.96
The factors multiply: 1.2 × 0.8 = 0.96, because the second change uses a new base.