IP Maths Notes (Lower Sec, Year 1-2): 03) Ratio, Rate & Percentage Reasoning

Q: What does IP Maths Notes (Lower Sec, Year 1-2): 03) Ratio, Rate & Percentage Reasoning cover?
A: Structure ratio simplifications, rate conversions, percentage change chains, and mixture questions with full working.

Mastery of ratio and percentage reasoning saves marks across chemistry mixtures, physics rates, and finance contexts. This post trains systematic setups and calculator-free checks.

Learning targets

• Simplify ratios and express them in different forms (part:part, part:whole).
• Convert between rates (speed, density, unit pricing) with clear units.
• Chain multiple percentage changes and interpret reverse percentages.
• Model mixtures and part-whole distributions using algebraic reasoning.

1. Ratio fundamentals

1.1 Simplification & scaling

• Divide all parts by the highest common factor to simplify.
• To increase a ratio, multiply each part by the same scale factor.

Example: The ratio of red:blue marbles is 18:24. Simplify: divide by 6 → 3:4.

1.2 Part-whole conversion

If the ratio of boys to girls is 5:4, the total number of parts is 9. Boys make $\frac{5}{9}$ of the class.

2. Rate conversions

Common rate templates:

• Speed: $\text{speed} = \frac{\text{distance}}{\text{time}}$