O Level MathematicsC1.11 Ratio and proportion (simplification, dividing in a ratio).

🔢 Mastering Ratios & Proportions for Exam Success!

Edudent Academy
6 Dec 25

Ratios and proportions are everywhere—from mixing paint colours to sharing prize money. **Understanding how to simplify ratios and divide quantities accurately is a must-have skill for your O Level exams and daily life.**

Main Concept: Ratios Made Simple

A *ratio* compares two or more quantities, while a *proportion* states that two ratios are equivalent. **Always write ratios in their simplest form**, just like reducing fractions. For example,
18:2418:24
simplifies to
1824=34\frac{18}{24}=\frac{3}{4}
, so the simplest ratio is
3:43:4
.

  • Key point 1: Add the parts of the ratio to find the total number of parts.
  • Key point 2: Use
    Each share=Total amountTotal parts×Required parts\text{Each share}=\dfrac{\text{Total amount}}{\text{Total parts}}\times\text{Required parts}

Worked Example: Sharing Prize Money

Problem: \60istobedividedbetweenAliandBenintheratio is to be divided between Ali and Ben in the ratio 3:23:2$. How much does each receive?

  • Step 1:
    Total parts=3+2=5\text{Total parts}=3+2=5
  • Step 2:
    \text{Ali's share}=60\times\frac{3}{5}=\3636
  • Step 3:
    \text{Ben's share}=60\times\frac{2}{5}=\2424

Practice makes perfect! **Work through past-paper questions and time yourself** to gain speed and accuracy. Keep simplifying ratios, check your proportion setups, and you’ll breeze through C1.11 questions in the exam.