What is a proportion?
A proportion is a statement that two ratios are equal. For example, 2 : 3 = 4 : 6 is a proportion because both simplify to 2 : 3. We can also write it as fractions: 2/3 = 4/6. Proportions let us find an unknown value when quantities change together at the same rate.
Key idea / Key idea
If a/b = c/d, then a × d = b × c (cross-multiplication). Use this to solve for a missing term.
Solving a proportion
Worked example / Worked example
3 pens cost RM12. How much do 5 pens cost at the same rate?
Set up the proportion: 3/12 = 5/x.
Cross-multiply: 3 × x = 12 × 5
3x = 60, so x = 60 ÷ 3 = RM20.
Check: 3 pens = RM12 means RM4 each, and 5 × RM4 = RM20. ✔
This is called direct proportion: when one quantity increases, the other increases at the same rate. More pens cost more money, and half as many pens cost half as much. Always keep the same order on both sides of the proportion (pens with pens, cost with cost), or the answer will be wrong.
The unitary method is another neat way to solve the same problems. First find the value of one item, then multiply. For the pens: one pen costs RM12 ÷ 3 = RM4, so 5 pens cost 5 × RM4 = RM20 — the same answer. Proportions appear everywhere: recipes, map scales, currency exchange and mixing paint all use equal ratios to scale amounts up or down.
Remember / Remember
- A proportion sets two equal ratios.
- Cross-multiply to find the unknown.
- Line up quantities of the same kind.
- In direct proportion, doubling one doubles the other.