How to Solve Ratio Problems in IGCSE Maths
Ratio questions appear frequently in IGCSE Maths exams, especially in sharing, scaling, and comparison problems. This guide explains a reliable step by step approach for solving ratios, with worked examples that mirror exam style questions. You'll learn how to find one part, multiply correctly, and check totals quickly before moving on to self marking practice.
How to Solve Ratio Problems: Step by Step
A ratio compares two or more quantities. Most IGCSE ratio questions follow the same method: split a total into parts, or use one known part to find the others.
- Add the parts. For a ratio like \(2:5\), add the numbers together: \(2 + 5 = 7\) total parts.
- Find the value of one part. If you know the total, divide by the total parts. If you know one share instead, divide that share by its ratio number.
- Multiply each ratio number by the one-part value. This gives the size of each share.
- Check your answer. Add the shares together: they should equal the original total.
Quick example: split \(£90\) in the ratio \(4:5\). Total parts \(= 9\), one part \(= 90 \div 9 = £10\), shares \(= £40\) and \(£50\). Check: \(40 + 50 = 90\). ✓
Key Ideas to Remember
The bar model shows how a total splits into parts. Try your own numbers in the scaler on the right.
Blue, orange and green blocks show each part of the ratio. Sizes are drawn to scale.
Worked Examples
💡 Example 1: Splitting a Total
A paint recipe uses blue and white paint in the ratio \(2:5\). How much of each is needed to make \(210\) ml?
Total parts \( = 2 + 5 = 7 \)
What's happening?
Add the ratio numbers to find how many parts the total is made of.
One part \( = \dfrac{210}{7} = 30 \) ml
What's happening?
Divide the total by the number of parts to find the value of one part.
Blue \( = 2 \times 30 = 60 \) ml
White \( = 5 \times 30 = 150 \) ml
Check: \( 60 + 150 = 210 \) ✓
What's happening?
Multiply each ratio number by the one-part value. Add the shares to check they equal the original total.
💡 Example 2: Sharing in Three Parts
Three friends share \(£600\) in the ratio \(1:2:3\). Find each person's share.
Total parts \( = 1 + 2 + 3 = 6 \)
What's happening?
Add all three ratio numbers.
One part \( = \dfrac{600}{6} = £100 \)
What's happening?
Divide the total by the total parts.
First \( = 1 \times 100 = £100 \)
Second \( = 2 \times 100 = £200 \)
Third \( = 3 \times 100 = £300 \)
Check: \( 100 + 200 + 300 = 600 \) ✓
What's happening?
Multiply each part and add to check. Notice each share grows in the same proportion as the ratio.
💡 Example 3: One Part Known, Find the Rest
Tomás and Mei share some money in the ratio \(3:8\). Mei gets \(£240\). How much does Tomás get?
Mei has 8 parts \( = £240 \)
One part \( = \dfrac{240}{8} = £30 \)
What's happening?
You know Mei's share and her ratio number. Divide to find one part.
Tomás \( = 3 \times 30 = £90 \)
What's happening?
Multiply Tomás' ratio number by one part to find his share.
Total \( = 240 + 90 = £330 \)
What's happening?
Add both shares to find the original total if needed.
💡 Example 4: Comparing Two Ratios
Which ratio is larger: \(7:4\) or \(11:6\)? Use the unit form \(n:1\).
\( 7:4 \to \dfrac{7}{4}:1 \)
\( = 1.75 : 1 \)
What's happening?
Divide both sides of the ratio by the second number so the right-hand side becomes 1.
\( 11:6 \to \dfrac{11}{6}:1 \)
\( \approx 1.833 : 1 \)
What's happening?
Do the same for the second ratio. Now both have the same right-hand side, so the left-hand sides can be compared directly.
\( 1.833 > 1.75 \)
\(11:6\) is the larger ratio.
What's happening?
The ratio with the larger left-hand side in unit form is the larger ratio overall.
🔑 Key Points
- A ratio stays the same if both sides are multiplied or divided by the same number: \(2:5 = 4:10 = 6:15\).
- When the total is known, divide by total parts first, then multiply.
- When one share is known, divide that share by its ratio number to find one part.
- Always check that the shares add up to the original total.
- Simplify ratios to their lowest terms using the HCF when asked.
- Unit form (\(n:1\) or \(1:n\)) is the standard way to compare ratios.
⚠️ Common Pitfalls
- Forgetting to add all the parts. Dividing by the wrong number gives the wrong value for one part.
- Mixing up the order. The ratio \(3:2\) is not the same as \(2:3\). Read the question carefully.
- Confusing "ratio of" with "fraction of". In \(2:5\), the first quantity is \(\dfrac{2}{7}\) of the total, not \(\dfrac{2}{5}\).
- Leaving a ratio unsimplified. \(8:12\) should usually be written as \(2:3\).
- Using the wrong share when one part is known. Always divide the known share by its own ratio number.