How to Solve Ratio Problems in Grade 12 Maths

Steps

1. Write the ratio as parts. If two amounts are in ratio a : b, treat them as a parts and b parts (total a + b parts).
2. Find what one part is worth. Divide the known total (or known quantity) by the relevant number of parts.
3. Multiply out each quantity. Multiply the value of one part by a and by b to get each amount.
4. Check the ratio still simplifies. Divide your two answers — they should reduce to the original ratio.

Worked example

Sipho and Thandi share R1 800 in the ratio 4 : 5. How much does each receive?

1. Total parts = 4 + 5 = 9.
2. One part = R1 800 ÷ 9 = R200.
3. Sipho = 4 × R200 = R800. Thandi = 5 × R200 = R1 000.
4. Check: R800 + R1 000 = R1 800 ✓ and 800 : 1000 = 4 : 5 ✓.

Common mistakes

• Dividing the total by 2 instead of by the sum of parts.
• Forgetting to simplify the ratio first (e.g. 6 : 9 → 2 : 3).
• Mixing up which person gets which share.

Exam tips

• Always write 'total parts = …' as your first line. It anchors the rest of the working.
• For 3-way ratios, the method is identical — just sum all three parts.
• Simplify ratios fully and keep the quantities in the same order as the question.

Frequently asked questions

Are ratio problems in Matric Maths?

Yes — they appear in algebra word problems, financial mathematics (interest splits) and probability.

How do I handle a 3-part ratio like 2 : 3 : 5?

Sum the parts (2 + 3 + 5 = 10), find what one part is worth, then multiply each by 2, 3 and 5.

How do I share an amount in a ratio?

Add the parts of the ratio, divide the amount by that total to get one part, then multiply by each share. For R600 in the ratio 2 : 3, one part is R600 ÷ 5 = R120, so the shares are R240 and R360.

How do I simplify a ratio?

Divide every part by their highest common factor: 12 : 18 simplifies to 2 : 3.

How do I share an amount in a given ratio?

Add the parts of the ratio, divide the amount by the total number of parts, then multiply by each part. To share R600 in the ratio 2 : 3, one part is R600 ÷ 5 = R120, so the shares are R240 and R360.

What is the difference between a ratio and a fraction?

A ratio compares parts with each other, such as 2 : 3. A fraction compares a part with the whole: in the ratio 2 : 3, the first part is 2/5 of the whole.