⚖️ Class 6 · Number system

Ratio and Proportion for Class 6: notes, worked examples and practice

A ratio compares two quantities and a proportion says two ratios are equal. They turn up in recipes, maps, sharing money and scale drawings.

Updated 21 October 2026. Every worked example and answer on this page is checked by automated tests.

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Notes

Ratio and Proportion: what you need to know

Chapter names and order differ by board and textbook edition, so follow your own textbook for the order.

What a ratio is

A ratio compares two quantities of the same kind, written a : b. The units must be the same, so convert first: 50 cm to 2 m is 50 : 200.

Simplifying a ratio

Divide both terms by their HCF. 24 : 36 becomes 2 : 3. Equivalent ratios come from multiplying or dividing both terms by the same number.

Proportion

Four numbers a, b, c, d are in proportion when a : b = c : d. Then the product of the outer terms equals the product of the inner terms: a × d = b × c.

The unitary method

Find the value of one unit first, then multiply. If 6 notebooks cost ₹90, one costs ₹15 and 10 cost ₹150.

Sharing in a ratio

Add the parts of the ratio, divide the total by that sum to get one part, then multiply by each term.

Formulas and rules to remember

a : b = a/b
If a : b = c : d then a × d = b × c
Share = (own part ÷ total parts) × total amount

Solved examples

Example 1

Simplify the ratio 24 : 36.

The HCF of 24 and 36 is 12.
24 ÷ 12 = 2 and 36 ÷ 12 = 3.

Answer: 2 : 3

Example 2

Find x if 3 : 5 = 12 : x.

3 × x = 5 × 12.
3x = 60, so x = 20.

Answer: 20

Example 3

Share ₹900 between two friends in the ratio 2 : 3.

Total parts = 2 + 3 = 5.
One part = 900 ÷ 5 = 180.
Shares: 2 × 180 = 360 and 3 × 180 = 540.

Answer: ₹360 and ₹540

Example 4

If 6 notebooks cost ₹90, what do 10 notebooks cost?

One notebook costs 90 ÷ 6 = ₹15.
10 notebooks cost 10 × 15 = ₹150.

Answer: 150

Avoid these

Common mistakes

Comparing different units

The ratio of 50 cm to 2 m is not 50 : 2. Change 2 m to 200 cm and the ratio is 50 : 200 = 1 : 4.

Simplifying only one term

Both terms must be divided by the same number.

Writing the ratio in the wrong order

The ratio of boys to girls (3 : 4) is not the same as girls to boys (4 : 3).

10 practice questions with answers

Try each question on paper first, then tap it to check your answer. The questions are generated by code and each answer is checked.

Simplify the ratio 32 : 48 =
Answer: 2:3
Simplify the ratio 24 : 32 =
Answer: 3:4
Simplify the ratio 48 : 40 =
Answer: 6:5
Find x if 4 : 9 = 32 : x. x =
Answer: 72
Find x if 7 : 5 = 70 : x. x =
Answer: 50
Find x if 5 : 9 = 10 : x. x =
Answer: 18
Divide ₹240 between two friends in the ratio 2 : 1. Their shares (in ₹) are
Answer: 160 and 80
Divide ₹240 between two friends in the ratio 1 : 3. Their shares (in ₹) are
Answer: 60 and 180
Divide ₹1,040 between two friends in the ratio 3 : 1. Their shares (in ₹) are
Answer: 780 and 260
Divide ₹1,320 between two friends in the ratio 3 : 3. Their shares (in ₹) are
Answer: 660 and 660

More practice

Ratio calculator

Simplify ratios, share an amount in a ratio, or solve a : b = c : x. Handy for recipes, profit sharing, maps and scaling.

Use the tool →

FAQ

Ratio and Proportion Class 6: questions students ask

What is the difference between ratio and proportion?

A ratio compares two quantities. A proportion is a statement that two ratios are equal.

How do I divide an amount in a given ratio?

Add the parts, divide the amount by the total to get one part, and multiply by each part of the ratio.

Can a ratio have more than two terms?

Yes, such as 2 : 3 : 5. The same rules apply to sharing: add all the parts first.

Does the order of a ratio matter?

Yes. 2 : 3 and 3 : 2 are different ratios.

Which board is this ratio and proportion page for?

It covers the ideas taught in CBSE, ICSE and state-board maths. Chapter names and order differ by board and textbook edition, so follow your own textbook for the exact order.

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