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Tamil Nadu (TNBSE)Class 6 Mathematics★ 6-10 marks in the TN Class 6 Term 1 exam through ratio, proportion and unitary-method sums

Ratio and Proportion

Samacheer Kalvi (TN State Board) Class 6 Maths — Term 1 Chapter 3, Ratio and Proportion. The meaning of a ratio, equivalent ratios and simplest form, the meaning of proportion, and the unitary method for solving everyday problems, with worked examples, exercises and quick revision.

⏱ 14 min readEasy difficulty✓ Free · NCERT-aligned

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By the end of this chapter you'll be able to…

1Write and simplify a ratio
2Form equivalent ratios
3Check whether two ratios are in proportion
4Apply the unitary method
5Solve everyday ratio problems

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Why this chapter matters

Ratio and proportion compare quantities and underlie percentages, scaling and the unitary method used in daily life. They are directly tested in the TN Class 6 Term 1 exam.

Before you start — revise these

A 5-minute refresher here will save you 30 minutes of confusion below.

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Class 5 — Comparing quantities

Fractions and division.

Ratio and Proportion — Class 6 Maths (Samacheer Kalvi)

TN State Board (Samacheer Kalvi) Class 6 Mathematics, Term 1 — Chapter 3. Comparing quantities with ratio and proportion.

1. About this chapter

This chapter covers the meaning of a ratio, equivalent ratios and the simplest form, the meaning of proportion, and the unitary method.

2. Ratio

A ratio compares two quantities of the same kind by division, written a : b (read "a to b").
The two quantities must be in the same units. Example: 2 m to 50 cm = 200 cm : 50 cm = 4 : 1.
Simplest form: divide both parts by their HCF. 12 : 18 = (÷6) 2 : 3.

3. Equivalent ratios

Equivalent ratios have the same value, formed by multiplying or dividing both parts by the same number: 2 : 3 = 4 : 6 = 6 : 9.

4. Proportion

A proportion says two ratios are equal: a : b = c : d.
In a proportion, product of the extremes = product of the means → a × d = b × c.
Example: 2 : 3 = 8 : 12 because 2 × 12 = 3 × 8 = 24.

5. The unitary method

Find the value of one unit first, then multiply for the required number.
Example: 4 pens cost ₹48 → 1 pen = ₹12 → 7 pens = ₹84.

6. Worked examples

Example 1. Express 15 : 25 in simplest form. HCF 5 → 3 : 5.

Example 2. Are 3 : 4 and 9 : 12 in proportion? 3 × 12 = 36, 4 × 9 = 36 → equal → yes.

Example 3. If 5 kg of rice cost ₹200, find the cost of 8 kg. 1 kg = ₹40 → 8 kg = ₹320.

7. Exercises (Samacheer Kalvi)

Write the ratio of 4 boys to 6 girls in simplest form.
Find two equivalent ratios of 3 : 7.
Check whether 6 : 9 and 8 : 12 are in proportion.
Find x: 4 : 5 = x : 20.
If 3 books cost ₹150, find the cost of 10 books.

8. Common mistakes

Mistake: Comparing quantities in different units. Fix: Convert to the same unit before forming a ratio.
Mistake: Adding to make equivalent ratios. Fix: Multiply or divide both parts by the same number, not add.
Mistake: Cross-multiplying a proportion wrongly. Fix: a : b = c : d means a × d = b × c.

9. Quick revision

Term 1 · Ch 3 · ratio and proportion.
Ratio a : b compares same-kind quantities in the same units; simplest form via HCF.
Equivalent ratios: multiply/divide both parts by the same number.
Proportion a : b = c : d → ad = bc; use the unitary method to solve.

Key formulas & results

Everything you need to memorise, in one card. Screenshot this for revision.

Ratio

a : b (same units); simplest form via HCF

Compare by division.

Equivalent ratios

multiply/divide both parts by the same number

Same value.

Proportion

a : b = c : d → a×d = b×c

Extremes × = means ×.

Unitary method

find one unit, then multiply

Solve word problems.

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Common mistakes & fixes

These are the exact errors that cost students marks in board exams. Read them once, save yourself the trouble.

WATCH OUT

✗ Comparing quantities in different units

✓ Convert to the same unit before forming a ratio.

WATCH OUT

✗ Adding to make equivalent ratios

✓ Multiply or divide both parts by the same number, not add.

WATCH OUT

✗ Cross-multiplying a proportion wrongly

✓ a : b = c : d means a × d = b × c.

NCERT exercises (with solutions)

Every NCERT exercise from this chapter — what it covers and how many questions to expect.

Ratios

Write and simplify ratios.

Questions

Proportion

Check proportions and find a missing term.

Questions

Unitary method

Cost and quantity word problems.

Questions

Practice problems

Try each one yourself before tapping "Show solution". Active recall > rereading.

Q1EASY· Simplify

Express 15 : 25 in simplest form.

▶ Show solution

3 : 5 (HCF 5).

Q2EASY· Equivalent

Write two equivalent ratios of 3 : 7.

▶ Show solution

6 : 14 and 9 : 21.

Q3MEDIUM· Proportion

Are 3 : 4 and 9 : 12 in proportion?

▶ Show solution

3 × 12 = 36 and 4 × 9 = 36 — equal, so yes.

Q4EASY· Proportion

Find x: 4 : 5 = x : 20.

▶ Show solution

4 × 20 = 5x → x = 16.

Q5MEDIUM· Unitary

If 5 kg of rice cost ₹200, find the cost of 8 kg.

▶ Show solution

1 kg = ₹40; 8 kg = ₹320.

Q6EASY· Ratio

Write the ratio of 4 boys to 6 girls in simplest form.

▶ Show solution

2 : 3.

5-minute revision

The whole chapter, distilled. Read this the night before the exam.

•Term 1 Chapter 3 of Samacheer Kalvi Class 6 Maths.
•A ratio a : b compares same-kind quantities in the same units.
•Simplest form: divide both parts by their HCF.
•Equivalent ratios are made by multiplying or dividing both parts by the same number.
•Proportion a : b = c : d means a × d = b × c.
•Use the unitary method (find one unit, then multiply) to solve problems.

Tamil Nadu (TNBSE) marks blueprint

Where the marks come from in this chapter — so you can plan your prep.

Typical chapter weightage: 6-10 marks across ratio, proportion and unitary method

Question type	Marks each	Typical count	What it tests
Ratio	1	2-3	Writing and simplifying
Proportion	1-2	1-2	Checking and missing term
Unitary method	2	1-2	Cost/quantity sums

Prep strategy

Convert to the same unit first
Simplify ratios using the HCF
Use ad = bc to test proportions
Find one unit before scaling

Where this shows up in the real world

This chapter isn't just an exam topic — it lives in the world around you.

Cooking

Recipes mix ingredients in fixed ratios.

Maps and models

Scales are ratios of drawing to real size.

Shopping

The unitary method finds the cost of any quantity.

Exam strategy

Battle-tested tips from teachers and toppers for this chapter.

Convert units before writing a ratio
Always reduce to simplest form
Use ad = bc for proportions
Show the one-unit value in unitary-method sums

Going beyond the textbook

For olympiad aspirants and curious learners — topics that build on this chapter.

Divide ₹600 between two people in the ratio 2 : 3.
If a : b = 2 : 3 and b : c = 4 : 5, find a : b : c.

Where else this chapter is tested

CBSE board isn't the only one — other exams test this chapter too.

TN Class 6 Term 1 ExamHigh

NMMS / Foundation MathsMedium

School unit testsHigh

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Questions students ask

The real ones — pulled from the Q&A community and tutor sessions.

A ratio compares how many times one quantity is of another; that comparison only makes sense if both are measured in the same unit, so we convert first (e.g. metres to centimetres).

Cross-multiply: a : b = c : d is a proportion only if a × d equals b × c.

Practice more, ask doubts, find a tutor

Tamil Nadu (TNBSE) Class 6 mock tests

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