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Tamil Nadu (TNBSE)Class 6 Mathematics★ 8-12 marks in the TN Class 6 Term 3 exam through fraction operations and comparison sums

Fractions

Samacheer Kalvi (TN State Board) Class 6 Maths — Term 3 Chapter 1, Fractions. Types of fractions, equivalent fractions and simplest form, comparing fractions, mixed and improper fractions, and the four operations on fractions, with worked examples, exercises and quick revision.

⏱ 15 min readEasy difficulty✓ Free · NCERT-aligned

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

1Identify proper, improper and mixed fractions
2Form equivalent fractions and reduce to simplest form
3Compare like and unlike fractions
4Add and subtract fractions
5Multiply and divide fractions

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Why this chapter matters

Fractions are essential for measurement, money and later ratio and algebra. The types, comparison and four operations on fractions are high-weight, directly tested topics in the TN Class 6 Term 3 exam.

Before you start — revise these

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

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Term 2 — Numbers (Factors and Multiples)

HCF and LCM.

Fractions — Class 6 Maths (Samacheer Kalvi)

TN State Board (Samacheer Kalvi) Class 6 Mathematics, Term 3 — Chapter 1. Working with parts of a whole.

1. About this chapter

This chapter covers types of fractions, equivalent fractions and simplest form, comparing fractions, mixed and improper fractions, and the four operations on fractions.

2. Types of fractions

A fraction a/b has a numerator (a) and a denominator (b).
Proper fraction: numerator < denominator (3/5). Improper fraction: numerator ≥ denominator (7/4). Mixed fraction: a whole number with a proper fraction (1¾).
Like fractions have the same denominator (2/7, 5/7); unlike fractions have different denominators.

3. Equivalent fractions and simplest form

Equivalent fractions have the same value, got by multiplying or dividing numerator and denominator by the same number: 1/2 = 2/4 = 3/6.
Simplest form: divide both parts by their HCF (6/8 = 3/4).

4. Comparing fractions

Like fractions: the one with the larger numerator is greater.
Unlike fractions: make the denominators the same (LCM), then compare, or cross-multiply.

5. Operations on fractions

Add/subtract like fractions: add/subtract numerators, keep the denominator (2/7 + 3/7 = 5/7).
Add/subtract unlike fractions: convert to the same denominator (LCM) first.
Multiply: multiply numerators and denominators (2/3 × 4/5 = 8/15).
Divide: multiply by the reciprocal (2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6).

6. Worked examples

Example 1. Reduce 12/18 to simplest form. HCF 6 → 2/3.

Example 2. Add 1/4 + 1/6. LCM 12 → 3/12 + 2/12 = 5/12.

Example 3. Convert 7/3 to a mixed fraction. 7 ÷ 3 = 2 remainder 1 → 2⅓.

7. Exercises (Samacheer Kalvi)

Classify as proper, improper or mixed: 3/8, 9/4, 2½.
Write two equivalent fractions of 3/5.
Compare: (a) 3/7 and 5/7 (b) 2/3 and 3/4.
Add 2/5 + 1/3 and subtract 5/6 − 1/4.
Multiply 3/4 × 2/9 and divide 5/8 ÷ 1/2.

8. Common mistakes

Mistake: Adding denominators when adding fractions. Fix: Keep (or equalise) the denominator; add only the numerators.
Mistake: Forgetting to use the reciprocal when dividing. Fix: Divide = multiply by the reciprocal of the second fraction.
Mistake: Not reducing to simplest form. Fix: Always simplify the final fraction using the HCF.

9. Quick revision

Term 3 · Ch 1 · fractions.
Proper (< 1), improper (≥ 1), mixed; like = same denominator.
Equivalent fractions: × or ÷ both parts by the same number; simplest form via HCF.
Add/subtract: same denominator (LCM); multiply across; divide = × reciprocal.

Key formulas & results

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

Types

proper (< 1), improper (≥ 1), mixed

By numerator vs denominator.

Equivalent / simplest

× or ÷ both parts by the same number; reduce by HCF

Same value.

Add / subtract

make denominators equal (LCM), then add/subtract numerators

Like fractions only.

Multiply / divide

multiply across; divide = × reciprocal

Then simplify.

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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

✗ Adding denominators when adding fractions

✓ Keep (or equalise) the denominator; add only the numerators.

WATCH OUT

✗ Forgetting to use the reciprocal when dividing

✓ Divide = multiply by the reciprocal of the second fraction.

WATCH OUT

✗ Not reducing to simplest form

✓ Always simplify the final fraction using the HCF.

NCERT exercises (with solutions)

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

Types and equivalent

Classify and form equivalent fractions.

Questions

Comparing

Compare like and unlike fractions.

Questions

Operations

Add, subtract, multiply and divide fractions.

Questions

Practice problems

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

Q1EASY· Simplify

Reduce 12/18 to simplest form.

▶ Show solution

2/3 (HCF 6).

Q2MEDIUM· Add

Add 1/4 + 1/6.

▶ Show solution

LCM 12: 3/12 + 2/12 = 5/12.

Q3EASY· Convert

Convert 7/3 to a mixed fraction.

▶ Show solution

2⅓.

Q4MEDIUM· Compare

Which is greater, 2/3 or 3/4?

▶ Show solution

LCM 12: 8/12 vs 9/12, so 3/4 is greater.

Q5EASY· Multiply

Multiply 3/4 × 2/9.

▶ Show solution

6/36 = 1/6.

Q6MEDIUM· Divide

Divide 5/8 ÷ 1/2.

▶ Show solution

5/8 × 2/1 = 10/8 = 5/4 = 1¼.

5-minute revision

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

•Term 3 Chapter 1 of Samacheer Kalvi Class 6 Maths.
•Proper fraction < 1, improper ≥ 1, mixed = whole + proper.
•Equivalent fractions: multiply/divide both parts by the same number; simplest form via HCF.
•Compare like fractions by numerator; unlike by making denominators equal.
•Add/subtract: equalise denominators (LCM), then operate on numerators.
•Multiply across; divide by multiplying by the reciprocal.

Tamil Nadu (TNBSE) marks blueprint

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

Typical chapter weightage: 8-12 marks across fraction work

Question type	Marks each	Typical count	What it tests
Objective	1	3-4	Types, simplest form
Add/subtract	2	2	Like and unlike fractions
Multiply/divide	2	2	Product and reciprocal

Prep strategy

Use the LCM for unlike denominators
Add only numerators after equalising
Multiply by the reciprocal to divide
Always reduce the answer

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 use fractions of cups and spoons.

Measurement

Lengths and weights are split into fractions.

Sharing

Dividing things equally uses fractions.

Exam strategy

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

Find the LCM for unlike denominators
Add only the numerators after equalising
Flip and multiply to divide
Reduce the final answer

Going beyond the textbook

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

Arrange 2/3, 3/4, 5/6 in ascending order.
Find 2/3 of 3/5 of 90.

Where else this chapter is tested

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

TN Class 6 Term 3 ExamHigh

NMMS / Foundation MathsHigh

School unit testsHigh

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Questions students ask

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

Because the denominator tells the size of each part; only when the parts are the same size can you simply add how many parts you have (the numerators).

Multiply the first fraction by the reciprocal (the flipped form) of the second — for example, 2/3 ÷ 4/5 = 2/3 × 5/4.

Practice more, ask doubts, find a tutor

Tamil Nadu (TNBSE) Class 6 mock tests

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