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Tamil Nadu (TNBSE)Class 6 Mathematics★ 6-10 marks in the TN Class 6 Term 3 exam through integer ordering and operation sums

Integers

Samacheer Kalvi (TN State Board) Class 6 Maths — Term 3 Chapter 2, Integers. Positive and negative numbers, representing integers on the number line, ordering integers, the additive inverse, and adding and subtracting integers, 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…

1Identify positive and negative integers
2Represent integers on the number line
3Order integers
4Find the additive inverse
5Add and subtract integers

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Why this chapter matters

Integers extend numbers below zero — needed for temperature, money and later algebra. Ordering integers and adding/subtracting them are directly tested 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 1 — Numbers (Whole Numbers)

The number line.

Integers — Class 6 Maths (Samacheer Kalvi)

TN State Board (Samacheer Kalvi) Class 6 Mathematics, Term 3 — Chapter 2. Numbers below zero and the number line.

1. About this chapter

This chapter introduces integers — positive and negative whole numbers — their representation on the number line, ordering, the additive inverse, and addition and subtraction.

2. What are integers?

Integers are … −3, −2, −1, 0, 1, 2, 3 … — the positive numbers, the negative numbers and zero.
Negative integers are used for ideas like below zero, below sea level, loss and owing money.

3. The number line and ordering

On the number line, 0 is the centre; positive integers lie to the right and negative integers to the left.
A number to the right is greater: so −5 < −2 < 0 < 3.

4. Additive inverse, addition and subtraction

The additive inverse of an integer is the number that adds with it to give 0: the additive inverse of 4 is −4 (and of −7 is 7).
Adding integers: same signs → add and keep the sign; different signs → subtract and take the sign of the larger. (−3) + 5 = 2; (−3) + (−5) = −8.
Subtracting an integer = adding its additive inverse: 4 − (−2) = 4 + 2 = 6.

5. Worked examples

Example 1. Which is greater, −8 or −3? −3 is to the right of −8 → −3 is greater.

Example 2. Find the additive inverse of −9. 9 (since −9 + 9 = 0).

Example 3. Evaluate 6 + (−10). Different signs → 10 − 6 = 4, sign of larger (10) → −4.

6. Exercises (Samacheer Kalvi)

Represent −4, 0 and 2 on the number line.
Arrange in ascending order: 3, −5, 0, −1, 4.
Write the additive inverse of (a) 7 (b) −12.
Find: (a) (−6) + 9 (b) (−4) + (−7) (c) 5 − (−3).
The temperature was −2 °C and rose by 5 °C. Find the new temperature.

7. Common mistakes

Mistake: Thinking −8 is greater than −3. Fix: On the number line, the number further right is greater, so −3 > −8.
Mistake: Treating subtraction of a negative as subtraction. Fix: Subtracting a negative is the same as adding: 4 − (−2) = 4 + 2.
Mistake: Wrong sign when adding different signs. Fix: Subtract and take the sign of the larger number.

8. Quick revision

Term 3 · Ch 2 · integers.
Integers: … −2, −1, 0, 1, 2 …; negatives to the left of 0, positives to the right; right = greater.
Additive inverse adds to 0 (inverse of 5 is −5).
Same signs: add and keep sign; different signs: subtract, take sign of larger; subtracting a negative = adding.

Key formulas & results

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

Integers

… −2, −1, 0, 1, 2 …

Negatives, zero, positives.

Ordering

number further right on the line is greater

−5 < −2 < 0 < 3.

Additive inverse

the number that adds to give 0

Inverse of 4 is −4.

Subtraction

subtract a negative = add its inverse

4 − (−2) = 6.

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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

✗ Thinking −8 is greater than −3

✓ The number further right on the number line is greater, so −3 > −8.

WATCH OUT

✗ Treating subtraction of a negative as subtraction

✓ Subtracting a negative is the same as adding: 4 − (−2) = 4 + 2.

WATCH OUT

✗ Wrong sign when adding different signs

✓ Subtract and take the sign of the larger number.

NCERT exercises (with solutions)

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

Number line and ordering

Represent and order integers.

Questions

Additive inverse

Find additive inverses.

Questions

Operations

Add and subtract integers.

Questions

Practice problems

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

Q1EASY· Order

Which is greater, −8 or −3?

▶ Show solution

−3.

Q2EASY· Inverse

Find the additive inverse of −9.

▶ Show solution

9.

Q3EASY· Add

Evaluate 6 + (−10).

▶ Show solution

−4.

Q4EASY· Subtract

Evaluate 5 − (−3).

▶ Show solution

5 + 3 = 8.

Q5MEDIUM· Order

Arrange in ascending order: 3, −5, 0, −1, 4.

▶ Show solution

−5 < −1 < 0 < 3 < 4.

Q6MEDIUM· Word problem

The temperature was −2 °C and rose by 5 °C. Find the new temperature.

▶ Show solution

−2 + 5 = 3 °C.

5-minute revision

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

•Term 3 Chapter 2 of Samacheer Kalvi Class 6 Maths.
•Integers are … −2, −1, 0, 1, 2 …; negatives left of 0, positives right.
•A number further right on the number line is greater.
•The additive inverse of a number adds with it to give 0.
•Same signs: add and keep sign; different signs: subtract, take sign of larger.
•Subtracting a negative is the same as adding.

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 integers

Question type	Marks each	Typical count	What it tests
Objective	1	3-4	Ordering, inverse, operations
Ordering	2	1	Ascending/descending
Word problem	2	1	Temperature/level

Prep strategy

Picture the number line for ordering
Remember right = greater
Use additive inverse for subtraction
Apply the sign rules for addition

Where this shows up in the real world

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

Temperature

Below-zero temperatures are negative integers.

Money

Debts and losses are shown as negatives.

Elevation

Depths below sea level use negative integers.

Exam strategy

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

Draw a number line for ordering
Use right = greater
Convert subtraction of a negative to addition
Apply the sign rules carefully

Going beyond the textbook

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

Find the sum of all integers from −5 to 5.
A diver at −30 m rises 12 m. Find the new depth.

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 MathsMedium

School unit testsHigh

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Questions students ask

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

On the number line −3 lies to the right of −8, and any number to the right is greater; −3 is closer to zero, while −8 is further below it.

It is the number you add to a given integer to get 0 — for example, the additive inverse of 6 is −6 because 6 + (−6) = 0.

Practice more, ask doubts, find a tutor

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