Class 7 · NCERT Maths

Chapter 1

Integers

Revise integer operations and apply them in word problems. Learn the ideas, see how they connect, and practise until you can choose the next step without help.

AdditionSubtractionMultiplication

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Study board

Quick reference
Concept 01Addition
Concept 02Subtraction
Concept 03Multiplication

NCERT chapter notes

Integers, clearly explained

Integers uses positive and negative numbers to describe direction and change: gains and losses, temperatures above and below zero, elevations, and movement on a number line. The chapter then develops reliable sign rules for all four operations.

Students should model unfamiliar questions on a number line or with a real context before applying rules. A memorised rule without direction sense is the main reason signs are reversed.

Core concepts

Key concepts and formulae

01

Order on the number line

Numbers increase as we move right and decrease as we move left. Every positive integer is greater than zero; zero is greater than every negative integer; among negative integers, the one closer to zero is greater.

02

Addition and subtraction

Adding a positive integer moves right and adding a negative integer moves left. Subtracting an integer is the same as adding its additive inverse: a − b = a + (−b).

03

Multiplication and division signs

Same signs give a positive result; different signs give a negative result. This applies to both multiplication and division, but division by zero is not defined.

04

Properties

Integers are closed under addition, subtraction, and multiplication. Addition and multiplication are commutative and associative; subtraction is neither. Multiplication distributes over addition and subtraction.

Exam practice

Important questions, with worked answers

Use each answer to check the method and wording—not as a paragraph to memorise.

Q1Arrange −3, 5, 0, −8, and 2 in ascending order.

Answer

From smallest to greatest: −8, −3, 0, 2, 5.

Q2Find −7 − (−12).

Answer

Subtracting a negative means adding its opposite: −7 − (−12) = −7 + 12 = 5.

Q3Find (−6) × 8 and explain the sign.

Answer

The factors have different signs, so the product is negative. 6 × 8 = 48, therefore (−6) × 8 = −48.

Q4A temperature of 4°C falls by 9°C. What is the new temperature?

Answer

A fall of 9 means add −9: 4 + (−9) = −5. The new temperature is −5°C.

Fast recall

Key terms to remember

Integer: A whole number, its negative, or zero.

Additive inverse: The number that adds to a given number to make zero.

Absolute value: A number's distance from zero, written without a sign.

Closure: A property where performing an operation on members of a set gives a result in the same set.

A repeatable method

How to learn Integers properly

  1. 1

    Start with the chapter promise

    Revise integer operations and apply them in word problems. Before solving, the student should be able to say what the chapter is trying to teach and which kind of problem it helps solve.

  2. 2

    Build the core vocabulary

    The important words for this chapter are Addition, Subtraction and Multiplication. Eduro should make the student define each one in simple language, then use it in a question or explanation.

  3. 3

    Move from recognition to recall

    Recognition means the answer makes sense after seeing it. Recall means the student can produce the next step independently. This page is built for recall, because that is what tests reward.

  4. 4

    Close the loop with practice

    A strong study session ends with mixed numericals, not only reading. The student should solve, review the mistake, and then attempt a similar question before moving on.

Before the test

Where students usually lose marks

Look for the first wrong decision—not only the final wrong answer. That is the mistake worth repairing.

Mistake 1

Knowing Addition only after seeing the solution

This is the most common hidden gap. The student feels confident while reading, but cannot choose the starting step alone. Eduro should ask a short diagnostic question before explaining the method.

Mistake 2

Treating Integers as a memory chapter

Even memory-heavy chapters need reasoning. A memorised line becomes fragile when the question changes. The student should explain why the answer works, not only what the answer is.

Mistake 3

Skipping the checking step

calculation slip usually survives because the student finishes the answer and moves on. Eduro should make review part of the answer: what was asked, what was used, and whether the final response fits.

Try it with Eduro

Practice that builds real confidence

Say it naturally, as you would to a patient teacher. Each prompt below is designed to make understanding visible.

Prompt 1

Ask Eduro to explain Integers through Addition before showing any solved answer.

Prompt 2

Create five questions that separately test Addition, Subtraction and Multiplication.

Prompt 3

Give one wrong answer from Integers and ask the student to find the first incorrect step.

Prompt 4

End with a mixed mini-test where Eduro does not reveal which skill is being tested.

For parents

A better way to ask, “Is the chapter done?”

For Class 7 Maths, a good sign is not that the child says 'Integers is done.' A better sign is that they can explain Addition, solve one fresh question, and correct one mistake without panic.

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Reviewed for the 2025-26 CBSE/NCERT study cycle

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Quick help

Common questions

How can I study Integers for NCERT Class 7?

Start with the NCERT examples, understand the key ideas in Addition, Subtraction, Multiplication, then practice exercise questions and ask Eduro where you get stuck.

Can Eduro help with Integers?

Yes. Eduro can explain Integers step by step, answer follow-up doubts, and help students practice related Maths questions.