Class 7 · NCERT Maths

Chapter 8

Rational Numbers

Compare, represent, and operate on rational numbers. Learn the ideas, see how they connect, and practise until you can choose the next step without help.

Number lineComparisonOperations

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Study board

Quick reference
Concept 01Number line
Concept 02Comparison
Concept 03Operations

NCERT chapter notes

Rational Numbers, clearly explained

Rational Numbers extends fractions to include positive and negative numbers written as p/q, where p and q are integers and q is not zero. The chapter focuses on standard form, comparison, number-line representation, and the four operations.

Sign rules are the main source of mistakes. Students should decide the sign first, then work with the numerical parts, and simplify the final fraction using a common factor.

Core concepts

Key concepts and formulae

01

Meaning and standard form

A rational number is p/q with integers p and q and q ≠ 0. In standard form, the denominator is positive and p and q have no common factor other than 1.

02

Equivalent rational numbers

Multiplying or dividing numerator and denominator by the same non-zero integer gives an equivalent rational number. This is used to compare numbers and find common denominators.

03

Operations

For addition and subtraction, use a common denominator. For multiplication, multiply numerators and denominators. For division, multiply by the reciprocal of the non-zero divisor.

04

Properties

Rational numbers are closed under addition, subtraction, and multiplication, and under division by a non-zero rational number. Addition and multiplication are commutative and associative; subtraction and division are not.

Exam practice

Important questions, with worked answers

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

Q1Write −18/24 in standard form.

Answer

Divide numerator and denominator by their HCF, 6: −18/24 = −3/4. The denominator is positive and 3 and 4 are coprime.

Q2Which is greater: −3/5 or −4/7?

Answer

Use denominator 35: −3/5 = −21/35 and −4/7 = −20/35. Since −20/35 is greater, −4/7 is greater.

Q3Find −2/3 + 5/6.

Answer

Use denominator 6: −2/3 = −4/6. Then −4/6 + 5/6 = 1/6.

Q4Find (−7/8) ÷ (14/3).

Answer

Multiply by the reciprocal: (−7/8) × (3/14). Cancel 7 with 14 to get (−1/8) × (3/2) = −3/16.

Fast recall

Key terms to remember

Rational number: A number expressible as p/q, where p and q are integers and q is not zero.

Standard form: A rational number with positive denominator and coprime numerator and denominator.

Reciprocal: For non-zero p/q, the reciprocal is q/p.

Additive inverse: The number that gives zero when added; the additive inverse of p/q is −p/q.

A repeatable method

How to learn Rational Numbers properly

  1. 1

    Start with the chapter promise

    Compare, represent, and operate on rational numbers. 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 Number line, Comparison and Operations. 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 Number line 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 Rational Numbers 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 Rational Numbers through Number line before showing any solved answer.

Prompt 2

Create five questions that separately test Number line, Comparison and Operations.

Prompt 3

Give one wrong answer from Rational Numbers 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 'Rational Numbers is done.' A better sign is that they can explain Number line, solve one fresh question, and correct one mistake without panic.

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Quick help

Common questions

How can I study Rational Numbers for NCERT Class 7?

Start with the NCERT examples, understand the key ideas in Number line, Comparison, Operations, then practice exercise questions and ask Eduro where you get stuck.

Can Eduro help with Rational Numbers?

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