The World of Numbers Exercise 3.3 Class 9 Maths NCERT Solutions

This page solves The World of Numbers Exercise 3.3 from the new Ganita Manjari book of the 2026-27 syllabus. The NCERT Solutions Class 9 Maths Chapter 3 The World of Numbers Exercise 3.3 add, subtract, multiply, and divide rational numbers, with every common denominator shown in clear steps.

• Questions solved: all 8 problems of Exercise 3.3, with full working.
• Main skills: equal fractions and the four operations on rational numbers.
• Chapter link: it builds the fraction skills needed for ordering and decimals next.

These solutions are prepared by subject teachers, matched to the 2026-27 NCERT, and checked step by step so a Class 9 student can follow each line.

What Does Class 9 Maths Chapter 3 The World of Numbers Exercise 3.3 Cover?

Exercise 3.3 is the main practice set for rational numbers. You prove that two fractions are equal, then add, subtract, multiply, and divide them. The set also uses the distributive property and asks you to find an unknown rational number. Every part relies on finding a common denominator or cancelling common factors.

Rational numbers are the heart of this chapter, so Exercise 3.3 gives the most practice. Each of the four operations follows one clear habit: match the denominators, then work with the numerators. Addition and subtraction need a common denominator. Multiplication is a straight product of the tops and the bottoms. Division flips the second fraction and then multiplies. Once these become routine, the harder questions on ordering and decimals feel much easier. A good habit is to reduce every answer to its lowest terms, since the exam expects the simplest form. Working through all eight questions here builds the speed and accuracy you need for the End-of-Chapter test and for Class 10.

Video Walkthrough

Source: Vedantu CBSE 10th on YouTube

The World of Numbers Exercise 3.3 Question Breakdown

The eight questions cover each operation on rational numbers in turn. Here is what each one asks.

• Q1: Prove that two given rational numbers are equal.
• Q2 to Q5: Find the sum, difference, product, and quotient of rational numbers.
• Q6: Show a stated equality between rational numbers.
• Q7: Simplify an expression using the distributive property.
• Q8: Find the rational number x that satisfies a given equation.

Sample Solved Question from Exercise 3.3

Here is Question 2 of Exercise 3.3, solved step by step so you can see how a common denominator works.

Question: Find the sum: (i) 25+310, (ii) 712+58, (iii) -47+314.

Step 1. For part (i), the LCM of 5 and 10 is 10. Write 25=410, so 410+310=710.

Step 2. For part (ii), the LCM of 12 and 8 is 24. Write 712=1424 and 58=1524, so the sum is 2924.

Step 3. For part (iii), the LCM of 7 and 14 is 14. Write -47=-814, so -814+314=-514.

Final answer. The three sums are 710, 2924, and -514.

How to Use These The World of Numbers Exercise 3.3 Solutions

Work each fraction sum by hand first, then open the Collegedunia solution to check your denominator. You can also confirm any answer by turning the fractions into decimals.

• Find the LCM, rewrite both fractions, then add or subtract only the numerators.
• Cancel common factors at the end so the answer is in lowest terms.
• Download the free Collegedunia PDF to revise Exercise 3.3 offline.

More Class 9 Maths The World of Numbers Solutions

Use the table below to open the full chapter page or any other exercise of Class 9 Maths Chapter 3.