The World of Numbers Exercise 3.4 Class 9 Maths NCERT Solutions

This page solves The World of Numbers Exercise 3.4 from the new Ganita Manjari book of the 2026-27 syllabus. The NCERT Solutions Class 9 Maths Chapter 3 The World of Numbers Exercise 3.4 place rational numbers on the line, find numbers between two others, and simplify signed fractions in clear steps.

• Questions solved: all 6 problems of Exercise 3.4, with full working.
• Main skills: ordering rational numbers and finding numbers between any two.
• Chapter link: it shows how densely rational numbers sit on the number line.

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 3.4 Cover?

Exercise 3.4 puts rational numbers on the number line and in order. You represent fractions on the line, then find numbers that lie between two given ones. The set also simplifies a signed fraction sum and solves a cloth-measuring word problem. It ends by asking for another method to find a number between any two rationals.

Ordering rational numbers is a quiet but important skill for the whole year. Many students can add fractions yet still struggle to say which of two fractions is larger. This exercise fixes that by asking you to place numbers on the line and to find numbers between them. The main idea is simple: rewrite the fractions with the same denominator, then compare or list the numerators. Because you can always choose a larger denominator, there are infinitely many rational numbers between any two points. Seeing this clearly now makes the later work on real numbers in Class 10 much smoother, and it removes the guesswork from ordering questions in the annual exam.

Video Walkthrough

Source: Vedantu CBSE 10th on YouTube

The World of Numbers Exercise 3.4 Question Breakdown

The six questions build ordering and betweenness skills. Here is what each one asks.

• Q1: Represent 23, -54, and another fraction on the number line.
• Q2: Find three distinct rational numbers strictly between two given fractions.
• Q3: Simplify (-14)+(512).
• Q4: Solve a tailor's silk problem using division of mixed numbers.
• Q5: Find three rational numbers between 3.1415 and 3.1416.
• Q6: Suggest another way to find a rational number between any two.

Sample Solved Question from Exercise 3.4

Here is Question 3 of Exercise 3.4, solved step by step so you can see how signed fractions add.

Question: Simplify the expression (-14)+(512).

Step 1. Find the common denominator. The LCM of 4 and 12 is 12. Rewrite -14=-312.

Step 2. Add the numerators over the common denominator: -312+512=-3+512=212.

Step 3. Reduce to lowest terms by dividing top and bottom by 2: 212=16.

Final answer. The value of the expression is 16.

How to Use These The World of Numbers Exercise 3.4 Solutions

Draw the number line and try each question first, then open the Collegedunia solution to check your order. Seeing the steps helps you place any fraction with confidence.

• Rewrite fractions with a shared denominator before you compare or place them.
• Pick a bigger common denominator when you need more numbers between two points.
• Download the free Collegedunia PDF to revise Exercise 3.4 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.