---
title: "NCERT Solutions for Class 9 Maths Chapter 3 Exercise 3.4"
url: https://www.swavid.com/maths/class/9/chapter/the-world-of-numbers/ncert-solutions/exercise-3-4
dateModified: 2026-10-07T15:46:03+00:00
---

# NCERT Solutions for Class 9 Maths Chapter 3 Exercise 3.4

Chapter 3: The World of Numbers. Every question from Exercise 3.4, with full working and the final answer.

Free PDF (22 pages): https://www.swavid.com/api/seo/pdf/ncert/maths/class-9/swavid-ncert-solutions-class-9-maths-chapter-3-the-world-of-numbers-521b6f38aa.pdf

## Exercise Set 3.4

### Question 1

*3 marks · Short answer*

Represent the rational numbers $\frac{2}{3}$, $-\frac{5}{4}$ and $1\frac{1}{2}$ on a single number line.

**Solution**

1. Draw a number line with integers marked at equal intervals.
2. To represent $\frac{2}{3}$, divide the unit interval between 0 and 1 into 3 equal parts and mark the 2nd part to the right of 0.
3. To represent $-\frac{5}{4} = -1\frac{1}{4}$, divide the unit interval between $-1$ and $-2$ into 4 equal parts and move 1 part to the left of $-1$.
4. To represent $1\frac{1}{2} = \frac{3}{2}$, mark the point exactly halfway between 1 and 2.
5. The rational numbers $\frac{2}{3}$, $-\frac{5}{4}$, and $1\frac{1}{2}$ are marked on the single number line.

**Answer:** The rational numbers $\frac{2}{3}$, $-\frac{5}{4}$, and $1\frac{1}{2}$ represented on the number line.

> Common mistake: Dividing the wrong unit interval or miscounting the subdivisions.

### Question 2

*3 marks · Short answer*

Find three distinct rational numbers that lie strictly between $-\frac{1}{2}$ and $\frac{1}{4}$.

**Solution**

1. First, express the given rational numbers $-\frac{1}{2}$ and $\frac{1}{4}$ with a common denominator.
2. The LCM of 2 and 4 is 4, so $-\frac{1}{2} = -\frac{2}{4}$ and $\frac{1}{4} = \frac{1}{4}$.
3. To easily find three distinct rational numbers between $-\frac{2}{4}$ and $\frac{1}{4}$, multiply both the numerator and denominator of both fractions by a suitable factor, say 4, to get $-\frac{8}{16}$ and $\frac{4}{16}$.
4. Three distinct rational numbers between $-\frac{8}{16}$ and $\frac{4}{16}$ are $-\frac{3}{16}, -\frac{2}{16}, \frac{1}{16}$ (or any other valid choices such as $-\frac{1}{4}, 0, \frac{1}{8}$).
5. Hence, three rational numbers strictly between $-\frac{1}{2}$ and $\frac{1}{4}$ are $-\frac{1}{4}, 0, \frac{1}{8}$.

**Answer:** $-\frac{1}{4}, 0, \frac{1}{8}$

> Common mistake: Failing to make the denominators equal before comparing or finding numbers between them.

### Question 3

*3 marks · Short answer*

Simplify the expression: $-\left(-\frac{1}{4}\right) + \left(\frac{5}{12}\right)$.

**Solution**

1. Given the expression: $-\left(-\frac{1}{4}\right) + \left(\frac{5}{12}\right)$.
2. Using the rule that the product of two negatives is positive, $-\left(-\frac{1}{4}\right) = \frac{1}{4}$.
3. Now add $\frac{1}{4}$ and $\frac{5}{12}$ by finding a common denominator.
4. The least common multiple of $4$ and $12$ is $12$, so convert $\frac{1}{4}$ to an equivalent fraction with denominator $12$: $\frac{1 \times 3}{4 \times 3} = \frac{3}{12}$.
5. Add the numerators: $\frac{3}{12} + \frac{5}{12} = \frac{3 + 5}{12} = \frac{8}{12}$.
6. Simplify the fraction by dividing the numerator and denominator by their highest common factor, $4$, to get $\frac{2}{3}$.

**Answer:** $\frac{2}{3}$

> Common mistake: Failing to change the sign of $-\left(-\frac{1}{4}\right)$ to positive.

### Question 4

*3 marks · Short answer*

A tailor has $15\frac{3}{4}$ metres of fine silk. If making one kurta requires $2\frac{1}{4}$ metres of silk, exactly how many kurtas can he make?

**Solution**

1. Total length of silk available = $15\frac{3}{4} = \frac{63}{4}$ metres.
2. Silk required for one kurta = $2\frac{1}{4} = \frac{9}{4}$ metres.
3. To find the number of kurtas, divide the total length by the length required for one kurta: $\frac{63}{4} \div \frac{9}{4}$.
4. Multiply by the reciprocal of the divisor: $\frac{63}{4} \times \frac{4}{9} = \frac{63}{9}$.
5. Calculate the final result: $\frac{63}{9} = 7$.

**Answer:** $7$ kurtas

> Common mistake: Multiplying the fractions instead of dividing.

### Question 5

*3 marks · Short answer*

Find three rational numbers between $3.1415$ and $3.1416$.

**Solution**

1. Given decimal numbers are $3.1415$ and $3.1416$.
2. Pad the decimals with trailing zeros to make them comparable: $3.14150$ and $3.14160$.
3. Choose numbers whose decimal parts lie strictly between $150$ and $160$ at the fifth decimal place.
4. Three such rational numbers are $3.14151$, $3.14152$, and $3.14155$.

**Answer:** $3.14151$, $3.14152$, $3.14155$

> Common mistake: Failing to equalize the number of decimal places before finding intermediate values.

### Question 6

*3 marks · Short answer*

Can you think of other way(s) to find a rational number between any two rational numbers?

**Solution**

1. One common method is converting the two rational numbers to equivalent fractions with a common denominator and choosing numerators between them.
2. Another method is using decimal representations of the rational numbers and finding terminating or repeating decimals strictly between them.
3. A third method is repeatedly applying the mean (average) formula $\frac{a + b}{2}$ to find successive midpoints between the numbers.

**Answer:** Using equivalent fractions with common denominators, decimal representations, or repeated averaging.

> Common mistake: Stating only one method when multiple ways are asked.

## Related pages

- [All Chapter 3 NCERT solutions](https://www.swavid.com/maths/class/9/chapter/the-world-of-numbers/ncert-solutions)
- [Exercise 3.1](https://www.swavid.com/maths/class/9/chapter/the-world-of-numbers/ncert-solutions/exercise-3-1)
- [Exercise 3.2](https://www.swavid.com/maths/class/9/chapter/the-world-of-numbers/ncert-solutions/exercise-3-2)
- [Exercise 3.3](https://www.swavid.com/maths/class/9/chapter/the-world-of-numbers/ncert-solutions/exercise-3-3)
- [Exercise 3.5](https://www.swavid.com/maths/class/9/chapter/the-world-of-numbers/ncert-solutions/exercise-3-5)

Solutions written by SwaVid, a personal AI tutor for Class 6 to 10 Maths and Science. Practise this chapter free: https://www.swavid.com/start/student