Class 9 Maths Chapter 3 Exercise 3.4 Solutions | 2026-27

-5/4 lies between -2 and -1.

2/3 lies between 0 and 1.

1 1/2 lies between 1 and 2.

Question 2: Find three distinct rational numbers that lie strictly between -1/2 and 1/4.

Solution:

We need to find three rational numbers greater than -1/2 and less than 1/4.

One simple way is to use the average method.

First, find the average of -1/2 and 1/4.

Average = (-1/2 + 1/4) ÷ 2

Now add -1/2 and 1/4.

LCM of 2 and 4 is 4.

-1/2 = -2/4

So:

-1/2 + 1/4 = -2/4 + 1/4 = -1/4

Now divide by 2:

-1/4 ÷ 2 = -1/8

So, -1/8 lies between -1/2 and 1/4.

Now find another rational number between -1/2 and -1/8.

Average = (-1/2 + -1/8) ÷ 2

Convert -1/2 to a denominator of 8.

-1/2 = -4/8

So:

-4/8 + -1/8 = -5/8

Now divide by 2:

-5/8 ÷ 2 = -5/16

So, -5/16 lies between -1/2 and -1/8.

Now find a rational number between -1/8 and 1/4.

Average = (-1/8 + 1/4) ÷ 2

Convert 1/4 to a denominator of 8.

1/4 = 2/8

So:

-1/8 + 2/8 = 1/8

Now divide by 2:

1/8 ÷ 2 = 1/16

So, 1/16 lies between -1/8 and 1/4.

Final Answer:

Three rational numbers strictly between -1/2 and 1/4 are:

-5/16, -1/8 and 1/16

Question 3: Simplify the expression -1/4 + 5/12.

Solution:

We need to simplify:

-1/4 + 5/12

The denominators are 4 and 12.

LCM of 4 and 12 is 12.

Now convert -1/4 into a fraction with a denominator of 12.

-1/4 = -3/12

Now add:

-3/12 + 5/12 = 2/12

Simplify 2/12.

Both 2 and 12 are divisible by 2.

2/12 = 1/6

Final Answer:

-1/4 + 5/12 = ⅙

Question 4: A tailor has 15 3/4 metres of fine silk. If making one kurta requires 2 1/4 metres of silk, exactly how many kurtas can he make?

Solution:

Total silk available = 15 3/4 metres

Silk required for one kurta = 2 1/4 metres

To find the number of kurtas, divide the total silk by the silk required for one kurta.

First, convert the mixed fractions into improper fractions.

15 3/4 = (15 × 4 + 3) / 4

= (60 + 3) / 4

= 63/4

Now:

2 1/4 = (2 × 4 + 1) / 4

= (8 + 1) / 4

= 9/4

Now divide:

63/4 ÷ 9/4

To divide by a fraction, multiply by its reciprocal.

So:

63/4 × 4/9

Now cancel 4 from the numerator and denominator.

We get:

63/9 = 7

Therefore, the tailor can make 7 kurtas.

Final Answer:

The tailor can make exactly 7 kurtas.

Question 5: Find three rational numbers between 3.1415 and 3.1416.

Solution:

We need to find three rational numbers that lie between 3.1415 and 3.1416.

First, write both numbers with the same number of decimal places.

3.1415 = 3.14150

3.1416 = 3.14160

Now choose any three decimal numbers between 3.14150 and 3.14160.

For example:

• 3.14151

• 3.14152

• 3.14153

These numbers are greater than 3.14150 and smaller than 3.14160.

They are also terminating decimals, so they are rational numbers.

Final Answer:

Three rational numbers between 3.1415 and 3.1416 are:

3.14151, 3.14152, and 3.14153

Question 6: Can you think of other ways to find a rational number between any two rational numbers?

Solution:

Yes, there are many ways to find a rational number between two rational numbers.

One useful method is the common denominator method.

Suppose we need to find a rational number between 1/3 and 1/2.

First, write both fractions with a common denominator.

LCM of 3 and 2 is 6.

So:

1/3 = 2/6

1/2 = 3/6

No integer numerator lies between 2 and 3.

So, we can make the denominator bigger.

Multiply both fractions by 2/2.

1/3 = 4/12

1/2 = 6/12

Now 5/12 lies between 4/12 and 6/12.

Therefore, 5/12 lies between 1/3 and 1/2.

Another method is the average method.

The average of any two rational numbers always lies between them.

For example:

Average of 1/3 and 1/2

= (1/3 + 1/2) ÷ 2

= (2/6 + 3/6) ÷ 2

= 5/6 ÷ 2

= 5/12

So, 5/12 lies between 1/3 and 1/2.

We can also use decimal form.

1/3 = 0.333...

1/2 = 0.5

A number like 0.4 lies between them.

Since 0.4 = 4/10 = 2/5, it is also a rational number between 1/3 and 1/2.

Final Answer:

Yes, you can find rational numbers between two rational numbers using the common denominator method, average method, or decimal method.

Think and Reflect

1. Try and represent 8/5 and -7/4 on a number line.

Solution:

To represent 8/5 and -7/4 on a number line, first understand where they lie.

8/5 is a positive rational number.

• 8/5 = 1 3/5

So, 8/5 lies between 1 and 2.

To mark 8/5, divide the interval between 1 and 2 into 5 equal parts. Then count 3 parts to the right of 1. That point represents 8/5.

Now consider -7/4.

• -7/4 = -1 3/4

So, -7/4 lies between -2 and -1.

To mark -7/4, divide the interval between -2 and -1 into 4 equal parts. Since -7/4 equals -1 3/4, it is closer to -2 than to -1. It can be marked as the first division to the right of -2, or the third division to the left of -1.

Thus, on the number line:

• 8/5 is between 1 and 2.

• -7/4 is between -2 and -1.

Key Takeaways from Vedantu’s Class 9 Maths Exercise 3.4

• Learn how to locate positive and negative rational numbers accurately on a number line.

• Practise finding rational numbers between two given values using different methods.

• Strengthen your skills in adding and simplifying rational-number expressions.

• Convert mixed fractions into improper fractions when needed for calculations.

• Use decimal values to identify rational numbers within a very small interval.

• Understand how the average method and common-denominator method can help find numbers between two rational numbers.

• Apply rational-number concepts to everyday situations, such as calculating how much material is needed.

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