Important Questions on Rational Numbers for Class 8

Important Questions on Rational Numbers for Class 8 are available in this Maths article. Important Questions on Rational Numbers for Class 8 are very useful to solve the problems easily. This article helps the students to know the key questions and answers about Rational Numbers. A rational number is any number that can be expressed in the form p/q, where p and q are integers and q ≠ 0.

Our subject experts have provided detailed solutions for these problems based on the CBSE syllabus and the NCERT textbook. This material helps students revise the chapter easily and perform well in the final examination.
 

Table of Contents

• Exercise 1.1: Introduction to Rational Numbers
• Exercise 1.2: Equivalent Rational Numbers and Standard Form
• Exercise 1.3: Comparison of Rational Numbers
• Exercise 1.4: Addition and Subtraction of Rational Numbers
• Exercise 1.5: Multiplication and Division of Rational Numbers
• Exercise 1.6: Properties of Rational Numbers and Applications
• Practice Questions on Rational Numbers for Class 8
• Tips for Solving Rational Numbers Problems

Exercise 1.1: Introduction to Rational Numbers

This exercise focuses on understanding the definition of rational numbers, identifying them, and learning the basic concepts of their representation.

Question 1: What is a Rational Number?

Answer: A rational number is a number that can be written in the form p/q, where p is an integer (numerator) and q is a non-zero integer (denominator).

Examples include:

• 3/4
• -5/2
• 7/1
• 0/5

The denominator must never be zero because division by zero is undefined. Rational numbers can be positive, negative, or zero.

Question 2: Name Five Rational Numbers Between 0 and 1

Answer:

• 1/2 = 0.5
• 1/3 ≈ 0.333...
• 2/5 = 0.4
• 3/4 = 0.75
• 1/4 = 0.25

Each of these numbers lies between 0 and 1. There are infinitely many rational numbers between any two rational numbers.

Question 3: Can Zero Be a Rational Number?

Answer: Yes, zero is a rational number because it can be written as:

• 0/1
• 0/2
• 0/3

Since zero can be expressed in the form p/q where q ≠ 0, it is a rational number.

Question 4: Is Every Integer a Rational Number? 

Answer: Yes, every integer is a rational number because any integer can be written in the form n/1.

Examples:

• 5 = 5/1
• -3 = -3/1
• 0 = 0/1

Therefore, integers are a subset of rational numbers.

Question 5: Write Any Three Rational Numbers with Denominator 6

Answer:

• 2/6
• -5/6
• 7/6

Infinitely many rational numbers can be formed with denominator 6 by changing the numerator.

Exercise 1.2: Equivalent Rational Numbers and Standard Form

This exercise helps students learn equivalent rational numbers and express them in standard form.

Question 6: Express - 48/60 in Standard Form

Solution:

GCD of 48 and 60 = 12

-48/60 = (-48 ÷ 12) / (60 ÷ 12)

= -4/5

Answer: -4/5

Question 7: Check if 15/20 and 9/12 are Equal Rational Numbers

Solution:

15/20 = 3/4

9/12 = 3/4

Since both fractions simplify to the same value, they are equal rational numbers.

Verification:

15 × 12 = 180

20 × 9 = 180

Answer: Yes, they are equal.

Question 8: Find Three Equivalent Rational Numbers of 2/5

Solution:

• 2/5 × 2/2 = 4/10
• 2/5 × 3/3 = 6/15
• 2/5 × 4/4 = 8/20

Answer: 4/10, 6/15, and 8/20

Question 9: Is 5/-8 in Standard Form?

Solution:

No, because the denominator is negative.

5/−8=−5/8

Answer:−5/8

Question 10: Reduce−36/48 to Its Simplest Form

Solution:

GCD of 36 and 48 = 12

−36/48=(−36÷12)/(48÷12)

=  −3/4

Answer:−3/4

Exercise 1.3: Comparison of Rational Numbers

Question 11: Which is Greater: 3/5 or 4/7?

Solution:

3/5 = 0.6

4/7 ≈ 0.571

Since 0.6 > 0.571, 3/5 is greater.

Answer: 3/5 is greater.

Question 12: Arrange in Ascending Order: -3/2, -1/4, 2/3, -5/6

Solution:

• -3/2 = -1.5
• -1/4 = -0.25
• 2/3 ≈ 0.667
• -5/6 ≈ -0.833

Ascending order:

-3/2 < -5/6 < -1/4 < 2/3

Answer: -3/2, -5/6, -1/4, 2/3

Question 13: Is -2/3 Greater Than -3/4?

Solution:

-2/3 ≈ -0.667

-3/4 = -0.75

Since -0.667 > -0.75, -2/3 is greater.

Answer: Yes, -2/3 > -3/4

Question 14: Find Three Rational Numbers Between 2/3 and 3/4

Answer:

• 11/16
• 17/24
• 35/48

Question 15: Compare -5/6 and -7/9

Solution:

-5 × 9 = -45

-7 × 6 = -42

Since -45 < -42, -5/6 < -7/9

Answer: -5/6 is smaller than -7/9

Exercise 1.4: Addition and Subtraction of Rational Numbers

Question 16: Add the Rational Numbers 2/3 and 3/4

Solution:

LCM of 3 and 4 = 12

2/3 = 8/12

3/4 = 9/12

8/12 + 9/12 = 17/12

Answer: 17/12

Question 17: Subtract 5/6 from 7/8

Solution:

7/8 - 5/6

LCM of 8 and 6 = 24

21/24 - 20/24 = 1/24

Answer: 1/24

Question 18: Add -3/7 and 2/7

Solution:

(-3 + 2)/7 = -1/7

Answer: -1/7

Question 19: Subtract−4/9 from−1/9

Solution:

-1/9 - (-4/9)

= -1/9 + 4/9

= 3/9

= 1/3

Answer: 1/3

Question 20: Find 5/12 + (-7/12) + 3/12

Solution:

(5 - 7 + 3)/12 = 1/12

Answer: 1/12

Exercise 1.5: Multiplication and Division of Rational Numbers

Question 21: Multiply -3/5 by 2/7

Solution:

(-3 × 2)/(5 × 7) = -6/35

Answer: -6/35

Question 22: Divide 4/9 by 8/3

Solution:

(4/9) ÷ (8/3)

= (4/9) × (3/8)

= 12/72

= 1/6

Answer: 1/6

Question 23: Multiply 5/6 by 12/15

Solution:

(5 × 12)/(6 × 15) = 60/90 = 2/3

Answer: 2/3

Question 24: Divide -7/12 by 14/3

Solution:

(-7/12) × (3/14) = -21/168 = -1/8

Answer: -1/8

Question 25: Find the Product of 3/5 and its Reciprocal

Solution:

Reciprocal of 3/5 = 5/3

(3/5) × (5/3) = 1

Answer: 1

Exercise 1.6: Properties of Rational Numbers and Applications

Question 26: What is the Additive Inverse of 5/7?

Answer: -5/7

Question 27: Find the Multiplicative Inverse of -3/8

Answer: -8/3

Question 28: Verify Closure Property Under Addition: 1/2 + 3/4

Solution:

1/2 + 3/4 = 5/4

Since 5/4 is a rational number, closure property is verified.

Question 29: Demonstrate Distributive Property: 2/3 × (1/2 + 1/4)

Solution:

2/3 × (1/2 + 1/4)

= (2/3 × 1/2) + (2/3 × 1/4)

= 1/3 + 1/6

= 1/2

Answer: Distributive property verified.

Question 30: A Recipe Requires 3/4 Cup of Sugar. If You Want to Make Half the Recipe, How Much Sugar Do You Need?

Solution:

3/4 × 1/2 = 3/8

Answer: 3/8 cup

Question 31: A Piece of Rope is 12 Meters Long. If It is Divided into Pieces of 2/3 Meter Each, How Many Pieces Will You Get?

Solution:

12 ÷ (2/3)

= 12 × (3/2)

= 18

Answer: 18 pieces

Question 32: A Student Spends 1/3 of Their Pocket Money on Food and 1/4 on Books. What Fraction of Money is Left?

Solution:

1/3 + 1/4 = 7/12

Money left = 1 - 7/12 = 5/12

Answer: 5/12

Question 33: If 2/5 of a Class Consists of Girls and There are 30 Girls, How Many Students Are in the Class?

Solution:

(2/5) × x = 30

x = 30 × 5/2

x = 75

Answer: 75 students

Question 34: A Tank is 3/4 Full. After Using 1/3 of the Water, How Much of the Tank's Capacity is Used?

Solution:

1/3 × 3/4 = 1/4

Answer: 1/4 of the tank's capacity

Question 35: Simplify: (1/2 + 1/3) × (3/2 - 1/4) ÷ (2/3)

Solution:

1/2 + 1/3 = 5/6

3/2 - 1/4 = 5/4

5/6 × 5/4 = 25/24

25/24 ÷ 2/3 = 25/16

Answer: 25/16

Question 36: Is Subtraction Commutative for Rational Numbers?

Solution:

3/4 - 1/4 = 2/4

1/4 - 3/4 = -2/4

Since 2/4 ≠ -2/4, subtraction is not commutative.

Answer: No.

Question 37: Find Three Rational Numbers Between -1/2 and 1/2

Answer:

• 0
• 1/4
• -1/4

Practice Questions on Rational Numbers for Class 8

1. Identify whether the following numbers are rational numbers or not:
   • 79
   • 5
   • −3
   • 0.75
2. Write the following rational numbers in their simplest form:
   • 2436
   • 4560
   • 84126
3. Compare the following rational numbers and write the greater number:
   •  58 and 712
   •  −35 and −27
4. Arrange the following rational numbers in ascending order:

    34, 56, 23,78

5. Find the sum of the following rational numbers:
   • 79+23
   • −58+34
6. Subtract the following rational numbers:
   • 1112−518
   • −710−25
7. Multiply the following rational numbers:
   • 47×1415
   • −38×169
8. Divide the following rational numbers:
   • 56÷109
   • −712÷1415
9. Verify the commutative property of addition for the rational numbers 25 and  710.
10. A water tank was 35 full in the morning. During the day,  14 of the tank was filled more. What fraction of the tank is filled now?

Tips for Solving Rational Numbers Problems

• Check denominators are not zero. Give your answers in standard form.
• Adding and subtracting fractions easily with LCM of denominators.
• Always simplify fractions by dividing both top and bottom by GCD.
• Cross-multiply fractions to compare them, no decimals required.
• Negative signs carefully move minus from bottom to top.
• Convert fractions to decimals to check work