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Rational Numbers Class 7 Extra Questions Maths Chapter 9
By Maitree Choube
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Updated on 17 Oct 2025, 16:37 IST
Chapter 9, "Rational Numbers," is a key topic in the Class 7 Maths curriculum that help students understand numbers beyond integers, including positive and negative fractions. This FREE PDF offers a well-organized set of extra questions designed to strengthen your grasp on rational numbers through regular practice.
Perfectly aligned with the latest CBSE Class 7 Maths syllabus, these questions give students the opportunity to revise and apply core concepts in a clear and structured way. Use this resource for flexible self-study sessions and boost your exam preparation with confidence.
Rational Numbers Class 7 Extra Questions with Solutions
1. Find three rational numbers equivalent to:
(a) -2/5
Multiplying both numerator and denominator by 2, 3, and 4: - (-4/10), (-6/15), (-8/20)
(b) 3/7
Multiplying both numerator and denominator by 2, 3, and 4: - (6/14), (9/21), (12/28)
2. Reduce the following rational numbers to their standard form:
(a) 35/-15
GCD of 35 and 15 is 5. Simplified form: -7/3
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(b) -36/-216
GCD of 36 and 216 is 36. Simplified form: 1/6
3. Represent the following rational numbers on the number line:
(a) 3/2
Convert to decimal: 3/2 = 1.5. Mark 1.5 between 1 and 2 on the number line.
(b) -3/4
Convert to decimal: -3/4 = -0.75. Mark -0.75 between 0 and -1 on the number line.
4. Compare and state which is greater:
(a) 3/4 and 1/2
Convert to decimal: 3/4 = 0.75, 1/2 = 0.5. Hence, 3/4 is greater.
(b) -3/2 and -3/4
Convert to decimal: -3/2 = -1.5, -3/4 = -0.75. Hence, -3/4 is greater.
5. Find the sum:
(a) 2/5 + 3/7
LCM of 5 and 7 is 35. (14/35) + (15/35) = 29/35
(b) -4/9 + 5/12
LCM of 9 and 12 is 36. (-16/36) + (15/36) = -1/36
6. Subtract:
(a) 3/5 - 7/10
LCM of 5 and 10 is 10. (6/10) - (7/10) = -1/10
(b) -2/3 - 4/9
LCM of 3 and 9 is 9. (-6/9) - (4/9) = -10/9
7. Multiply:
(a) 2/3 × 4/5
(2 × 4) / (3 × 5) = 8/15
(b) -7/9 × 3/4
(-7 × 3) / (9 × 4) = -21/36 = -7/12
8. Divide:
(a) 5/6 ÷ 2/3
(5/6) ÷ (2/3) = (5/6) × (3/2) = (5 × 3) / (6 × 2) = 15/12 = 5/4
(b) -3/8 ÷ 9/10
(-3/8) ÷ (9/10) = (-3/8) × (10/9) = (-3 × 10) / (8 × 9) = -30/72 = -5/12
Rational Numbers Class 7 Extra Questions - Very Short Answer Type
Below are some advanced level Rational Numbers Class 7 Extra Questions with answers and short explanations. Try each question and check your solution.
1. If x = 5/6 and y = -3/4, find x + y.
x + y = 5/6 - 3/4 = (10 - 9)/12 = 1/12
Find the LCM of 6 and 4 (12), convert to like denominators, then add.
2. Simplify: 7/8 ÷ 14/16.
7/8 * 16/14 = 112/112 = 1
Dividing by a fraction = multiply by its reciprocal.
3. Multiply -5/9 × 27/10.
(-5 × 27)/(9 × 10) = -135/90 = -3/2
Simplify numerator and denominator by dividing by 45.
4. Write the additive inverse of 11/13.
-11/13
Additive inverse means the number that gives 0 when added to the original.
5. Find the multiplicative inverse of -3/5.
-5/3
Flip numerator and denominator while keeping the sign.
6. If a = 2/3 and b = 3/2, find a × b × a.
2/3 × 3/2 × 2/3 = 4/9
Simplify step-by-step; one pair cancels out.
7. Simplify: 4/7 + (-3/7).
4/7 - 3/7 = 1/7
Combine like denominators carefully with signs.
8. Find the product: -2/5 × -15/8.
(−2 × −15)/(5 × 8) = 30/40 = 3/4
Negative × Negative = Positive.
9. Divide -7/9 by 14/27.
-7/9 × 27/14 = -189/126 = -3/2
Multiply by the reciprocal and reduce.
10. Which of the following is a rational number? (a) √2 (b) π (c) 0 (d) √3
(c) 0
Rational numbers can be written as p/q; 0 = 0/1 fits this form.
11. Simplify: 5/6 − (−4/9).
5/6 + 4/9 = (15 + 8)/18 = 23/18
Subtracting a negative becomes addition.
- If x = -7/8, find -x.
-x = 7/8
Negative of a negative gives a positive.
- Compare -2/3 and -3/4.
-2/3 = -0.666, -3/4 = -0.75 ⇒ -2/3 > -3/4
The number closer to zero is greater on the number line.
- Find the value of 3/5 × 10/9 × 15/2.
(3 × 10 × 15) / (5 × 9 × 2) = 450 / 90 = 5
Multiply and simplify step by step.
- Check if 2/3 and 6/9 are equal.
Yes, 6/9 = 2/3
Simplify 6/9 by dividing by 3.
- Express -0.4 as a rational number.
-0.4 = -4/10 = -2/5
Move the decimal one place and reduce.
- Find the average of 1/4, 1/2, 3/4.
(1/4 + 1/2 + 3/4) = 6/4 ÷ 3 = 2/1 = 2
Add all numbers and divide by 3.
- If a = 1/3 and b = -2/5, find a − b.
1/3 − (−2/5) = 1/3 + 2/5 = 11/15
Subtracting a negative adds the number.
- Find three rational numbers between 1/2 and 3/4.
Between them: 9/16, 10/16, 11/16
Multiply numerator and denominator to get more divisions.
- The sum of two rational numbers is 7/9. One number is 2/9. Find the other.
x + 2/9 = 7/9 ⇒ x = 5/9
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Rational Numbers Class 7 Extra Questions Maths Chapter 9 FAQs
What is a Rational Number? Give Examples.
A rational number is any number that can be written in the form p/q, where
p and q are integers, and q ≠ 0
For example, ⅔ , − 5, 0 and − 7/ 9 are all rational numbers.
How Do You Identify Rational Numbers Between Two Numbers?
To find rational numbers between two given rational numbers, express both with a common denominator and list the fractions between them.
What Operations Can Be Done on Rational Numbers?
You can add, subtract, multiply, and divide rational numbers just like regular fractions. To add or subtract, use a common denominator. For multiplication and division, multiply/divide both numerators and denominators (for division, use the reciprocal of the second number).
How is Rational Number Useful for Class 7 Students?
Learning rational numbers forms a good foundation to the more complex concepts, such as decimals, percentages and algebra. Extra questions (NCERT) will help the students to be confident and precise in their operations, comparisons, and applications in real life.