A Story of Numbers — Class 8 Mathematics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 8 Mathematics chapter "A Story of Numbers" — 8 important questions with detailed answers for CBSE board exam preparation.

TL;DR: Free step-by-step NCERT solutions for Class 8 Mathematics chapter "A Story of Numbers" — 8 important questions with detailed answers for CBSE board ex…

By Syllab.in · Updated Jun 14, 2026

Key Questions Covered:

Which of the following is a rational number? 0, √2, π, 1/3
Find two rational numbers between 1/4 and 1/2.
Add: 3/7 + 2/5
Subtract: 7/8 - 1/6
Simplify: (3/4) × (8/9)
Divide: (5/6) ÷ (10/12)
+ 2 more questions in the full chapter

Solutions Summary:

Question	Status
Which of the following is a rational number? 0, √2, π, 1/3	✓ Solved
Find two rational numbers between 1/4 and 1/2.	✓ Solved
Add: 3/7 + 2/5	✓ Solved
Subtract: 7/8 - 1/6	✓ Solved
Simplify: (3/4) × (8/9)	✓ Solved
Divide: (5/6) ÷ (10/12)	✓ Solved

Showing 6 of 8 questions

Q1: Which of the following is a rational number? 0, √2, π, 1/3

A rational number is a number that can be expressed in the form p/q where p and q are integers and q ≠ 0. Step 1: Check 0 0 can be written as 0/1 ✓ This is a rational number Step 2: Check √2 √2 = 1.414213... (non-terminating, non-repeating decimal) It cannot be expressed as p/q where p and q are integers ✗ This is irrational Step 3: Check π π = 3.14159... (non-terminating, non-repeating decimal) It cannot be expressed as p/q ✗ This is irrational Step 4: Check 1/3 1/3 is already in the form p...

Q2: Find two rational numbers between 1/4 and 1/2.

We need to find two rational numbers that lie between 1/4 and 1/2. Step 1: Convert to a common form 1/4 = 0.25 1/2 = 0.50 Step 2: Method 1 - Using simple fractions We can find the average of the two numbers: (1/4 + 1/2)/2 = (1/4 + 2/4)/2 = (3/4)/2 = 3/8 Check: 1/4 = 2/8, 3/8, 4/8 = 1/2 ✓ 3/8 is between 1/4 and 1/2 Step 3: Find another rational number Let's find the average of 1/4 and 3/8: (1/4 + 3/8)/2 = (2/8 + 3/8)/2 = (5/8)/2 = 5/16 Check: 1/4 = 4/16, 5/16, 8/16 = 1/2 ✓ 5/16 is between 1/4 ...

Q3: Add: 3/7 + 2/5

We need to add two fractions with different denominators. Step 1: Find the LCM of denominators 7 and 5 Since 7 and 5 are both prime and different: LCM(7, 5) = 7 × 5 = 35 Step 2: Convert to equivalent fractions with denominator 35 3/7 = (3 × 5)/(7 × 5) = 15/35 2/5 = (2 × 7)/(5 × 7) = 14/35 Step 3: Add the fractions 3/7 + 2/5 = 15/35 + 14/35 = (15 + 14)/35 = 29/35 Step 4: Check if the answer can be simplified GCD(29, 35) = 1 (29 is prime, 35 = 5 × 7) 29/35 is already in simplest form Answer: ...

Q4: Subtract: 7/8 - 1/6

We need to subtract two fractions with different denominators. Step 1: Find the LCM of denominators 8 and 6 8 = 2³ 6 = 2 × 3 LCM(8, 6) = 2³ × 3 = 24 Step 2: Convert to equivalent fractions with denominator 24 7/8 = (7 × 3)/(8 × 3) = 21/24 1/6 = (1 × 4)/(6 × 4) = 4/24 Step 3: Subtract the fractions 7/8 - 1/6 = 21/24 - 4/24 = (21 - 4)/24 = 17/24 Step 4: Check if the answer can be simplified GCD(17, 24) = 1 (17 is prime, 24 = 2³ × 3) 17/24 is already in simplest form Answer: 7/8 - 1/6 = 17/24

Q5: Simplify: (3/4) × (8/9)

We need to multiply two fractions. Step 1: Multiply numerators and denominators (3/4) × (8/9) = (3 × 8)/(4 × 9) = 24/36 Step 2: Simplify by canceling common factors Before multiplying, we can cancel: 3 and 9 have GCD = 3: 3/9 = 1/3 8 and 4 have GCD = 4: 8/4 = 2/1 Or: (3/4) × (8/9) = (3 × 8)/(4 × 9) Cancel 3 with 9: (1 × 8)/(4 × 3) = 8/12 Cancel 4 with 8: (2)/(3) = 2/3 Step 3: Verify 24/36 = (24÷12)/(36÷12) = 2/3 ✓ Answer: (3/4) × (8/9) = 2/3

Q6: Divide: (5/6) ÷ (10/12)

We need to divide two fractions. Step 1: Use the rule a/b ÷ c/d = a/b × d/c (5/6) ÷ (10/12) = (5/6) × (12/10) Step 2: Multiply the fractions (5/6) × (12/10) = (5 × 12)/(6 × 10) = 60/60 Step 3: Simplify 60/60 = 1 Step 4: Alternative method - cancel before multiplying (5/6) × (12/10) Cancel 5 and 10: (1/6) × (12/2) Cancel 6 and 12: (1/1) × (2/2) = 1 Answer: (5/6) ÷ (10/12) = 1

Showing 6 of 8 questions. Visit the full page for complete solutions.