Fractions in Disguise — Class 8 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 8 Mathematics chapter "Fractions in Disguise" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 8 Mathematics chapter "Fractions in Disguise" — 8 important questions with detailed answers for CBSE board…
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NCERT Solutions for Class 8 Mathematics — Fractions in Disguise. Step-by-step answers to all 8 textbook questions from this chapter, written for CBSE board preparation and free to use.
Fractions in Disguise — All 8 Questions Solved
Q1. Express 4/5 as a rational number with denominator 20.
Step 1: We need to express 4/5 with denominator 20.
Step 2: Multiply numerator and denominator by 4:
(4 × 4)/(5 × 4) = 16/20
Step 3: Therefore, 4/5 = 16/20
Q2. Find the sum: 3/8 + 5/8
Step 1: Both fractions have the same denominator (8).
Step 2: Add the numerators: 3 + 5 = 8
Step 3: Sum = (3 + 5)/8 = 8/8
Step 4: Simplify: 8/8 = 1
Q3. Subtract: 7/12 − 5/12
Step 1: Both fractions have the same denominator (12).
Step 2: Subtract the numerators: 7 − 5 = 2
Step 3: Difference = (7 − 5)/12 = 2/12
Step 4: Simplify by dividing by GCD(2,12) = 2:
2/12 = 1/6
Q4. Add: 1/3 + 1/4
Step 1: Find LCM of 3 and 4 = 12
Step 2: Convert 1/3 to denominator 12: (1 × 4)/(3 × 4) = 4/12
Step 3: Convert 1/4 to denominator 12: (1 × 3)/(4 × 3) = 3/12
Step 4: Add: 4/12 + 3/12 = 7/12
Q5. Multiply: (2/3) × (3/5)
Step 1: Multiply numerators: 2 × 3 = 6
Step 2: Multiply denominators: 3 × 5 = 15
Step 3: Product = 6/15
Step 4: Simplify by dividing by GCD(6,15) = 3:
6/15 = 2/5
Q6. Divide: (5/7) ÷ (2/3)
Step 1: Division of fractions: (5/7) ÷ (2/3) = (5/7) × (3/2)
Step 2: Multiply numerators: 5 × 3 = 15
Step 3: Multiply denominators: 7 × 2 = 14
Step 4: Result = 15/14
Q7. What is the additive inverse (negative) of −3/7?
Step 1: The additive inverse of a number a is −a.
Step 2: Additive inverse of −3/7 is −(−3/7) = 3/7
Step 3: Therefore, the answer is 3/7
Q8. Find: (−2/5) + (−3/5)
Step 1: Both fractions have the same denominator (5).
Step 2: Add the numerators: −2 + (−3) = −5
Step 3: Sum = (−2 − 3)/5 = −5/5
Step 4: Simplify: −5/5 = −1
Fractions in Disguise — Practice MCQs with Answers
Attempt these 20 multiple-choice questions after working through the solutions above. Each carries the correct option and the reasoning behind it, so a wrong answer tells you which idea to revisit.
MCQ 1. Convert the mixed fraction 3 2/5 into an improper fraction.
- A. 17/5
- B. 11/5
- C. 6/5
- D. 32/5
Answer: A. 17/5 — To convert a mixed fraction to an improper fraction, multiply the whole number by the denominator and add the numerator. The denominator remains the same. So, 3 × 5 + 2 = 15 + 2 = 17, making the improper fraction 17/5.
MCQ 2. Express 0.75 as a fraction in its simplest form.
- A. 3/4
- B. 75/100
- C. 1/4
- D. 3/5
Answer: A. 3/4 — The decimal 0.75 can be written as 75/100. Simplifying this by dividing both numerator and denominator by their greatest common divisor, 25, gives 3/4.
MCQ 3. What is 20% expressed as a fraction?
- A. 1/5
- B. 2/10
- C. 20/100
- D. 1/20
Answer: A. 1/5 — To express a percentage as a fraction, divide the percentage by 100. So, 20% = 20/100. Simplifying this fraction by dividing both numerator and denominator by 20 gives 1/5.
MCQ 4. Evaluate: 1/3 + 1/6
- A. 1/2
- B. 2/9
- C. 3/6
- D. 1/9
Answer: A. 1/2 — To add fractions, find a common denominator, which is 6 for 3 and 6. So, 1/3 = 2/6. Then, 2/6 + 1/6 = 3/6, which simplifies to 1/2.
MCQ 5. Calculate: 2/3 × 5/7
- A. 10/21
- B. 7/10
- C. 10/7
- D. 2/21
Answer: A. 10/21 — To multiply fractions, multiply the numerators together and the denominators together. So, 2 × 5 = 10 and 3 × 7 = 21, resulting in 10/21.
MCQ 6. Which of the following fractions is the largest: 1/2, 1/3, 1/4, 1/5?
- A. 1/2
- B. 1/3
- C. 1/4
- D. 1/5
Answer: A. 1/2 — When comparing unit fractions (fractions with a numerator of 1), the fraction with the smallest denominator is the largest. Therefore, 1/2 is the largest.
MCQ 7. What is 3/4 of 48?
- A. 36
- B. 12
- C. 48
- D. 64
Answer: A. 36 — To find '3/4 of 48', multiply 48 by 3/4. This means (48 ÷ 4) × 3 = 12 × 3 = 36.
MCQ 8. Evaluate: 5/6 ÷ 2/3
- A. 5/4
- B. 10/18
- C. 4/5
- D. 15/12
Answer: A. 5/4 — To divide by a fraction, multiply by its reciprocal. The reciprocal of 2/3 is 3/2. So, 5/6 × 3/2 = 15/12. Simplifying this by dividing numerator and denominator by 3 gives 5/4.
MCQ 9. Calculate: 1/2 + 1/3 × 1/4
- A. 7/12
- B. 5/24
- C. 1/24
- D. 2/9
Answer: A. 7/12 — According to the order of operations (BODMAS/PEMDAS), multiplication must be performed before addition. First, 1/3 × 1/4 = 1/12. Then, 1/2 + 1/12 = 6/12 + 1/12 = 7/12.
MCQ 10. What is the value of 0.2 + 1/4?
- A. 0.45
- B. 0.29
- C. 0.5
- D. 0.7
Answer: A. 0.45 — Convert both to decimals or both to fractions. 0.2 = 2/10 = 1/5. So, 1/5 + 1/4. The common denominator is 20. 4/20 + 5/20 = 9/20. As a decimal, 9/20 = 45/100 = 0.45.
MCQ 11. A full tank contains 60 litres of water. If 1/3 of the water is used, and then 1/4 of the remaining water is used, how much water is left in the tank?
- A. 30 litres
- B. 20 litres
- C. 15 litres
- D. 25 litres
Answer: A. 30 litres — Initially, 60 litres. 1/3 used means 60 × 1/3 = 20 litres used. Remaining water is 60 - 20 = 40 litres. Then, 1/4 of the remaining water is used, so 40 × 1/4 = 10 litres used. Water left is 40 - 10 = 30 litres.
MCQ 12. If 3/5 of a number is 24, what is the number?
- A. 40
- B. 14.4
- C. 72
- D. 60
Answer: A. 40 — Let the number be x. Then (3/5)x = 24. To find x, multiply 24 by the reciprocal of 3/5, which is 5/3. So, x = 24 × 5/3 = (24 ÷ 3) × 5 = 8 × 5 = 40.
MCQ 13. Evaluate: 2 1/4 × (1 1/3 + 1/2)
- A. 4 1/8
- B. 3 3/4
- C. 4 1/2
- D. 5 1/4
Answer: A. 4 1/8 — First, solve the expression inside the parenthesis: 1 1/3 + 1/2 = 4/3 + 1/2 = 8/6 + 3/6 = 11/6. Then, multiply this by 2 1/4 (which is 9/4): 9/4 × 11/6 = 99/24. Simplifying the fraction gives 33/8, which is 4 1/8.
MCQ 14. What is the reciprocal of 7/9?
- A. 9/7
- B. 7/9
- C. -7/9
- D. 1
Answer: A. 9/7 — The reciprocal of a fraction is obtained by swapping its numerator and denominator. So, the reciprocal of 7/9 is 9/7.
MCQ 15. Rohit spent 1/4 of his money on books and 1/2 of his money on food. What fraction of his money is left?
- A. 1/4
- B. 3/4
- C. 1/2
- D. 1/8
Answer: A. 1/4 — Total money spent is 1/4 + 1/2. Find a common denominator (4): 1/4 + 2/4 = 3/4. The fraction of money left is 1 - 3/4 = 1/4.
MCQ 16. If 2x/3 - x/4 = 5/6, what is the value of x?
- A. 2
- B. 10/3
- C. 1/2
- D. 2/3
Answer: A. 2 — To solve for x, find a common denominator for the fractions, which is 12 for 3, 4, and 6. Multiply the entire equation by 12: 12 × (2x/3) - 12 × (x/4) = 12 × (5/6). This simplifies to 8x - 3x = 10. So, 5x = 10, which means x = 2.
MCQ 17. Which of the following fractions is equivalent to 2/3?
- A. 8/12
- B. 4/9
- C. 6/8
- D. 10/18
Answer: A. 8/12 — To find an equivalent fraction, multiply (or divide) both the numerator and denominator by the same non-zero number. For 2/3, multiplying by 4 gives (2 × 4) / (3 × 4) = 8/12.
MCQ 18. Arrange the following in ascending order: 3/5, 0.62, 58%, 5/8.
- A. 58%, 3/5, 0.62, 5/8
- B. 3/5, 58%, 0.62, 5/8
- C. 58%, 3/5, 5/8, 0.62
- D. 5/8, 0.62, 3/5, 58%
Answer: A. 58%, 3/5, 0.62, 5/8 — Convert all to decimals for comparison: 3/5 = 0.6; 0.62; 58% = 0.58; 5/8 = 0.625. In ascending order: 0.58, 0.6, 0.62, 0.625. This corresponds to 58%, 3/5, 0.62, 5/8.
MCQ 19. A student scores 75% in a test. If the maximum marks were 80, and the passing marks were 3/5 of the maximum marks, by how many marks did the student pass?
- A. 12 marks
- B. 15 marks
- C. 48 marks
- D. 60 marks
Answer: A. 12 marks — Student's score: 75% of 80 = (75/100) × 80 = 60 marks. Passing marks: 3/5 of 80 = (3/5) × 80 = 48 marks. The student passed by 60 - 48 = 12 marks.
MCQ 20. Convert the fraction 3/8 into a decimal.
- A. 0.375
- B. 0.38
- C. 0.83
- D. 0.625
Answer: A. 0.375 — To convert a fraction to a decimal, divide the numerator by the denominator. 3 ÷ 8 = 0.375.
How to Use These Solutions
Attempt each question yourself first and only then compare with the worked answer. Marks in the CBSE board exam are awarded for the METHOD as much as the final result, so reproduce the steps rather than memorising the last line. Where a solution states a law, a formula or a definition, learn that wording — examiners look for it.
Related practice for this chapter: chapter MCQs, previous-year questions, revision notes and sample papers.