Fractions — Class 6 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 6 Mathematics chapter "Fractions" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 6 Mathematics chapter "Fractions" — 8 important questions with detailed answers for CBSE board exam prepar…
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NCERT Solutions for Class 6 Mathematics — Fractions. Step-by-step answers to all 8 textbook questions from this chapter, written for CBSE board preparation and free to use.
Fractions — All 8 Questions Solved
Q1. Write 3/4 in words and identify the numerator and denominator.
The fraction 3/4 is read as 'three-fourths'
Step 1: In the fraction 3/4
Step 2: Numerator = 3 (the part taken)
Step 3: Denominator = 4 (the total parts)
Step 4: It means 3 parts out of 4 equal parts
Final Answer: Numerator = 3, Denominator = 4, Read as 'three-fourths'
Q2. Find an equivalent fraction to 2/5 with denominator 20.
To find equivalent fractions, multiply both numerator and denominator by the same number
Step 1: We have 2/5 and need denominator 20
Step 2: 20 ÷ 5 = 4
Step 3: Multiply both numerator and denominator by 4
Step 4: (2 × 4)/(5 × 4) = 8/20
Final Answer: 8/20
Q3. Compare 3/5 and 2/5. Which is greater?
When fractions have the same denominator, compare the numerators
Step 1: Fractions are 3/5 and 2/5
Step 2: Both have denominator 5
Step 3: Compare numerators: 3 > 2
Step 4: Therefore 3/5 > 2/5
Final Answer: 3/5 is greater
Q4. Add 1/4 + 3/4.
When fractions have the same denominator, add the numerators
Step 1: Fractions are 1/4 and 3/4
Step 2: Both have denominator 4
Step 3: Add numerators: 1 + 3 = 4
Step 4: 1/4 + 3/4 = 4/4 = 1
Final Answer: 1
Q5. Subtract 3/8 from 7/8.
When fractions have the same denominator, subtract the numerators
Step 1: Fractions are 7/8 and 3/8
Step 2: Both have denominator 8
Step 3: Subtract numerators: 7 - 3 = 4
Step 4: 7/8 - 3/8 = 4/8 = 1/2
Final Answer: 1/2
Q6. Simplify the fraction 12/18 to its simplest form.
Find the GCD (Greatest Common Divisor) and divide both numerator and denominator
Step 1: Fraction is 12/18
Step 2: Find factors: 12 = 1, 2, 3, 4, 6, 12 and 18 = 1, 2, 3, 6, 9, 18
Step 3: GCD = 6
Step 4: 12/18 = (12 ÷ 6)/(18 ÷ 6) = 2/3
Final Answer: 2/3
Q7. Identify the type of fraction: 5/8, 9/4, 4/4.
Fractions are classified based on numerator and denominator
Step 1: 5/8 - numerator < denominator, so it is a Proper Fraction
Step 2: 9/4 - numerator > denominator, so it is an Improper Fraction
Step 3: 4/4 - numerator = denominator, so it is also an Improper Fraction
Final Answer: 5/8 is proper; 9/4 and 4/4 are improper
Q8. Compare 2/3 and 3/4 using a common denominator.
Convert to a common denominator to compare
Step 1: Fractions are 2/3 and 3/4
Step 2: LCM of 3 and 4 = 12
Step 3: 2/3 = (2 × 4)/(3 × 4) = 8/12
Step 4: 3/4 = (3 × 3)/(4 × 3) = 9/12
Step 5: Compare: 8/12 < 9/12
Final Answer: 3/4 is greater than 2/3
Fractions — 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. Which of the following represents 'three-fifths' as a fraction?
- A. 3/5
- B. 5/3
- C. 3-5
- D. 5-3
Answer: A. 3/5 — In a fraction, the numerator represents the number of parts taken, and the denominator represents the total number of equal parts. 'Three-fifths' means 3 out of 5 equal parts.
MCQ 2. In the fraction 7/12, what is the denominator?
- A. 7
- B. 12
- C. 7/12
- D. 1
Answer: B. 12 — The denominator is the bottom number in a fraction, representing the total number of equal parts into which the whole is divided. Here, 12 is the denominator.
MCQ 3. Which of the following is an improper fraction?
- A. 2/5
- B. 7/9
- C. 11/8
- D. 1/3
Answer: C. 11/8 — An improper fraction is a fraction where the numerator is greater than or equal to the denominator. In 11/8, the numerator (11) is greater than the denominator (8).
MCQ 4. Convert the mixed fraction 3 1/4 into an improper fraction.
- A. 13/4
- B. 4/13
- C. 31/4
- D. 7/4
Answer: A. 13/4 — To convert a mixed fraction to an improper fraction, multiply the whole number by the denominator and add the numerator. Keep the same denominator: (3 * 4 + 1) / 4 = 13/4.
MCQ 5. Convert the improper fraction 17/5 into a mixed fraction.
- A. 5 2/17
- B. 3 2/5
- C. 2 3/5
- D. 17 1/5
Answer: B. 3 2/5 — To convert an improper fraction to a mixed fraction, divide the numerator by the denominator. The quotient is the whole number, the remainder is the new numerator, and the denominator stays the same. 17 ÷ 5 = 3 with a remainder of 2, so it's 3 2/5.
MCQ 6. Which fraction is equivalent to 2/3?
- A. 4/5
- B. 6/9
- C. 8/10
- D. 1/3
Answer: B. 6/9 — Equivalent fractions represent the same value. Multiplying both the numerator and denominator of 2/3 by 3 gives (2*3)/(3*3) = 6/9.
MCQ 7. What is the simplest form of the fraction 10/15?
- A. 5/3
- B. 2/3
- C. 1/5
- D. 10/15
Answer: B. 2/3 — To find the simplest form, divide both the numerator and the denominator by their greatest common factor (GCF). The GCF of 10 and 15 is 5. So, 10÷5 / 15÷5 = 2/3.
MCQ 8. Which of the following fractions is the smallest: 3/7, 5/7, 1/7, 6/7?
- A. 3/7
- B. 5/7
- C. 1/7
- D. 6/7
Answer: C. 1/7 — When fractions have the same denominator (like fractions), the fraction with the smallest numerator is the smallest. Here, 1 is the smallest numerator.
MCQ 9. Which fraction is the largest: 1/2, 2/3, 3/4, 4/5?
- A. 1/2
- B. 2/3
- C. 3/4
- D. 4/5
Answer: D. 4/5 — To compare unlike fractions, find a common denominator or convert to decimals. The LCM of 2, 3, 4, 5 is 60. Converting them: 30/60, 40/60, 45/60, 48/60. The largest is 48/60, which simplifies to 4/5.
MCQ 10. Add the fractions: 2/9 + 4/9.
- A. 6/18
- B. 6/9
- C. 8/9
- D. 24/81
Answer: B. 6/9 — To add like fractions, add the numerators and keep the denominator the same. So, (2+4)/9 = 6/9.
MCQ 11. Subtract 3/10 from 7/10.
- A. 10/10
- B. 4/0
- C. 4/10
- D. 10/20
Answer: C. 4/10 — To subtract like fractions, subtract the numerators and keep the denominator the same. So, (7-3)/10 = 4/10.
MCQ 12. What is the sum of 1/3 and 1/4?
- A. 2/7
- B. 1/12
- C. 7/12
- D. 5/12
Answer: C. 7/12 — To add unlike fractions, find the least common multiple (LCM) of the denominators (3 and 4), which is 12. Convert the fractions to equivalent fractions with denominator 12: 1/3 = 4/12 and 1/4 = 3/12. Then add: 4/12 + 3/12 = 7/12.
MCQ 13. Find the difference: 5/6 - 1/3.
- A. 4/3
- B. 3/6
- C. 4/6
- D. 2/3
Answer: B. 3/6 — To subtract unlike fractions, find the LCM of the denominators (6 and 3), which is 6. Convert 1/3 to an equivalent fraction with denominator 6: 1/3 = 2/6. Then subtract: 5/6 - 2/6 = 3/6.
MCQ 14. Riya ate 2/5 of a cake, and her brother Rohan ate 1/5 of the same cake. What fraction of the cake did they eat together?
- A. 3/10
- B. 3/5
- C. 1/5
- D. 4/5
Answer: B. 3/5 — To find the total fraction eaten, add the fractions Riya and Rohan ate: 2/5 + 1/5 = (2+1)/5 = 3/5.
MCQ 15. A wire is 7/8 meter long. If 1/4 meter is cut from it, what length of the wire is left?
- A. 6/8 meter
- B. 5/8 meter
- C. 3/8 meter
- D. 1/2 meter
Answer: B. 5/8 meter — To find the remaining length, subtract the cut length from the total length: 7/8 - 1/4. The LCM of 8 and 4 is 8. Convert 1/4 to 2/8. So, 7/8 - 2/8 = (7-2)/8 = 5/8 meter.
MCQ 16. In the fraction 5/8, what is the numerator?
- A. 5
- B. 8
- C. 5/8
- D. None of these
Answer: A. 5 — The numerator is the number above the fraction bar, representing the number of parts taken. In 5/8, 5 is the numerator.
MCQ 17. Which of the following is a proper fraction?
- A. 7/5
- B. 9/9
- C. 2/3
- D. 11/4
Answer: C. 2/3 — A proper fraction has its numerator smaller than its denominator. 2/3 is a proper fraction as 2 < 3.
MCQ 18. Convert the mixed fraction 2 1/4 into an improper fraction.
- A. 9/4
- B. 7/4
- C. 21/4
- D. 4/9
Answer: A. 9/4 — To convert a mixed fraction to an improper fraction, multiply the whole number by the denominator and add the numerator. Keep the same denominator. So, 2 x 4 + 1 = 9, making it 9/4.
MCQ 19. Add: 3/7 + 2/7
- A. 5/7
- B. 6/7
- C. 5/14
- D. 1/7
Answer: A. 5/7 — When adding fractions with the same denominator, add the numerators and keep the denominator the same. So, 3/7 + 2/7 = (3+2)/7 = 5/7.
MCQ 20. Subtract: 8/9 - 5/9
- A. 3/9
- B. 13/9
- C. 3/0
- D. 1
Answer: A. 3/9 — When subtracting fractions with the same denominator, subtract the numerators and keep the denominator the same. So, 8/9 - 5/9 = (8-5)/9 = 3/9.
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.