Working with Fractions — Class 7 Mathematics NCERT Solutions (Free)

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TL;DR: Free step-by-step NCERT solutions for Class 7 Mathematics chapter "Working with Fractions" — 8 important questions with detailed answers for CBSE boar…

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NCERT Solutions for Class 7 Mathematics — Working with Fractions. Step-by-step answers to all 8 textbook questions from this chapter, written for CBSE board preparation and free to use.

Working with Fractions — All 8 Questions Solved

Q1. Multiply: 2/3 × 4/5

Step 1: To multiply fractions, multiply numerators together and denominators together.
(a/b) × (c/d) = (a × c)/(b × d)

Step 2: Apply the rule:
2/3 × 4/5 = (2 × 4)/(3 × 5) = 8/15

Step 3: Check if the fraction can be simplified:
GCD(8, 15) = 1 (8 and 15 share no common factors)
So 8/15 is already in lowest terms.

Answer: 8/15

Q2. Divide: 3/4 ÷ 2/5

Step 1: To divide by a fraction, multiply by its reciprocal.
(a/b) ÷ (c/d) = (a/b) × (d/c)

Step 2: Find reciprocal of 2/5:
Reciprocal = 5/2

Step 3: Multiply:
3/4 × 5/2 = (3 × 5)/(4 × 2) = 15/8

Step 4: Check if simplifiable:
GCD(15, 8) = 1
So 15/8 is in lowest terms.

Step 5: Convert to mixed number if needed:
15/8 = 1 7/8 (since 15 = 8 × 1 + 7)

Answer: 15/8 or 1 7/8

Q3. Find 2/3 of 15.

Step 1: "Of" means multiply in mathematics.
2/3 of 15 = 2/3 × 15

Step 2: Multiply:
2/3 × 15 = (2 × 15)/3 = 30/3

Step 3: Simplify:
30/3 = 10

Answer: 10

Q4. Multiply: 1 2/3 × 2 1/4

Step 1: Convert mixed numbers to improper fractions:
1 2/3 = (1 × 3 + 2)/3 = 5/3
2 1/4 = (2 × 4 + 1)/4 = 9/4

Step 2: Multiply the improper fractions:
5/3 × 9/4 = (5 × 9)/(3 × 4) = 45/12

Step 3: Simplify by finding GCD:
GCD(45, 12) = 3
45 ÷ 3 = 15
12 ÷ 3 = 4
So 45/12 = 15/4

Step 4: Convert to mixed number:
15/4 = 3 3/4 (since 15 = 4 × 3 + 3)

Answer: 15/4 or 3 3/4

Q5. Divide: 3 1/2 ÷ 1 1/4

Step 1: Convert mixed numbers to improper fractions:
3 1/2 = (3 × 2 + 1)/2 = 7/2
1 1/4 = (1 × 4 + 1)/4 = 5/4

Step 2: To divide, multiply by reciprocal:
7/2 ÷ 5/4 = 7/2 × 4/5

Step 3: Multiply:
(7 × 4)/(2 × 5) = 28/10

Step 4: Simplify:
GCD(28, 10) = 2
28 ÷ 2 = 14
10 ÷ 2 = 5
So 28/10 = 14/5

Step 5: Convert to mixed number:
14/5 = 2 4/5 (since 14 = 5 × 2 + 4)

Answer: 14/5 or 2 4/5

Q6. Simplify: (3/4 × 8/9) ÷ 2/3

Step 1: Simplify the bracket first: 3/4 × 8/9
(3 × 8)/(4 × 9) = 24/36
Simplify: GCD(24, 36) = 12
24 ÷ 12 = 2, 36 ÷ 12 = 3
So 24/36 = 2/3

Step 2: Now divide by 2/3:
2/3 ÷ 2/3 = 2/3 × 3/2

Step 3: Multiply:
(2 × 3)/(3 × 2) = 6/6 = 1

Answer: 1

Q7. A recipe requires 3/4 cup of sugar. How much sugar is needed for 5 batches?

Step 1: Sugar per batch = 3/4 cup
Number of batches = 5

Step 2: Total sugar needed = 3/4 × 5
Rewrite 5 as a fraction: 5 = 5/1

Step 3: Multiply:
3/4 × 5/1 = (3 × 5)/(4 × 1) = 15/4

Step 4: Convert to mixed number:
15/4 = 3 3/4 (since 15 = 4 × 3 + 3)
Or as decimal: 15/4 = 3.75 cups

Answer: 3 3/4 cups or 3.75 cups

Q8. A rope of length 12 meters is cut into pieces of 2 1/2 meters each. How many pieces are obtained?

Step 1: Total length of rope = 12 meters
Length of each piece = 2 1/2 = 5/2 meters

Step 2: Number of pieces = Total length ÷ Length per piece
Number of pieces = 12 ÷ 5/2

Step 3: Convert 12 to a fraction and divide:
12/1 ÷ 5/2 = 12/1 × 2/5

Step 4: Multiply:
(12 × 2)/(1 × 5) = 24/5

Step 5: Convert to mixed number:
24/5 = 4 4/5 (since 24 = 5 × 4 + 4)

Step 6: Since we need whole pieces:
4 4/5 pieces means 4 complete pieces can be cut.
Remainder = 4/5 of a meter (0.8 meters)

Answer: 4 complete pieces (with 0.8 meters of rope remaining)

Working with 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 is a proper fraction?

• A. 7/5
• B. 9/9
• C. 3/8
• D. 11/6

Answer: C. 3/8 — A proper fraction is one where the numerator is smaller than the denominator. In 3/8, the numerator (3) is less than the denominator (8).

MCQ 2. Convert the mixed fraction 4 2/3 into an improper fraction.

• A. 10/3
• B. 14/3
• C. 8/3
• D. 12/3

Answer: B. 14/3 — To convert a mixed fraction to an improper fraction, multiply the whole number by the denominator and add the numerator. Then, keep the same denominator. So, (4 * 3 + 2) / 3 = 14/3.

MCQ 3. Convert the improper fraction 23/5 into a mixed fraction.

• A. 4 3/5
• B. 5 3/4
• C. 3 4/5
• D. 4 5/3

Answer: A. 4 3/5 — 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 remains the same. 23 ÷ 5 gives a quotient of 4 and a remainder of 3, so it's 4 3/5.

MCQ 4. Which fraction is equivalent to 3/7?

• A. 6/10
• B. 9/21
• C. 12/28
• D. Both B and C

Answer: D. Both B and C — Equivalent fractions are obtained by multiplying both the numerator and the denominator by the same non-zero number. 3/7 * 3/3 = 9/21 and 3/7 * 4/4 = 12/28. So, both B and C are correct.

MCQ 5. Simplify the fraction 24/36 to its simplest form.

• A. 6/9
• B. 12/18
• C. 2/3
• D. 4/6

Answer: C. 2/3 — To simplify a fraction, divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 24 and 36 is 12. So, 24 ÷ 12 = 2 and 36 ÷ 12 = 3, resulting in 2/3.

MCQ 6. Compare the fractions: 5/9 and 7/9.

• A. 5/9 > 7/9
• B. 5/9 < 7/9
• C. 5/9 = 7/9
• D. Cannot be compared

Answer: B. 5/9 < 7/9 — When fractions have the same denominator, the fraction with the larger numerator is greater. Since 5 is less than 7, 5/9 is less than 7/9.

MCQ 7. Which fraction is greater: 2/5 or 3/7?

• A. 2/5
• B. 3/7
• C. Both are equal
• D. Cannot be determined

Answer: B. 3/7 — To compare fractions with different denominators, find a common denominator (LCM of 5 and 7 is 35). 2/5 = 14/35 and 3/7 = 15/35. Since 15/35 > 14/35, 3/7 is greater.

MCQ 8. Add the fractions: 3/10 + 4/10.

• A. 7/20
• B. 12/100
• C. 7/10
• D. 1/2

Answer: C. 7/10 — When adding fractions with the same denominator, add the numerators and keep the denominator common. So, (3 + 4)/10 = 7/10.

MCQ 9. Subtract the fractions: 5/6 - 1/6.

• A. 4/12
• B. 6/6
• C. 4/6
• D. 2/3

Answer: D. 2/3 — When subtracting fractions with the same denominator, subtract the numerators and keep the common denominator. So, (5 - 1)/6 = 4/6. Simplifying 4/6 by dividing both numerator and denominator by 2 gives 2/3.

MCQ 10. Calculate: 1/3 + 1/4.

• A. 2/7
• B. 7/12
• C. 1/12
• D. 2/12

Answer: B. 7/12 — To add fractions with different denominators, find the least common multiple (LCM) of the denominators (LCM of 3 and 4 is 12). Convert both fractions to equivalent fractions with denominator 12: 1/3 = 4/12 and 1/4 = 3/12. Then add them: 4/12 + 3/12 = 7/12.

MCQ 11. Evaluate: 3/4 - 1/2.

• A. 2/2
• B. 2/4
• C. 1/4
• D. 1/8

Answer: C. 1/4 — To subtract fractions with different denominators, find the LCM of the denominators (LCM of 4 and 2 is 4). Convert 1/2 to an equivalent fraction with denominator 4: 1/2 = 2/4. Then subtract: 3/4 - 2/4 = 1/4.

MCQ 12. What is 2/3 of 18?

• A. 6
• B. 12
• C. 9
• D. 24

Answer: B. 12 — To find a fraction of a whole number, multiply the fraction by the whole number. (2/3) * 18 = (2 * 18) / 3 = 36 / 3 = 12.

MCQ 13. Multiply the fractions: 3/5 * 1/2.

• A. 3/10
• B. 4/7
• C. 6/5
• D. 1/3

Answer: A. 3/10 — To multiply fractions, multiply the numerators together and multiply the denominators together. (3 * 1) / (5 * 2) = 3/10.

MCQ 14. What is the reciprocal of 7/11?

• A. 7/11
• B. 11/7
• C. 1/ (7/11)
• D. Both B and C

Answer: D. Both B and C — The reciprocal of a fraction is obtained by swapping its numerator and denominator. So, the reciprocal of 7/11 is 11/7. Option C is also the mathematical definition of reciprocal, which simplifies to 11/7.

MCQ 15. Divide: 5 ÷ 1/3.

• A. 5/3
• B. 15
• C. 1/15
• D. 3/5

Answer: B. 15 — To divide by a fraction, multiply by its reciprocal. So, 5 ÷ 1/3 = 5 * (3/1) = 5 * 3 = 15.

MCQ 16. Calculate: 2/7 ÷ 4.

• A. 8/7
• B. 1/14
• C. 28/2
• D. 1/7

Answer: B. 1/14 — To divide a fraction by a whole number, multiply the fraction by the reciprocal of the whole number. 2/7 ÷ 4 = 2/7 * (1/4) = (2 * 1) / (7 * 4) = 2/28. Simplifying 2/28 gives 1/14.

MCQ 17. Divide: 3/4 ÷ 1/8.

• A. 3/32
• B. 24/4
• C. 6
• D. 1/6

Answer: C. 6 — To divide one fraction by another, multiply the first fraction by the reciprocal of the second fraction. So, 3/4 ÷ 1/8 = 3/4 * (8/1) = (3 * 8) / (4 * 1) = 24/4 = 6.

MCQ 18. Rohan painted 1/5 of a wall on Monday and 2/5 on Tuesday. What fraction of the wall did he paint in total?

• A. 3/10
• B. 3/5
• C. 2/25
• D. 7/5

Answer: B. 3/5 — To find the total fraction painted, add the fractions painted each day: 1/5 + 2/5 = (1+2)/5 = 3/5.

MCQ 19. A cake was cut into 8 equal pieces. If Reema ate 3 pieces and her brother ate 2 pieces, what fraction of the cake is left?

• A. 5/8
• B. 3/8
• C. 1/8
• D. 4/8

Answer: B. 3/8 — Total pieces eaten = 3 + 2 = 5 pieces. The fraction eaten is 5/8. Total cake is 8/8. Fraction left = 8/8 - 5/8 = 3/8.

MCQ 20. A recipe requires 1/2 cup of sugar. If you want to make 3 such recipes, how much sugar do you need?

• A. 3/2 cups
• B. 1/6 cup
• C. 3 cups
• D. 1 and 1/2 cups

Answer: A. 3/2 cups — To find the total sugar needed, multiply the sugar for one recipe by the number of recipes: (1/2) * 3 = 3/2 cups. This is equivalent to 1 and 1/2 cups.

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.

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