Class 9 Mathematics Chapter 7 Fractions: Important Questions & Solutions

Chapter 7: Fractions is a foundational chapter in the 2024–25 CBSE Class 9 Mathematics syllabus that appears across multiple question formats. Board examiners test fractions through direct computation (1-mark MCQs), conceptual understanding (2-mark short answers), and application-based problem-solving (3 and 5-mark questions). Fractions also act as a prerequisite for Chapters 8 (Exponents & Radicals), Chapter 12 (Heron's Formula), and Chapter 13 (Surface Area & Volume)—topics where fractional coefficients and rational operations are essential. Mastering like and unlike fractions, equivalent fraction recognition, and the ability to convert between fractional and decimal forms will directly boost your marks in arithmetic, algebra, and geometry sections. Moreover, HOTS (Higher Order Thinking Skills) questions now expect you to apply fraction operations to real contexts: recipe scaling, time division, or resource sharing. This guide mirrors the exact difficulty progression and format you'll encounter on exam day.

**Question 1:** Which pair represents equivalent fractions? (a) 3/4 and 6/8 (b) 5/6 and 10/13 (c) 2/5 and 4/9 (d) 7/8 and 14/15 **Answer:** (a) 3/4 and 6/8 **Explanation:** Two fractions are equivalent if one is a simplification of the other. For 3/4 and 6/8: 6/8 = (6÷2)/(8÷2) = 3/4. ✓ --- **Question 2:** Express 7/5 as a mixed number. (a) 1 2/5 (b) 2 1/5 (c) 1 3/5 (d) 2 2/5 **Answer:** (a) 1 2/5 **Explanation:** Divide 7 by 5: 7 = 5 × 1 + 2, so 7/5 = 1 2/5. --- **Question 3:** Compare: 4/9 ___ 5/11 (a) > (b) < (c) = (d) Cannot compare **Answer:** (a) > **Explanation:** Cross-multiply: 4 × 11 = 44 and 5 × 9 = 45. Since 44 < 45, we have 4/9 < 5/11. Wait—let me recalculate. Actually 4 × 11 = 44 and 9 × 5 = 45, so 44 < 45 means 4/9 < 5/11. The correct answer is **(b) <**. --- **Question 4:** Which fraction lies between 1/3 and 1/2 on a number line? (a) 2/5 (b) 2/7 (c) 1/5 (d) 3/7 **Answer:** (a) 2/5 **Explanation:** 1/3 ≈ 0.333, 1/2 = 0.5, 2/5 = 0.4. Since 0.333 < 0.4 < 0.5, 2/5 lies between them. --- **Question 5:** What is the decimal representation of 5/8? (a) 0.625 (b) 0.725 (c) 0.525 (d) 0.825 **Answer:** (a) 0.625 **Explanation:** 5 ÷ 8 = 0.625. Verification: 0.625 × 8 = 5. ✓

**Question 1:** Express 12/18 in its lowest terms and then write an equivalent fraction with denominator 30. **Solution:** Step 1: Find GCD(12, 18). Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 18: 1, 2, 3, 6, 9, 18 GCD = 6 Step 2: Simplify 12/18 = (12÷6)/(18÷6) = 2/3 Step 3: Find equivalent fraction with denominator 30. 2/3 = (2 × 10)/(3 × 10) = 20/30 **Answer:** Lowest form is 2/3; equivalent fraction with denominator 30 is 20/30. --- **Question 2:** Add 3/7 + 2/5. Express your answer as a mixed number. **Solution:** Step 1: Find LCM(7, 5) = 35 (since 7 and 5 are coprime). Step 2: Convert to like fractions: 3/7 = (3 × 5)/(7 × 5) = 15/35 2/5 = (2 × 7)/(5 × 7) = 14/35 Step 3: Add: 15/35 + 14/35 = 29/35 Step 4: Check if 29/35 can be simplified or expressed as a mixed number. Since 29 < 35, it remains 29/35 (proper fraction, not a mixed number). **Answer:** 29/35 --- **Question 3:** From 5/6, subtract 1/4 and verify your answer. **Solution:** Step 1: Find LCM(6, 4) = 12. Step 2: Convert: 5/6 = (5 × 2)/(6 × 2) = 10/12 1/4 = (1 × 3)/(4 × 3) = 3/12 Step 3: Subtract: 10/12 − 3/12 = 7/12 Step 4: Verify by adding back: 7/12 + 3/12 = 10/12 = 5/6 ✓ **Answer:** 7/12 --- **Question 4:** Multiply 4/9 by 3/8 and express in simplest form. **Solution:** Step 1: Multiply numerators and denominators: (4 × 3)/(9 × 8) = 12/72 Step 2: Simplify by finding GCD(12, 72). 12 = 2² × 3 72 = 2³ × 3² GCD = 2² × 3 = 12 Step 3: Reduce: 12/72 = (12÷12)/(72÷12) = 1/6 **Answer:** 1/6 --- **Question 5:** Divide 5/6 by 2/3 and simplify. **Solution:** Step 1: Recall: a/b ÷ c/d = a/b × d/c (multiply by reciprocal) Step 2: Apply: 5/6 ÷ 2/3 = 5/6 × 3/2 = (5 × 3)/(6 × 2) = 15/12 Step 3: Simplify: GCD(15, 12) = 3 15/12 = (15÷3)/(12÷3) = 5/4 = 1 1/4 **Answer:** 5/4 or 1 1/4

**Question 1:** A recipe requires 2 3/4 cups of flour. If you want to make 1/2 of the recipe, how much flour do you need? Show your working. **Solution:** Step 1: Convert mixed number to improper fraction: 2 3/4 = (2 × 4 + 3)/4 = 11/4 cups Step 2: Multiply by 1/2: 11/4 × 1/2 = 11/8 cups Step 3: Convert to mixed number: 11/8 = 1 3/8 cups **Answer:** You need 1 3/8 cups of flour. --- **Question 2:** A water tank is 3/5 full. If 1/4 of the tank's capacity is used, what fraction of the tank remains full? **Solution:** Step 1: The tank currently holds 3/5 of its capacity. Step 2: 1/4 of the tank's capacity is used. Remaining = 3/5 − 1/4 Step 3: Find LCM(5, 4) = 20. 3/5 = (3 × 4)/(5 × 4) = 12/20 1/4 = (1 × 5)/(4 × 5) = 5/20 Step 4: Subtract: 12/20 − 5/20 = 7/20 **Answer:** 7/20 of the tank remains full. --- **Question 3:** A field is divided among three farmers. Farmer A gets 2/5, Farmer B gets 3/10, and Farmer C gets the rest. What fraction does Farmer C get? Who receives the largest share? **Solution:** Step 1: Find what fraction Farmers A and B receive: A + B = 2/5 + 3/10 Step 2: Find LCM(5, 10) = 10: 2/5 = 4/10 A + B = 4/10 + 3/10 = 7/10 Step 3: Farmer C gets: C = 1 − 7/10 = 10/10 − 7/10 = 3/10 Step 4: Compare shares: A = 2/5 = 4/10 B = 3/10 C = 3/10 Since 4/10 > 3/10, Farmer A receives the largest share. **Answer:** Farmer C gets 3/10; Farmer A has the largest share (2/5). --- **Question 4:** Simplify: (3/4 + 1/8) ÷ (5/6 − 1/3) **Solution:** Step 1: Simplify the numerator (3/4 + 1/8): LCM(4, 8) = 8 3/4 = 6/8 6/8 + 1/8 = 7/8 Step 2: Simplify the denominator (5/6 − 1/3): LCM(6, 3) = 6 1/3 = 2/6 5/6 − 2/6 = 3/6 = 1/2 Step 3: Divide: 7/8 ÷ 1/2 = 7/8 × 2/1 = 14/8 = 7/4 = 1 3/4 **Answer:** 7/4 or 1 3/4

**Question 1:** A worker completes 2/5 of a project on Monday and 3/10 on Tuesday. On Wednesday, they complete 1/6 of the remaining work. What fraction of the work remains? If the project takes 6 more hours to complete on Thursday, what was the total project time? **Solution:** Step 1: Find work completed on Monday and Tuesday: Monday + Tuesday = 2/5 + 3/10 LCM(5, 10) = 10 2/5 = 4/10 4/10 + 3/10 = 7/10 completed Step 2: Work remaining after Tuesday: 1 − 7/10 = 3/10 of the project Step 3: Work completed on Wednesday: Wednesday = 1/6 of remaining work = 1/6 × 3/10 = 3/60 = 1/20 Step 4: Total work completed by Wednesday: 7/10 + 1/20 LCM(10, 20) = 20 7/10 = 14/20 14/20 + 1/20 = 15/20 = 3/4 Step 5: Work remaining after Wednesday: 1 − 3/4 = 1/4 Step 6: If 1/4 of work = 6 hours: Total project time = 6 ÷ (1/4) = 6 × 4 = 24 hours **Answer:** Fraction remaining = 1/4; Total project time = 24 hours. --- **Question 2:** Three containers hold juice. Container A has 5 1/2 litres, Container B has 3 2/3 litres, and Container C has 4 1/4 litres. If 2/3 of the total juice is poured into a large tank, how many litres remain in the containers? Round to one decimal place. **Solution:** Step 1: Convert mixed numbers to improper fractions: A = 5 1/2 = 11/2 litres B = 3 2/3 = 11/3 litres C = 4 1/4 = 17/4 litres Step 2: Find total juice: Total = 11/2 + 11/3 + 17/4 LCM(2, 3, 4) = 12 11/2 = 66/12 11/3 = 44/12 17/4 = 51/12 Total = (66 + 44 + 51)/12 = 161/12 litres Step 3: Juice poured into tank: Poured = 2/3 × 161/12 = 322/36 = 161/18 litres Step 4: Juice remaining: Remaining = 161/12 − 161/18 LCM(12, 18) = 36 161/12 = 483/36 161/18 = 322/36 Remaining = (483 − 322)/36 = 161/36 ≈ 4.472 litres **Answer:** Approximately 4.5 litres remain in the containers. --- **Question 3:** A tailor has 8 3/4 metres of cloth. They use 2/5 for a shirt, 1/3 of the remainder for trousers, and the rest for a jacket. (a) How much cloth is used for each garment? (b) Express each as a decimal. (c) Arrange in ascending order. **Solution:** Step 1: Convert initial cloth to improper fraction: 8 3/4 = 35/4 metres Step 2: Cloth used for shirt: Shirt = 2/5 × 35/4 = (2 × 35)/(5 × 4) = 70/20 = 7/2 metres Step 3: Cloth remaining after shirt: Remaining = 35/4 − 7/2 = 35/4 − 14/4 = 21/4 metres Step 4: Cloth used for trousers: Trousers = 1/3 × 21/4 = 21/12 = 7/4 metres Step 5: Cloth used for jacket: Jacket = 21/4 − 7/4 = 14/4 = 7/2 metres Step 6: Convert to decimals: Shirt = 7/2 = 3.5 metres Trousers = 7/4 = 1.75 metres Jacket = 7/2 = 3.5 metres Step 7: Arrange in ascending order: 1.75 < 3.5 = 3.5 Trousers < Shirt = Jacket **Answer:** (a) Shirt: 7/2 m, Trousers: 7/4 m, Jacket: 7/2 m. (b) Shirt: 3.5 m, Trousers: 1.75 m, Jacket: 3.5 m. (c) Trousers (1.75 m) < Shirt & Jacket (3.5 m).

**Case Study:** A school cafeteria serves lunch to students. On Monday, 3/8 of students chose biryani and 2/5 chose noodles. The rest chose dal-rice. On Tuesday, due to lower attendance, the number of students was 4/5 of Monday's total. Of Tuesday's students, 1/2 chose biryani, 1/4 chose noodles, and the rest chose dal-rice. **Part (a):** On Monday, what fraction chose dal-rice? **Solution:** Fraction choosing biryani and noodles = 3/8 + 2/5 LCM(8, 5) = 40 3/8 = 15/40 2/5 = 16/40 Total = 31/40 Fraction choosing dal-rice = 1 − 31/40 = 9/40 --- **Part (b):** If there were 800 students on Monday, how many chose each item on both days? **Solution:** **Monday (800 students):** Biryani: 3/8 × 800 = 300 students Noodles: 2/5 × 800 = 320 students Dal-rice: 9/40 × 800 = 180 students **Tuesday (4/5 × 800 = 640 students):** Biryani: 1/2 × 640 = 320 students Noodles: 1/4 × 640 = 160 students Dal-rice: (1 − 1/2 − 1/4) × 640 = 1/4 × 640 = 160 students --- **Part (c):** On which day did fewer students choose dal-rice, and by what fraction of Monday's total? **Solution:** Monday dal-rice: 180 students Tuesday dal-rice: 160 students Difference: 180 − 160 = 20 students As a fraction of Monday's total (800): 20/800 = 1/40 On Tuesday, 1/40 fewer students (relative to Monday's total) chose dal-rice. **Answers:** (a) 9/40 chose dal-rice on Monday. (b) Monday: Biryani 300, Noodles 320, Dal-rice 180; Tuesday: Biryani 320, Noodles 160, Dal-rice 160. (c) Tuesday had fewer; difference is 1/40 of Monday's total.

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