NCERT Solutions for Class 7 Maths Chapter 8: Working with Fractions – Ganita Prakash

Complete NCERT Solutions for Class 7 Maths Chapter 8 “Working with Fractions” from the Ganita Prakash textbook, covering multiplication and division of fractions with real-world applications. These Class 7 Mathematics Chapter 8 solutions are also useful as quick revision notes before exams.

Figure It Out (Pages 176-177): Multiplying Fractions

Q1. Tenzin drinks 1/2 glass of milk daily. In a week: 7 × 1/2 = 7/2 = 3½ glasses. In January (31 days): 31 × 1/2 = 31/2 = 15½ glasses.

Q2. Workers make 1 km of canal in 8 days. In a week (5 working days): 5 × 1/8 = 5/8 km.

Q3. Manju and 2 neighbours share 5 litres of oil weekly among 3 families. Each family gets 5/3 litres/week. In 4 weeks: 4 × 5/3 = 20/3 = 6⅔ litres.

Q4. The Moon sets 5/6 hour later each day. From Monday to Thursday is 3 days: 3 × 5/6 = 15/6 = 5/2 hours = 2 hours 30 minutes later.

Q5. Multiply and convert to mixed fractions: (a) 7×3/5 = 21/5 = 4₁⁄₅ (b) 4×1/3 = 4/3 = 1⅓ (c) 9/7×6 = 54/7 = 7⁵⁄₄ (d) 13/11×6 = 78/11 = 7₁⁄₁₁

Figure It Out (Pages 180-181): Multiplying Fractions Using Area Models

Using unit-square area models to multiply fractions:

• 1/3 × 1/5 = 1/15
• 1/4 × 1/3 = 1/12
• 1/5 × 1/2 = 1/10
• 1/6 × 1/5 = 1/30
• 2/3 × 4/5 = 8/15
• 1/4 × 2/3 = 2/12 = 1/6
• 3/5 × 1/2 = 3/10
• 4/6 × 3/5 = 12/30 = 2/5 (in lowest terms)

General rule: to multiply two fractions, multiply the numerators together and the denominators together: (a/b) × (c/d) = (a×c)/(b×d).

Figure It Out (Pages 183-184): Fraction Word Problems

Q1. A tap fills 7/10 of a tank in 1 hour. How much fills in: 1/3 hour → 1/3×7/10 = 7/30; 2/3 hour → 2/3×7/10 = 14/30 = 7/15; 3/4 hour → 3/4×7/10 = 21/40; 7/10 hour → 7/10×7/10 = 49/100. Time for a full tank: since 7/10 fills in 1 hour, a full tank needs 10/7 = 1₁⁄₇ hours.

Q2. The government takes 1/6 of Somu’s land, leaving 5/6. Krishna gets half of the remainder: 1/2×5/6 = 5/12. Bora gets a third of the remainder: 1/3×5/6 = 5/18. Somu keeps the rest: 1 − 1/6 − 5/12 − 5/18 = 5/36 of the original land.

Q3. Area of a rectangle with sides 3¾ ft and 9⅝ ft: 3¾=15/4, 9⅝=48/5. Area = 15/4 × 48/5 = 720/20 = 36 sq ft.

Q4. Tsewang plants 4 saplings in a row, 3/4 m apart (3 gaps). Distance from first to last: 3 × 3/4 = 9/4 = 2¼ m.

Q5. Which is heavier: 12/15 of 500g, or 3/20 of 4 kg? 12/15 of 500g = 400g. 3/20 of 4000g = 600g, which is heavier.

Understanding Products of Fractions

When is a product smaller than the numbers being multiplied? When one factor is between 0 and 1, the product is smaller than the other factor (e.g., 1/2×100=50, which is less than 100). When one factor is greater than 1, the product is greater than the other factor (e.g., 1½×1/4=3/8, which is greater than 1/4=2/8).

Division of Fractions

To divide by a fraction, multiply by its reciprocal (flip the fraction upside down): 1/2 ÷ 1/3 = 1/2 × 3/1 = 3/2 = 1½ (note: the result is larger, since we’re dividing by a number less than 1). Similarly, 1/5 ÷ 2 = 1/5 × 1/2 = 1/10. Dividing by 1 always returns the original number: 3/5 ÷ 1 = 3/5.

The Four Fountains Problem

Four fountains fill a cistern: fountain 1 in 1 day, fountain 2 in half a day, fountain 3 in a quarter day, fountain 4 in a fifth of a day. Their per-day filling rates: fountain 1 = 1÷1 = 1; fountain 2 = 1÷(1/2) = 2; fountain 3 = 1÷(1/4) = 4; fountain 4 = 1÷(1/5) = 5. Combined rate = 1+2+4+5 = 12 cisterns per day, so together they fill one cistern in 1/12 of a day.

A Dramma-tic Donation (Ancient Indian Currency Units)

Given: 1 gold dinar = 12 silver drammas; 1 silver dramma = 4 copper panas; 1 pana = 30 cowrie shells. So, 1 copper pana = 1/12 × 1/4 = 1/48 gold dinar. And 1 cowrie shell = 1/48 × 1/30 = 1/1440 gold dinar.

Figure It Out (Pages 196-198): Applying Multiplication and Division

Q2. Choosing the correct expression and solving: (a) Maria has 8m lace, uses 1/4m per bag: 8 ÷ 1/4 = 32 bags. (b) 1/2m ribbon shared among 8 badges: 1/2 ÷ 8 = 1/2 × 1/8 = 1/16 m each. (c) A baker has 5kg flour, uses 1/6kg per loaf: 5 ÷ 1/6 = 30 loaves.

Q3. If 1/4 kg flour makes 12 rotis, flour for 6 rotis (half as many) = 1/4 ÷ 2 = 1/8 kg.

Q4. Sum of 1÷1/6, 1÷1/10, 1÷1/13, 1÷1/9, and 1÷1/2: = 6+10+13+9+2 = 40.

Q5. Mira reads 1/5 of a 400-page novel yesterday, and 3/10 today: 1/5 of 400=80 pages; 3/10 of 400=120 pages; total read=200 pages. Remaining = 400−200 = 200 pages.

Q6. A car runs 16 km per litre of petrol. Distance on 2¾ litres: 2¾=11/4; 16 × 11/4 = 176/4 = 44 km.

Q7. A train takes 5⅙ hours; a plane takes 1/2 hour for the same trip. Time saved: 5⅙ − 1/2 = 31/6 − 3/6 = 28/6 = 4⅔ hours.

Q8. Mariam and cousins finish 4/5 of a cake; the remaining 1/5 is shared equally among 3 friends: 1/5 ÷ 3 = 1/5 × 1/3 = 1/15 of the cake each.

Q9. For the product (565/465) × (707/676): since both fractions are greater than 1, the product is greater than 1, greater than 565/465, and greater than 707/676 (options a, c, e are correct).

Q10. A big square is divided into 4 identical squares; one small square (1/4 of the whole) is divided into 8 triangles, with 3 shaded: shaded fraction of the whole = 1/4 × 3/8 = 3/32.

Q11. An ant colony repeatedly splits at branch points before reaching two food sources. Tracking each split as a fraction of the original group (halving/quartering at each split), the mango tree receives 29/32 of the original group, and the sugarcane field receives 3/32 (these sum to 32/32 = 1, confirming all ants are accounted for).

Q12. General pattern: (1−1/2)×(1−1/3)×(1−1/4)×…×(1−1/n) = 1/n (this telescoping product can be verified for small n, e.g., n=3: (1/2)(2/3)=1/3; n=4: (1/2)(2/3)(3/4)=1/4).

Extra Questions: Class 7 Maths Chapter 8
Revision Notes: Class 7 Maths Chapter 8