Which is heavier: 12 &frasl; 15 of 500 grams or 3 &frasl; 20 of 4 kg?

Bring both to the same unit — grams. 12/15 of 500 g = (12 × 500)/15 = 6000/15 = 400 g 4 kg = 4000 g 3/20 of 4000 g = (3 × 4000)/20 = 12000/20 = 600 g 3 &frasl; 20 of 4 kg (600 g) is heavier than 12 &frasl; 15 of 500 g (400 g), by 200 g. Why the small fraction wins: 3 &frasl; 20 is a much smaller fraction than 12 &frasl; 15 , but it is taken of a quantity 8 times bigger. Always check the whole before comparing fractions.

NCERT Solutions Ganita Prakash (Part 1) Chapter 8 –184Section 8.1 Multiplication of Fractions — Figure it Out

Book page 183 Updated on2026-09-05

Q1.

A water tank is filled from a tap. If the tap is open for 1 hour, ⁷⁄₁₀ of the tank gets filled. How much of the tank is filled if the tap is open for (a) ¹⁄₃ hour ____ (b) ²⁄₃ hour ____ (c) ³⁄₄ hour ____ (d) ⁷⁄₁₀ hour ____ (e) For the tank to be full, how long should the tap be running?

Answer

Each part is (time) × ⁷⁄₁₀.

Tap open for	Working	Part of tank filled
(a) 1/3 hour	1/3 × 7/10	7/30
(b) 2/3 hour	2/3 × 7/10 = 14/30	7/15
(c) 3/4 hour	3/4 × 7/10	21/40
(d) 7/10 hour	7/10 × 7/10	49/100

(e) The tank is full when the filled part is 1.

Time = 1 ÷ 7/10
= 1 × 10/7
= 10/7 hours = 1 3/7 hours ≈ 1 hour 26 minutes

Why it happens: in ⁷⁄₁₀ of an hour only ⁴⁹⁄₁₀₀ of the tank fills — less than half — because you are taking a part of a part.

Q2.

The government has taken ¹⁄₆ of Somu’s land to build a road. What part of the land remains with Somu now? She gives half of the remaining part of the land to her daughter Krishna and ¹⁄₃ of it to her son Bora. After giving them their shares, she keeps the remaining land for herself. (a) What part of the original land did Krishna get? (b) What part of the original land did Bora get? (c) What part of the original land did Somu keep for herself?

Answer

First find what is left after the road is built.

Land left = 1 − 1/6 = 5/6 of the original land

(a) Krishna gets half of that:

1/2 × 5/6 = 5/12

(b) Bora gets one-third of that:

1/3 × 5/6 = 5/18

(c) Somu keeps the rest:

5/6 − 5/12 − 5/18
LCM of 6, 12, 18 = 36
= 30/36 − 15/36 − 10/36
= 5/36

Check it yourself: 1/6 + 5/12 + 5/18 + 5/36 = 6/36 + 15/36 + 10/36 + 5/36 = 36/36 = 1 ✔ All the land is accounted for.

Q3.

Find the area of a rectangle of sides 3 ³⁄₄ ft and 9 ³⁄₅ ft.

Answer

Change both mixed fractions into improper fractions, then multiply.

3 3/4 = 15/4 9 3/5 = 48/5
Area = 15/4 × 48/5
Cancel: 15 and 5 → 3 and 1; 48 and 4 → 12 and 1
= 3 × 12
= 36 square feet

Why it works: the area rule you know for whole-number sides holds for fractional sides too — that is exactly what the unit-square picture showed.

Q4.

Tsewang plants four saplings in a row in his garden. The distance between two saplings is ³⁄₄ m. Find the distance between the first and last sapling. [Hint: Draw a rough diagram with four saplings with distance between two saplings as ³⁄₄ m]

Answer

Four saplings in a row leave 3 gaps, not 4.

Four saplings, three gaps of ³⁄₄ m each.

Distance = 3 × 3/4
= 9/4
= 2 1/4 m

Tip: this is the classic “fence-post” trap — for n objects in a row there are only n − 1 gaps.

Q5.

Which is heavier: ¹²⁄₁₅ of 500 grams or ³⁄₂₀ of 4 kg?

Answer

Bring both to the same unit — grams.

12/15 of 500 g = (12 × 500)/15
= 6000/15
= 400 g

4 kg = 4000 g
3/20 of 4000 g = (3 × 4000)/20
= 12000/20
= 600 g

³⁄₂₀ of 4 kg (600 g) is heavier than ¹²⁄₁₅ of 500 g (400 g), by 200 g.

Why the small fraction wins: ³⁄₂₀ is a much smaller fraction than ¹²⁄₁₅, but it is taken of a quantity 8 times bigger. Always check the whole before comparing fractions.

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