NCERT Solutions for Class 7 Maths Chapter 8 Working with Fractions (PDF) – 2027

Walking for 5 hours means covering the 1-hour distance 5 times.

The speed is a fraction now, but nothing else changes — still multiply.

The tortoise can walk ³⁄₄ km in 3 hours.

One-fifth of an hour covers one-fifth of the 1-hour distance.

So ¹⁄₅ × 3 = ³⁄₅.

Work in two steps — first one-fifth of an hour, then double it.

So ²⁄₅ × 3 = ⁶⁄₅.

Five equal shares of ²⁄₃ acre each.

First change the mixed fraction into an improper fraction.

Multiply the daily amount by the number of days.

One kilometre of work is spread equally over 8 days.

Five litres shared equally by 3 families.

Monday to Thursday is 3 days, so the delay builds up three times.

So the Moon sets at about 12:30 am (past midnight).

Multiply the whole number into the numerator, then split off the whole part.

Half an hour covers half of the one-hour distance.

The whole is now in 8 equal parts and one of them is shaded.

So ¹⁄₂ × ¹⁄₄ = ¹⁄₈, and the tortoise walks ¹⁄₈ km in half an hour.

Same two steps: divide by 4, then multiply by 3.

So ³⁄₄ × ²⁄₅ = ⁶⁄₂₀ = ³⁄₁₀.

Draw ³⁄₂ as one whole and a half, then cut it into 4 equal parts.

The big square is a unit square, so each side is 1 unit long.

Eight of these rectangles tile the unit square.

They are equal — the area of a rectangle with fractional sides is the product of its sides.

Cut the unit square into rows (denominator of the second fraction) and columns (denominator of the first fraction), then shade one cell.

Use the rows-and-columns pattern instead of drawing 216 cells.

In general, for two fractional units:

Now more than one cell gets shaded — as many as (numerator × numerator).

Follow the same two steps, but with the general numbers.

⁵⁄₁₂ × ⁷⁄₁₈ = ³⁵⁄₂₁₆

Cancel the common factor before multiplying.

Cancel across the numerators and denominators, then multiply.

Each part is (time) × ⁷⁄₁₀.

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

First find what is left after the road is built.

(a) Krishna gets half of that:

(b) Bora gets one-third of that:

(c) Somu keeps the rest:

Change both mixed fractions into improper fractions, then multiply.

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

Bring both to the same unit — grams.

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

Everything depends on where each number sits compared with 1.

• When one of the numbers is between 0 and 1, the product is less than the other number.
• When one of the numbers is greater than 1, the product is greater than the other number.

It is ¹⁄₈ too.

12 ÷ 4 = 3, and the same fact can be written the other way round.

Ask instead: what times ²⁄₃ gives 1?

We already know what makes ²⁄₃ into 1 — now make it 3 times as much.

Rewrite as a multiplication and use the reciprocal of the divisor.

The reciprocal of the divisor ³⁄₅ is ⁵⁄₃.

Yes. To divide two fractions:

1. Find the reciprocal of the divisor (turn it upside down).
2. Multiply the dividend by that reciprocal.

It depends on the divisor, exactly as with multiplication.

• Divisor greater than 1 → quotient is less than the dividend.
• Divisor between 0 and 1 → quotient is greater than the dividend.
• Divisor equal to 1 → quotient equals the dividend.

Yes — for a fixed dividend, the divisor and the quotient move in opposite directions.

So the bigger the divisor, the smaller the quotient, and the smaller the divisor, the bigger the quotient. The two are equal only when divisor × divisor = dividend, for example 9 ÷ 3 = 3.

One-quarter litre of milk is shared equally by 5 cups.

Find the area of one brick first.

Count how many cisterns each fountain fills in one full day.

Peel the picture one layer at a time, taking the whole square as 1 square unit.

So the shaded region occupies ³⁄₃₂ of the whole square.

³⁄₄ of the yellow triangle is shaded.

Figure (a): ³⁄₈. The shaded band lies between two parallel diagonals.

Figure (b): ¹⁄₁₆. Everything happens inside the top-left quarter.

“Of” means multiply — so multiply all six fractions.

Work backwards along the chain of coins.

Turn every divisor upside down and multiply.

(a) Option (iii) — how many quarter-metre pieces are in 8 m?

(b) Option (iv) — half a metre is shared among 8 badges.

(c) Option (iii) — how many sixth-kilogram scoops are in 5 kg?

Six rotis are half of twelve rotis.

Dividing 1 by a unit fraction just gives back its denominator.

The friend should say 40.

Find the pages read on each day, then subtract from 400.

Multiply the mileage by the number of litres.

The time saved is the difference of the two times.

The plane saves 4 ²⁄₃ hours, that is 4 hours 40 minutes.

Find what is left, then split it three ways.

You do not have to multiply — just check where each fraction sits compared with 1.

Both numbers are greater than 1. So the product is greater than each of them, and greater than 1.

Correct options: (a), (c) and (e).

The shading lies entirely inside the bottom-right quarter of the square.

Take the whole colony as 1. At each red point the ants that arrive split equally among the paths going out.

General statement:

Explanation: each bracket 1 − ¹⁄_k = ^{k − 1}⁄_k. So the product is ¹⁄₂ × ²⁄₃ × … × ^{n − 1}⁄_n, and each denominator cancels the next numerator, leaving ¹⁄_n.

Chess grew out of the ancient Indian game chaturanga. Here is how the six pieces move.

The aim is checkmate — trapping the opponent’s King so that it cannot escape capture.

On a 4 × 4 board there must be exactly one Queen in every row and every column, and no two on a diagonal.

Again, one Queen per row and per column, with all diagonals clear.

So no two Queens share a row, a column or a diagonal.