NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 4: Fractions & Decimals

Problems and Solutions

Write the fraction represented by the shaded portion of the adjoining figure:

Write the fraction represented by the unshaded portion of the adjoining figure:

Ali divided one fruit cake equally among six persons. What part of the cake did each person get?

Arrange in ascending order: 12.142, 12.124, 12.104, 12.401, 12.214.

Using the digits 1, 5, 3 and 8 once each, write the largest four-digit decimal number less than 1.

Using the digits 2, 4, 5 and 3 once, write the smallest four-digit decimal number (less than 1).

Express \(\dfrac{11}{20}\) as a decimal.

Express \(6\dfrac{2}{3}\) as an improper fraction.

Express \(3\dfrac{2}{5}\) as a decimal.

Express 0.041 as a fraction.

Express 6.03 as a mixed fraction.

Convert 5201 g to kg.

Convert 2009 paise to rupees and express the result as a mixed fraction.

Convert 1537 cm to m and express the result as an improper fraction.

Convert 2435 m to km and express the result as a mixed fraction.

Arrange the fractions \(\dfrac{2}{3},\ \dfrac{3}{4},\ \dfrac{1}{2},\ \dfrac{5}{6}\) in ascending order.

Arrange the fractions \(\dfrac{6}{7},\ \dfrac{7}{8},\ \dfrac{4}{5},\ \dfrac{3}{4}\) in descending order.

Write \(\dfrac{3}{4}\) as a fraction with denominator 44.

Write \(\dfrac{5}{6}\) as a fraction with numerator 60.

Write \(\dfrac{129}{8}\) as a mixed fraction.

Round off 20.83 to the nearest tenths.

Round off 75.195 to the nearest hundredths.

Round off 27.981 to the nearest tenths.

Add the fractions \(\dfrac{3}{8}\) and \(\dfrac{2}{3}\).

Add the fractions \(\dfrac{3}{8}\) and \(6\dfrac{3}{4}\).

Subtract \(\dfrac{1}{6}\) from \(\dfrac{1}{2}\).

Subtract \(8\dfrac{1}{3}\) from \(\dfrac{100}{9}\).

Subtract \(1\dfrac{1}{4}\) from \(6\dfrac{1}{2}\).

Add \(1\dfrac{1}{4}\) and \(6\dfrac{1}{2}\).

Katrina rode her bicycle \(6\dfrac{1}{2}\,\text{km}\) in the morning and \(8\dfrac{3}{4}\,\text{km}\) in the evening. Find the total distance travelled that day.

A rectangle is divided into a certain number of equal parts. If 16 of the parts represent the fraction \(\tfrac{1}{4}\), find the total number of equal parts into which the rectangle has been divided.

Grip size of a tennis racquet is \(11\dfrac{9}{80}\,\text{cm}\). Express this size as an improper fraction.

On an average, \(\tfrac{1}{10}\) of the food eaten becomes available to the next level in a food chain. What fraction of the food eaten is not available for the next level?

Mr. Rajan got a job at the age of 24 and retired at 60. What fraction of his age at retirement had he been in the job?

Food remains in the stomach for a maximum of 4 hours. For what fraction of a day does it remain there?

What should be added to 25.5 to get 50?

Alok purchased 1 kg 200 g potatoes, 250 g dhania, 5 kg 300 g onion, 500 g palak and 2 kg 600 g tomatoes. Find the total weight of his purchases in kilograms.

Arrange in ascending order: 0.011, 1.001, 0.101, 0.110.

Add: 20.02 and 2.002.

By the end of 2007, savings due to Metro trains were: 33000 tonnes of CNG, 3300 tonnes of diesel and 21000 tonnes of petrol. Find the fraction of (i) diesel saved to petrol saved; (ii) diesel saved to CNG saved.

Energy content of foods (per kg) is tabulated below.

Which food provides the least energy and which provides the maximum? Also express the least energy as a fraction of the maximum energy.

A cup is \(\dfrac{1}{3}\) full of milk. What part of the cup is still to be filled to make it full?

Mary bought \(3\dfrac{1}{2}\) m of lace. She used \(1\dfrac{3}{4}\) m. How much lace is left?

Sunita found on Monday that she had gained \(1\dfrac{1}{4}\,\text{kg}\). Earlier her weight was \(46\dfrac{3}{8}\,\text{kg}\). What was her weight on Monday?

Sunil purchased \(12\dfrac{1}{2}\) litres of juice on Monday and \(14\dfrac{3}{4}\) litres on Tuesday. How many litres did he purchase together in two days?

Nazima gave \(2\dfrac{3}{4}\) litres out of the \(5\dfrac{1}{2}\) litres of juice she purchased to her friends. How many litres are left with her?

Roma gave a wooden board of length \(150\dfrac{1}{4}\,\text{cm}\) to a carpenter. The carpenter sawed off a piece of \(40\dfrac{1}{5}\,\text{cm}\). What is the length of the remaining piece?

Nasir travelled \(3\tfrac{1}{2}\) km in a bus and then walked \(1\tfrac{1}{8}\) km to reach a town. How much did he travel to reach the town?

The fish caught by Neetu weighed \(3\tfrac{3}{4}\) kg and the fish caught by Narendra weighed \(2\tfrac{1}{2}\) kg. How much more did Neetu’s fish weigh than Narendra’s?

Neelam’s father needs \(1\tfrac{3}{4}\) m of cloth for the skirt and \(\tfrac{1}{2}\) m for the scarf. How much cloth must he buy in all?

What is wrong in the following additions?

Which is greater: \(1\,\text{m}\ 40\,\text{cm} + 60\,\text{cm}\) or \(2.6\,\text{m}\)?

Match the fractions of Column I with the shaded/marked portion of figures of Column II.

Find the fraction that represents the number of natural numbers to total numbers in the collection \(0,1,2,3,4,5\). What fraction will it be for whole numbers?

For the collection \(-3,-2,-1,0,1,2,3\), write the fraction representing total natural numbers; what will it be for whole numbers and for integers?

Write a pair of fractions whose sum is \(\dfrac{7}{11}\) and difference is \(\dfrac{2}{11}\).

What fraction of a straight angle is a right angle?

Put each card in the correct bag.