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

Complete NCERT Exemplar for Class 6 - Unit 3: Fractions & Decimals with answers and step by step solutions.

Multiple Choice Questions

In questions 1 to 20, out of the four options, only one is correct. Write the correct answer.

Question.  1

The fraction which is not equal to \(\tfrac{4}{5}\) is

(A)

\(\tfrac{40}{50}\)

(B)

\(\tfrac{12}{15}\)

(C)

\(\tfrac{16}{20}\)

(D)

\(\tfrac{9}{15}\)

Open

Question.  2

The two consecutive integers between which \(\tfrac{5}{7}\) lies are

(A)

5 and 6

(B)

0 and 1

(C)

5 and 7

(D)

6 and 7

Open

Question.  3

When \(\tfrac{1}{4}\) is written with denominator 12, its numerator is

(A)

3

(B)

8

(C)

24

(D)

12

Open

Question.  4

Which of the following is not in the lowest form?

(A)

\(\tfrac{7}{5}\)

(B)

\(\tfrac{15}{20}\)

(C)

\(\tfrac{13}{33}\)

(D)

\(\tfrac{27}{28}\)

Open

Question.  5

If \(\tfrac{5}{8}=\tfrac{20}{p}\), then the value of \(p\) is

(A)

23

(B)

2

(C)

32

(D)

16

Open

Question.  6

Which of the following is not equal to the others?

(A)

\(\tfrac{6}{8}\)

(B)

\(\tfrac{12}{16}\)

(C)

\(\tfrac{15}{25}\)

(D)

\(\tfrac{18}{24}\)

Open

Question.  7

Which of the following fractions is the greatest?

(A)

\(\tfrac{5}{7}\)

(B)

\(\tfrac{5}{6}\)

(C)

\(\tfrac{5}{9}\)

(D)

\(\tfrac{5}{8}\)

Open

Question.  8

Which of the following fractions is the smallest?

(A)

\(\tfrac{7}{8}\)

(B)

\(\tfrac{9}{8}\)

(C)

\(\tfrac{3}{8}\)

(D)

\(\tfrac{5}{8}\)

Open

Question.  9

Sum of \(\tfrac{4}{17}\) and \(\tfrac{15}{17}\) is

(A)

\(\tfrac{19}{17}\)

(B)

\(\tfrac{11}{17}\)

(C)

\(\tfrac{19}{34}\)

(D)

\(\tfrac{2}{17}\)

Open

Question.  10

On subtracting \(\tfrac{5}{9}\) from \(\tfrac{19}{9}\), the result is

(A)

\(\tfrac{24}{9}\)

(B)

\(\tfrac{14}{9}\)

(C)

\(\tfrac{14}{18}\)

(D)

\(\tfrac{14}{0}\)

Open

Question.  11

0.7499 lies between

(A)

0.7 and 0.74

(B)

0.75 and 0.79

(C)

0.749 and 0.75

(D)

0.74992 and 0.75

Open

Question.  12

0.023 lies between

(A)

0.2 and 0.3

(B)

0.02 and 0.03

(C)

0.03 and 0.029

(D)

0.026 and 0.024

Open

Question.  13

\(11/7\) can be expressed in the form

(A)

\(7\tfrac{1}{4}\)

(B)

\(1\tfrac{4}{7}\)

(C)

\(1\tfrac{4}{7}\)

(D)

\(11\tfrac{1}{7}\)

Open

Question.  14

The mixed fraction \(5\tfrac{4}{7}\) can be expressed as

(A)

\(33/7\)

(B)

\(39/7\)

(C)

\(33/4\)

(D)

\(39/4\)

Open

Question.  15

0.07 + 0.008 is equal to

(A)

0.15

(B)

0.015

(C)

0.078

(D)

0.78

Open

Question.  16

Which of the following decimals is the greatest?

(A)

0.182

(B)

0.0925

(C)

0.29

(D)

0.038

Open

Question.  17

Which of the following decimals is the smallest?

(A)

0.27

(B)

1.5

(C)

0.082

(D)

0.103

Open

Question.  18

13.572 correct to the tenths place is

(A)

10

(B)

13.57

(C)

14.5

(D)

13.6

Open

Question.  19

15.8 − 6.73 is equal to

(A)

8.07

(B)

9.07

(C)

9.13

(D)

9.25

Open

Question.  20

The decimal 0.238 is equal to the fraction

(A)

119/500

(B)

238/25

(C)

119/25

(D)

119/50

Open

Fill in the Blanks

In questions 21 to 44, fill in the blanks to make the statements true:

Question. 21

A number representing a part of a ______ is called a fraction.

Answer:

A number representing a part of a whole is called a fraction.

Open

Question. 22

A fraction with denominator greater than the numerator is called a ______ fraction.

Answer:

A fraction with denominator greater than the numerator is called a proper fraction.

Open

Question. 23

Fractions with the same denominator are called ______ fractions.

Answer:

Fractions with the same denominator are called like fractions.

Open

Question. 24

\(13\tfrac{5}{18}\) is a ______ fraction.

Answer:

\(13\tfrac{5}{18}\) is a mixed fraction.

Open

Question. 25

\(\tfrac{18}{5}\) is an _____ fraction.

Answer:

\(\tfrac{18}{5}\) is an improper fraction.

Open

Question. 26

\(\tfrac{7}{19}\) is a _____ fraction.

Answer:

\(\tfrac{7}{19}\) is a proper fraction.

Open

Question. 27

\(\tfrac{5}{8}\) and \(\tfrac{3}{8}\) are _____ proper fractions.

Answer:

\(\tfrac{5}{8}\) and \(\tfrac{3}{8}\) are like proper fractions.

Open

Question. 28

\(\tfrac{6}{11}\) and \(\tfrac{6}{13}\) are _____ proper fractions.

Answer:

\(\tfrac{6}{11}\) and \(\tfrac{6}{13}\) are unlike proper fractions.

Open

Question. 29

The fraction \(\tfrac{6}{15}\) in simplest form is _____.

Answer:

The fraction \(\tfrac{6}{15}\) in simplest form is \(\tfrac{2}{5}\).

Open

Question. 30

The fraction \(\tfrac{17}{34}\) in simplest form is _____.

Answer:

The fraction \(\tfrac{17}{34}\) in simplest form is \(\tfrac{1}{2}\).

Open

Question. 31

\(\tfrac{18}{135}\) and \(\tfrac{90}{675}\) are proper, unlike and _____ fractions.

Answer:

\(\tfrac{18}{135}\) and \(\tfrac{90}{675}\) are proper, unlike and equivalent fractions.

Open

Question. 32

\(8\tfrac{2}{7}\) is equal to the improper fraction _____.

Answer:

\(8\tfrac{2}{7}\) is equal to the improper fraction \(\tfrac{58}{7}\).

Open

Question. 33

\(\tfrac{87}{7}\) is equal to the mixed fraction _____.

Answer:

\(\tfrac{87}{7}\) is equal to the mixed fraction \(12\tfrac{3}{7}\).

Open

Question. 34

\(9+\tfrac{2}{10}+\tfrac{6}{100}\) is equal to the decimal number _____.

Answer:

\(9+\tfrac{2}{10}+\tfrac{6}{100}\) is equal to the decimal number 9.26.

Open

Question. 35

Decimal 16.25 is equal to the fraction _____.

Answer:

Decimal 16.25 is equal to the fraction \(\tfrac{65}{4}\).

Open

Question. 36

Fraction \(\tfrac{7}{25}\) is equal to the decimal number _____.

Answer:

Fraction \(\tfrac{7}{25}\) is equal to the decimal number 0.28.

Open

Question. 37

\(\tfrac{17}{9}+\tfrac{41}{9}=\) _____.

Answer:

\(\tfrac{17}{9}+\tfrac{41}{9}=\) \(\tfrac{58}{9}\).

Open

Question. 38

\(\tfrac{67}{14}-\tfrac{24}{14}=\) _____.

Answer:

\(\tfrac{67}{14}-\tfrac{24}{14}=\) \(\tfrac{43}{14}\).

Open

Question. 39

\(\tfrac{17}{2}+3\tfrac{1}{2}=\) _____.

Answer:

\(\tfrac{17}{2}+3\tfrac{1}{2}=\) 12.

Open

Question. 40

\(9\tfrac{1}{4}-\tfrac{5}{4}=\) _____.

Answer:

\(9\tfrac{1}{4}-\tfrac{5}{4}=\) 8.

Open

Question. 41

\(4.55+9.73=\) _____.

Answer:

\(4.55+9.73=\) 14.28.

Open

Question. 42

\(8.76-2.68=\) _____.

Answer:

\(8.76-2.68=\) 6.08.

Open

Question. 43

The value of 50 coins of 50 paisa = Rs _____.

Answer:

The value of 50 coins of 50 paisa = Rs 25.

Open

Question. 44

3 hundredths + 3 tenths = _____.

Answer:

3 hundredths + 3 tenths = 0.33.

Open

True or False Questions

In each of the questions 45 to 65, state whether the statement is true or false:

Question. 45

Fractions with same numerator are called like fractions.

Answer:

false

Open

Question. 46

Fraction \(\tfrac{18}{39}\) is in its lowest form.

Answer:

false

Open

Question. 47

Fractions \(\tfrac{15}{39}\) and \(\tfrac{45}{117}\) are equivalent fractions.

Answer:

true

Open

Question. 48

The sum of two fractions is always a fraction.

Answer:

true

Open

Question. 49

The result obtained by subtracting a fraction from another fraction is necessarily a fraction.

Answer:

true

Open

Question. 50

If a whole or an object is divided into a number of equal parts, then each part represents a fraction.

Answer:

true

Open

Question. 51

The place value of a digit at the tenths place is 10 times the same digit at the ones place.

Answer:

false

Open

Question. 52

The place value of a digit at the hundredths place is \(\tfrac{1}{10}\) times the same digit at the tenths place.

Answer:

true

Open

Question. 53

The decimal 3.725 is equal to 3.72 correct to two decimal places.

Answer:

true

Open

Question. 54

In the decimal form, fraction \(\tfrac{25}{8}=3.125\).

Answer:

true

Open

Question. 55

The decimal 23.2 = 23\(\tfrac{2}{5}\).

Answer:

true

Open

Question. 56

The fraction represented by the shaded portion in the adjoining figure is \(\tfrac{3}{8}\).

Answer:

true

Open

Question. 57

The fraction represented by the unshaded portion in the adjoining figure is \(\tfrac{5}{9}\).

Answer:

true

Open

Question. 58

\(\tfrac{25}{19}+\tfrac{6}{19}=\tfrac{31}{38}\).

Answer:

false

Open

Question. 59

\(\tfrac{8}{18}-\tfrac{8}{15}=\tfrac{8}{3}\).

Answer:

false

Open

Question. 60

\(\tfrac{7}{12}+\tfrac{11}{12}=\tfrac{3}{2}\).

Answer:

true

Open

Question. 61

3.03+0.016=3.019

Answer:

true

Open

Question. 62

42.28−3.19=39.09

Answer:

true

Open

Question. 63

\(\tfrac{16}{25}>\tfrac{13}{25}\)

Answer:

true

Open

Question. 64

19.25 < 19.053

Answer:

false

Open

Question. 65

13.730 = 13.73

Answer:

true

Open

Fill in the Blanks (Relation)

In each of the questions 66 to 71, fill in the blanks using ‘>’, ‘<’ or ‘=’ :

Question. 66

\(\tfrac{11}{16} \, ... \, \tfrac{14}{15}\)

Answer:

\(\tfrac{11}{16} \, < \, \tfrac{14}{15}\)

Open

Question. 67

\(\tfrac{8}{15} \, ... \, \tfrac{95}{14}\)

Answer:

\(\tfrac{8}{15} \, < \, \tfrac{95}{14}\)

Open

Question. 68

\(\tfrac{12}{75} \, ... \, \tfrac{32}{200}\)

Answer:

\(\tfrac{12}{75} \, = \, \tfrac{32}{200}\)

Open

Question. 69

3.25 ... 3.4

Answer:

3.25 < 3.4

Open

Question. 70

\(\tfrac{18}{15} \, ... \, 1.3\)

Answer:

\(\tfrac{18}{15} \, > \, 1.3\)

Open

Question. 71

6.25 ... \(\tfrac{25}{4}\)

Answer:

6.25 = \(\tfrac{25}{4}\)

Open

Problems and Solutions

Questions 72 to 118 with detailed solutions and explanations.

Question. 72

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

Q72 figure

Answer:

\(\dfrac{3}{8}\)

Open

Question. 73

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

Q73 figure

Answer:

\(\dfrac{5}{9}\)

Open

Question. 74

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

Answer:

\(\dfrac{1}{6}\)

Open

Question. 75

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

Answer:

12.104 < 12.124 < 12.142 < 12.214 < 12.401

Open

Question. 76

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

Answer:

\(0.8531\)

Open

Question. 77

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

Answer:

\(0.2345\)

Open

Question. 78

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

Answer:

\(0.55\)

Open

Question. 79

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

Answer:

\(\dfrac{20}{3}\)

Open

Question. 80

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

Answer:

\(3.4\)

Open

Question. 81

Express 0.041 as a fraction.

Answer:

\(\dfrac{41}{1000}\)

Open

Question. 82

Express 6.03 as a mixed fraction.

Answer:

\(6\dfrac{3}{100}\)

Open

Question. 83

Convert 5201 g to kg.

Answer:

\(5.201\,\text{kg}\)

Open

Question. 84

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

Answer:

Rs \(20\dfrac{9}{100}\)

Open

Question. 85

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

Answer:

\(\dfrac{1537}{100}\,\text{m}\)

Open

Question. 86

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

Answer:

\(2\dfrac{87}{200}\,\text{km}\)

Open

Question. 87

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

Answer:

\(\dfrac{1}{2} < \dfrac{2}{3} < \dfrac{3}{4} < \dfrac{5}{6}\)

Open

Question. 88

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

Answer:

\(\dfrac{7}{8} > \dfrac{6}{7} > \dfrac{4}{5} > \dfrac{3}{4}\)

Open

Question. 89

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

Answer:

\(\dfrac{33}{44}\)

Open

Question. 90

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

Answer:

\(\dfrac{60}{72}\)

Open

Question. 91

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

Answer:

\(16\dfrac{1}{8}\)

Open

Question. 92

Round off 20.83 to the nearest tenths.

Answer:

20.8

Open

Question. 93

Round off 75.195 to the nearest hundredths.

Answer:

75.20

Open

Question. 94

Round off 27.981 to the nearest tenths.

Answer:

28.0

Open

Question. 95

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

Answer:

\(\dfrac{25}{24}=1\dfrac{1}{24}\)

Open

Question. 96

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

Answer:

\(7\dfrac{1}{8}\)

Open

Question. 97

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

Answer:

\(\dfrac{1}{3}\)

Open

Question. 98

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

Answer:

\(\dfrac{25}{9}=2\dfrac{7}{9}\)

Open

Question. 99

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

Answer:

\(5\dfrac{1}{4}\)

Open

Question. 100

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

Answer:

\(7\dfrac{3}{4}\)

Open

Question. 101

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.

Answer:

\(15\dfrac{1}{4}\,\text{km}\)

Open

Question. 102

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.

Answer:

\(64\)

Open

Question. 103

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

Answer:

\(\dfrac{889}{80}\,\text{cm}\)

Open

Question. 104

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?

Answer:

\(\dfrac{9}{10}\)

Open

Question. 105

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?

Answer:

\(\dfrac{3}{5}\)

Open

Question. 106

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

Answer:

\(\dfrac{1}{6}\)

Open

Question. 107

What should be added to 25.5 to get 50?

Answer:

24.5

Open

Question. 108

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.

Answer:

\(9.85\,\text{kg}\)

Open

Question. 109

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

Answer:

0.011 < 0.101 < 0.110 < 1.001

Open

Question. 110

Add: 20.02 and 2.002.

Answer:

22.022

Open

Question. 111

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.

Answer:

(i) \(\dfrac{11}{70}\), (ii) \(\dfrac{1}{10}\)

Open

Question. 112

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

Q112 table placeholder
FoodEnergy (J/kg)
Wheat3.2
Rice5.3
Potatoes (Cooked)3.7
Milk3.0

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

Answer:

Least: Milk (3.0); Maximum: Rice (5.3); Least as a fraction of maximum: \(\dfrac{30}{53}\).

Open

Question. 113

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

Answer:

\(\dfrac{2}{3}\)

Open

Question. 114

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

Answer:

\(1\dfrac{3}{4}\,\text{m}\)

Open

Question. 115

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?

Answer:

\(47\dfrac{5}{8}\,\text{kg}\)

Open

Question. 116

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?

Answer:

\(27\dfrac{1}{4}\,\text{litres}\)

Open

Question. 117

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?

Answer:

\(2\dfrac{3}{4}\,\text{litres}\)

Open

Question. 118

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?

Answer:

\(110\dfrac{1}{20}\,\text{cm}\)

Open

Question. 119

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?

Answer:

\(4\tfrac{5}{8}\,\text{km}\)

Open

Question. 120

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?

Answer:

\(1\tfrac{1}{4}\,\text{kg}\)

Open

Question. 121

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?

Answer:

\(2\tfrac{1}{4}\,\text{m}\)

Open

Question. 122

What is wrong in the following additions?

Q122 figures

Answer:

(a) Denominators have been added wrongly; the correct sum is \(8\tfrac{2}{4}+4\tfrac{1}{4}=12\tfrac{3}{4}\), not \(12\tfrac{3}{8}\).

(b) Denominators must not be added; the correct sum is \(6\tfrac{1}{2}+2\tfrac{1}{4}=8\tfrac{3}{4}\), not \(8\tfrac{1}{3}\).

Open

Question. 123

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

Answer:

\(2.6\,\text{m}\) is greater.

Open

Question. 124

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

Q124 matching

Answer:

(i) \(\dfrac{6}{4}\) → (D)

(ii) \(\dfrac{6}{10}\) → (E)

(iii) \(\dfrac{6}{6}\) → (A)

(iv) \(\dfrac{6}{16}\) → (B)

Open

Question. 125

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?

Answer:

Natural numbers: \(\dfrac{5}{6}\); Whole numbers: \(\dfrac{6}{6}=1\)

Open

Question. 126

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?

Answer:

Natural numbers: \(\dfrac{3}{7}\); Whole numbers: \(\dfrac{4}{7}\); Integers: \(\dfrac{7}{7}=1\)

Open

Question. 127

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

Answer:

\(\dfrac{9}{22}\) and \(\dfrac{5}{22}\)

Open

Question. 128

What fraction of a straight angle is a right angle?

Answer:

\(\dfrac{1}{2}\)

Open

Question. 129

Put each card in the correct bag.

Q129 cards and bags

Answer:

Bag I (Fraction less than 1): \(\dfrac{3}{7},\ \dfrac{8}{9},\ \dfrac{5}{6},\ \dfrac{6}{11},\ \dfrac{19}{25},\ \dfrac{2}{3},\ \dfrac{13}{17}\)

Bag II (Fraction equal to 1): \(\dfrac{4}{4},\ \dfrac{18}{18}\)

Bag III (Fraction greater than 1): \(\dfrac{9}{8}\)

Open

NCERT Exemplar Solutions Class 6 – Mathematics – Unit 4: Fractions & Decimals | Detailed Answers