Class 6 Maths Chapter 7 Extra Questions Fractions
Class 6 Maths Fractions Extra Questions
NCERT Class 6 Maths Chapter 7 Fractions Extra Questions and Answers
Question 1.
Match each fractional unit with the correct picture.
Solution:
(a) – (ii),
(b) – (iii),
(c) – (iv),
(d) – (i)
Question 2.
Shade the parts of the figures according to the given fraction.
Solution:
Question 3.
Write the following fractions as mixed fractions.
(a) \(\frac{8}{3}\)
(b) \(\frac{12}{7}\)
(c) \(\frac{25}{9}\)
Solution:
(a) \(\frac{8}{3}\) = 2 + \(\frac{2}{3}\) = 2\(\frac{2}{3}\)
(b) \(\frac{12}{7}\) = 1 + \(\frac{5}{7}\) = 1\(\frac{5}{7}\)
(c) \(\frac{25}{9}\) = 2 + \(\frac{7}{9}\) = 2\(\frac{7}{9}\)
Question 4.
Express the following mixed fractins as improper fractions:
(a) 1\(\frac{3}{5}\)
(b) 6\(\frac{1}{8}\)
(c) 3\(\frac{1}{7}\)
(d) 1\(\frac{1}{4}\)
Solution:
(a) 1\(\frac{3}{5}\) = 1 + \(\frac{3}{5}\) = \(\frac{(1 \times 5)+3}{5}\) = \(\frac{5+3}{5}\) = \(\frac{8}{5}\)
(b) 6\(\frac{1}{8}\) = 6 + \(\frac{1}{8}\) = \(\frac{(6 \times 8)+1}{8}\) = \(\frac{48+1}{8}\) = \(\frac{49}{8}\)
(c) 3\(\frac{1}{7}\) = 3 + \(\frac{1}{7}\) = \(\frac{(3 \times 7)+1}{7}\) = \(\frac{21+1}{7}\) = \(\frac{22}{7}\)
(a) 1\(\frac{1}{4}\) = 1 + \(\frac{1}{4}\) = \(\frac{(1 \times 4)+1}{4}\) = \(\frac{4+1}{4}\) = \(\frac{5}{4}\)
Question 5.
Figure out the number of whole units in each of the following fractions.
(a) \(\frac{9}{5}\)
(b) \(\frac{7}{3}\)
(c) \(\frac{31}{8}\)
Solution:
(a) \(\frac{9}{5}\) = 1 + \(\frac{4}{5}\) = 1\(\frac{4}{5}\)
Here, the number of whole unit is 1.
(b) \(\frac{7}{3}\) = 2 + \(\frac{1}{3}\) = 2\(\frac{1}{3}\)
Here, the number of whole units is 2.
(c) \(\frac{31}{8}\) = 2 + \(\frac{1}{3}\) = 2\(\frac{1}{3}\)
Here, the number of whole units is 3.
Question 6.
Replace the box in
by the correct number.
Solution:
Since, 42 ÷ 6 = 7
∴ 84 ÷ 7 = 12 ⇒ \(\frac{42 \div 7}{84 \div 7}\) = \(\frac{6}{12}\)
Thus, \(\frac{42}{84}\) = \(\frac{6}{12}\)
Question 7.
Check whether the fractions \(\frac{5}{12}\) and \(\frac{30}{84}\) are equivalent or not.
Solution:
Let us have the cross multiplication of \(\frac{5}{17}\) and \(\frac{30}{84}\).
i.e. 420 ≠ 510 ⇒ [Both the products are different]
∴ The fractions are not equivalent.
Question 8.
Reduce the fraction \(\frac{40}{80}\) to its lowest term.
Solution:
The given fraction = \(\frac{48}{80}\)
First let us find the HCF of 48 and 80,
Now, dividing both the numerator and denominator by 16, we have \(\frac{48 \div 16}{80 \div 16}\) \(=\frac{3}{5}\)
∵ 3 and 5 have no common factor other than 1, i.e., \(\frac{3}{5}\) is in its lowest term.
∴ The lowest term of \(\frac{48}{80}\) is \(\frac{3}{5}\).
Question 9.
Arrange \(\frac{5}{6}\), \(\frac{1}{2}\), \(\frac{2}{3}\) and \(\frac{8}{9}\) in ascending order.
Solution:
Since, all the given fractions are unlike fractions.
∴ First, we convert them into equivalent fractions.
The denominators of the given fraction will be the LCM of 6, 2, 3 and 9.
Let us find the LCM of 6, 2, 3 and 9.
Now, let us write the equivalent fractions of the given fractions with denominator 18.
Question 10.
Write these fractions appropriately as additions or subtractions.
Solution:
(a) \(\frac{5}{5}\) – \(\frac{3}{5}\) = \(\frac{2}{5}\)
(b) \(\frac{2}{6}\) + \(\frac{3}{6}\) = \(\frac{5}{6}\)
(c) \(\frac{1}{5}\) + \(\frac{2}{5}\) = \(\frac{3}{5}\)
(d) \(\frac{3}{4}\) – \(\frac{1}{4}\) = \(\frac{2}{4}\)
Question 11.
Five balls together weigh 1 kg. If they are roughly the same size, then what is the weight of each ball?
Solution:
Total weight of five balls = 1 kg.
Therefore, the weight of each ball = \(\frac{1}{5}\) kg.
Question 12.
Add the following fractions by using Brahmagupta’s method:
(a) \(\frac{1}{3}\) and \(\frac{3}{5}\)
(b) \(\frac{2}{7}\) and \(\frac{4}{9}\)
(c) \(\frac{5}{6}\) and \(\frac{1}{2}\)
Solution:
(a) The denominators of the given fractions are 3 and 5.
The LCM of 3 and 5 is 15.
Then, \(\frac{1}{3}\) = \(\frac{1 \times 5}{3 \times 5}\) = \(\frac{5}{15}\) and \(\frac{3}{5}\) = \(\frac{3 \times 3}{5 \times 3}\) = \(\frac{9}{15}\)
Therefore, \(\frac{1}{3}\) + \(\frac{3}{5}\) = \(\frac{5}{15}\) + \(\frac{9}{15}\) = \(\frac{14}{15}\)
(b) The denominators of the given fractions are 7 and 9.
The LCM of 7 and 9 is 63.
Then, \(\frac{2}{7}\) = \(\frac{2 \times 9}{7 \times 9}\) = \(\frac{18}{63}\) and \(\frac{4}{9}\) = \(\frac{4 \times 7}{9 \times 7}\) = \(\frac{28}{63}\)
Therefore, \(\frac{2}{7}+\frac{4}{9}\) = \(\frac{18}{63}+\frac{28}{63}\) = \(\frac{46}{63}\)
(c) The denominators of the given fractions are 6 and 2.
The LCM of 6 and 2 is 6.
Then, \(\frac{5}{6}\) = \(\frac{5 \times 1}{6 \times 1}\) = \(\frac{5}{6}\) and \(\frac{1}{2}\) = \(\frac{1 \times 3}{2 \times 3}\) = \(\frac{3}{6}\)
Therefore, \(\frac{5}{6}+\frac{1}{2}\) = \(\frac{5}{6}+\frac{3}{6}\) = \(\frac{8}{6}\) = \(\frac{4}{3}\)
Question 13.
Subtract the following fractions by using Brahmagupta’s method:
(a) \(\frac{3}{5}\) – \(\frac{1}{2}\)
(b) \(\frac{2}{3}\) – \(\frac{1}{7}\)
(c) \(\frac{1}{8}\) – \(\frac{1}{9}\)
Solution:
(a) The denominators of the given fractions are 2 and 5. LCM of 2 and 5 is 10.
Then, \(\frac{1}{2}\) = \(\frac{1 \times 5}{2 \times 5}\) = \(\frac{5}{10}\) and \(\frac{3}{5}\) = \(\frac{3 \times 2}{5 \times 2}\) = \(\frac{6}{10}\)
Therefore, \(\frac{3}{5}\) – \(\frac{1}{2}\) = \(\frac{6}{10}\) – \(\frac{5}{10}\) = \(\frac{1}{10}\)
(b) The denominators of the given fractions are 3 and 7.
LCM of 3 and 7 is 21.
Then, \(\frac{2}{3}\) = \(\frac{2 \times 7}{3 \times 7}\) = \(\frac{14}{21}\) and \(\frac{1}{7}\) = \(\frac{1 \times 3}{7 \times 3}\) = \(\frac{3}{21}\)
Therefore, \(\frac{2}{3}\) – \(\frac{1}{7}\) = \(\frac{14}{21}\) – \(\frac{3}{21}\) = \(\frac{11}{21}\)
(c) The denominators of the given fractions are 8 and 9. LCM of 8 and 9 is 72.
Then \(\frac{1}{8}\) = \(\frac{1 \times 9}{8 \times 9}\) = \(\frac{9}{72}\) and \(\frac{1}{9}\) = \(\frac{1 \times 8}{9 \times 8}\) = \(\frac{8}{72}\)
Therefore, \(\frac{1}{8}\) – \(\frac{1}{9}\) = \(\frac{9}{72}\) – \(\frac{8}{72}\) = \(\frac{1}{72}\)
Question 14.
A bag of wheat weighs \(\frac{5}{2}\) kg. Another bag of rice weighs \(\frac{9}{4}\) kg. What is the total weight of the two bags?
Solution:
Weight of a bag of wheat = \(\frac{5}{2}\) kg
Weight of a bag of rice = \(\frac{9}{4}\) kg
Total weight = (\(\frac{5}{2}\) + \(\frac{9}{4}\)) kg
The denominators of the given fractions are 2 and 4.
∴ The LCM of 2 and 4 is 4.
Then, \(\frac{5}{2}\) = \(\frac{5 \times 2}{2 \times 2}\) = \(\frac{10}{4}\) and \(\frac{9}{4}\) = \(\frac{9 \times 1}{4 \times 1}\) = \(\frac{9}{4}\)
Therefore, \(\frac{5}{2}\) + \(\frac{9}{4}\) = \(\frac{10}{4}\) + \(\frac{9}{4}\) = \(\frac{19}{4}\)
Hence, the weight of the two bags is \(\frac{19}{4}\) = 4\(\frac{4}{3}\) kg.
Question 15.
Rahul takes \(\frac{11}{7}\) hours to finish his homework while Naman takes \(\frac{15}{8}\) hours to finish his homework. Who takes more time and by how much?
Solution:
Time taken by Rahul to finish his homework = \(\frac{11}{7}\) hours
Time taken by Naman to finish his homework = \(\frac{15}{8}\) hours
The difference in the time taken by the two = (\(\frac{15}{8}\) – \(\frac{11}{7}\)) jours
The denominators of the given fractions are 8 and 7.
∴ The LCM of 8 and 7 is 56.
Then, \(\frac{15}{8}\) = \(\frac{15 \times 7}{8 \times 7}\) = \(\frac{105}{56}\) and \(\frac{11}{7}\) = \(\frac{11 \times 8}{7 \times 8}\) = \(\frac{88}{56}\)
Therefore, \(\frac{15}{8}-\frac{11}{7}\) = \(\frac{105}{56}-\frac{88}{56}\) = \(\frac{17}{56}\)
Hence, Naman takes \(\frac{17}{56}\) hours more than Rahul to finish his homework.
Fractions Class 6 Extra Questions Very Short Answer Type
Question 1.
Represent the following fractions on number line.
Solution:
Question 2.
Write the fractions showing the shaded portions:
Solution:
(a) Shaded portion represents \(\frac { 1 }{ 4 }\)
Shaded portion represents \(\frac { 2 }{ 6 }\)
Question 3.
Colour the part according to the fraction given:
Solution:
Question 4.
Identify the proper and improper fractions:
Solution:
Proper fractions are: \(\frac { 5 }{ 6 }\), \(\frac { 1 }{ 2 }\) and \(\frac { 3 }{ 4 }\)
Improper fractions are: \(\frac { 7 }{ 2 }\), \(\frac { 11 }{ 5 }\) and \(\frac { 6 }{ 5 }\)
Question 5.
What fraction of these circles have ‘x’ in them?
Solution:
Fraction of the circles with ‘x’ in the given figure = \(\frac { 5 }{ 8 }\).
Question 6.
Write all the natural numbers from 1 to 15. What fraction of them are prime numbers?
Solution:
Natural numbers from 1 to 15 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 and 15 Prime numbers from 1 to 15 are 2, 3, 5, 7, 11, 13, i.e., 6 prime numbers.
∴ Fraction of prime numbers = \(\frac { 6 }{ 15 }\)
Question 7.
Identify the like fractions from the following:
Solution:
\(\frac { 2 }{ 3 }\) and \(\frac { 1 }{ 3 }\) have the same denominator.
∴ \(\frac { 2 }{ 3 }\) and \(\frac { 1 }{ 3 }\) are the like fractions.
Question 8.
Identify the unlike fractions from the following:
Solution:
\(\frac { 2 }{ 5 }\) , \(\frac { 2 }{ 7 }\) and \(\frac { 1 }{ 6 }\) have different denominators.
∴ \(\frac { 2 }{ 5 }\) , \(\frac { 2 }{ 7 }\) and \(\frac { 1 }{ 6 }\) are unlike fractions.
Question 9.
Convert the following improper fractions into mixed fraction.
Solution:
Question 10.
Convert the following mixed fractions into improper fractions:
Solution:
Fractions Class 6 Extra Questions Short Answer Type
Question 11.
Write the following fractions in ascending order:
Solution:
Here, the numerators of all the fractions are same.
Question 12.
Write any
(a) three proper and three improper fractions with denominator 7.
(b) two proper and two improper fractions with numerator 9.
Solution:
(a) Proper fractions with denominator 7 are: \(\frac { 2 }{ 7 }\) , \(\frac { 3 }{ 7 }\) and \(\frac { 5 }{ 7 }\)
Improper fractions with denominator 7 are: \(\frac { 9 }{ 7 }\) , \(\frac { 11 }{ 7 }\) and \(\frac { 13 }{ 6 }\)
(b) Proper fractions with numerator 9 are:
\(\frac { 9 }{ 11 }\) and \(\frac { 9 }{ 17 }\)
Improper fractions with numerator 9 are:
\(\frac { 9 }{ 2 }\) and \(\frac { 9 }{ 5 }\)
Question 13.
Compare the following fractions:
Solution:
Question 14.
Solution:
LCM of 12, 16 and 24 is 48
Question 15.
Find the sum of 1\(\frac { 2 }{ 3 }\) and 3\(\frac { 2 }{ 5 }\).
Solution:
Question 16.
Subtract 2\(\frac { 3 }{ 4 }\) from 4\(\frac { 1 }{ 8 }\).
Solution:
Question 17.
Insert > or < to make each of the following true.
Solution:
Fractions Class 6 Extra Questions Higher Order Thinking Skills (HOTS)
Question 18.
Find the difference between the greatest and the smallest fractions.
Solution:
Question 19.
Simran painted \(\frac { 2 }{ 3 }\) of the wall space in her room. Her brother Rahul helped and painted \(\frac { 1 }{ 5 }\) of the wall space. How much did they paint together? What part of the whole space is left unpainted?
Solution:
Space of the wall painted by Simran = \(\frac { 2 }{ 3 }\)
Space of the wall painted by Rahul = \(\frac { 1 }{ 5 }\)
