NCERT Solutions for Class 6 Maths Chapter 7 Fractions

NCERT Solutions for Class 6 Maths Chapter 7 Fractions Exercise: 7.1

Q1 Write the fraction representing the shaded portion.

Answer: (i) $\frac{2}{4}\ =\ \frac{1}{2}$

(ii) $\frac{8}{9}$

(iii) $\frac{4}{8}\ =\ \frac{1}{2}$

(iv) $\frac{1}{4}$

(v) $\frac{3}{7}$

(vi) $\frac{9}{12}\ =\ \frac{3}{4}$

(vii) $\frac{10}{10}\ =\ 1$

(viii) $\frac{4}{9}$

(ix) $\frac{4}{8}\ =\ \frac{1}{2}$

(x) $\frac{1}{2}$

Q2 Colour the part according to the given fraction.

Answer: The coloured parts are shown below :-

Q3 Identify the error if any

This is $\frac{1}{2}$

This is $\frac{1}{4}$

This is $\frac{3}{4}$

Answer: Yes, the above fractions are wrong. For these fractions to be correct areas of each part should be same. But clearly, in the given figure, the areas are not the same.

Q4 What fraction of a day is $8$ hours?

Answer: Total hours in 1 day $=\ 24$

Thus the required fraction is :-

$=\ \frac{8}{24}\ =\ \frac{1}{3}$

Q5 What fraction of an hour is $40$ minutes?

Answer: We know that 1 hour has 60 minutes.

Thus fraction of 40 minutes is :-

$=\ \frac{40}{60}\ =\ \frac{4}{6}\ =\ \frac{2}{3}$

Q6 (a) Arya, Abhimanyu, and Vivek shared lunch. Arya has brought two sandwiches, one made of vegetable and one of jam. The other two boys forgot to bring their lunch. Arya agreed to share his sandwiches so that each person will have an equal share of each sandwich. How can Arya divide his sandwiches so that each person has an equal share?

Answer: Arya needs to divide one sandwich into 3 equal parts (as three persons are there.)

Thus each sandwich is divided into 3 parts.

Q6 (b) Arya, Abhimanyu, and Vivek shared lunch. Arya has brought two sandwiches, one made of vegetable and one of jam. The other two boys forgot to bring their lunch. Arya agreed to share his sandwiches so that each person will have an equal share of each sandwich. What part of a sandwich will each boy receive?

Answer: Since they have to distribute 1 part in 3 people, hence the fraction received by each boy will be:-

$F\ =\ \frac{1}{3}$

Q7 Kanchan dyes dresses. She had to dye $30$ dresses. She has so far finished $20$ dresses. What fraction of dresses has she finished?

Answer: The required fraction is:-

$=\ \frac{20}{30}\ =\ \frac{2}{3}$

Q8 Write the natural numbers from $2$ to $12.$ What fraction of them are prime numbers?

Answer: We have :- 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.

Prime number :- 2, 3, 5, 7, 11.

Thus the fraction of prime numbers is:- $\frac{5}{11}$

Q9 Write the natural numbers from $102$ to $113$ . What fraction of them are prime numbers?

Answer: The natural numbers are :- 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113.

Prime numbers are :- 103, 107, 109, 113.

Thus fraction is :- _{$=\ \frac{4}{12}\ =\ \frac{1}{3}$}

Q10 What fraction of these circles have $X$ ’s in them?

Answer: The number of boxes with X in them = 4

Total number of boxes = 8.

The required fraction is :

$=\ \frac{4}{8}\ =\ \frac{1}{2}$

Q11 Kristin received a CD player for her birthday. She bought 3

CDs and received 5 others as gifts. What fraction of her total

CDs did she buy and what fraction did she receive as gifts?

Answer: The fraction of the CDs she bought is :

$=\ \frac{3}{8}$

And the fraction of CDs received as gifts is :

$=\ \frac{5}{8}$

NCERT Solutions for Class 6 Maths Topic: Fractions on the Number Line

Q1 Show $\frac{3}{5}$ on a number line.

Answer: First we write $1$ as $\frac{5}{5}$ and divide the number line into 5 equal parts.

Q2 Show $\frac{1}{10},\frac{0}{10},\frac{5}{10}$ and $\frac{10}{10}$ on a number line.

Answer:

First, we write $1$ as $\frac{10}{10}$ and divide the number line in 10 equal parts.

Q3 Can you show any other fraction between $0$ and $1$ ?Write five more fractions that you can show.

Answer:

Yes. There are infinite number of fraction between $0$ and $1$ (Numerator is less than denominator)

Five more fractions are: $\frac{4}{5}, \frac{6}{11}, \frac{4}{7}, \frac{3}{8}, \frac{11}{25}$

Q4 How many fractions lie between $0$ and $1$ ? Think, discuss and write your answer?

Answer: There are infinite number of fractions between $0$ and $1$ .

A fraction is of form $\frac{a}{b}$ and for a number lying between $0$ and $1$ , the numerator has to be less than the denominator.

NCERT Solutions for Class 6 Maths Topic: Proper Fractions

Q1 Give a proper fraction : (a) whose numerator is $5$ and the denominator is $7.$
(b) whose denominator is $9$ and the numerator is $5.$

(c) whose numerator and denominator add up to $10$ . How many fractions of this kind can you make?

(d) whose denominator is $4$ more than the numerator.

(Give any five. How many more can you make?)

Answer: A proper fraction whose:

(a) the numerator is $5$ and the denominator is $7.$ = $\frac{5}{7}$

(b) denominator is $9$ and numerator is $5.$ = $\frac{5}{9}$

(c) numerator and denominator add up to $10$ .

Pairs of numbers having sum 10 = $(1,9),(2,8),(3,7),(4,6)(5,5)$

Therefore, the proper fractions are $\frac{1}{9}, \frac{2}{8}, \frac{3}{7}, \frac{4}{6}$

(d) denominator is $4$ more than the numerator. = $\frac{1}{5}, \frac{2}{6}, \frac{15}{19}, \frac{105}{109}, \frac{199}{203},$

Q2 A fraction is given. How will you decide, by just looking at it, whether, the fraction is

(a) less than $1$ ?

(b) equal to $1$ ?

Answer: (a) If the numerator is smaller than the denominator, then the fraction will be less than $1$ .

(b) If the numerator is equal to the denominator, then the fraction will be equal to $1$ .

Q3 Fill up using one of these: ‘ $>$ ’, ‘ $<$ ’ or ‘ $=$ ’

(a) $\frac{1}{2}\square 1$

(b) $\frac{3}{5}\square 1$

(c) $1\square \frac{7}{8}$

(d) $\frac{4}{4}\square 1$

(e) $\frac{2005}{2005}\square 1$

Answer: (a)

$\frac{1}{2}< 1$

(b)

$\frac{3}{5}< 1$

(c)

$1> \frac{7}{8}$

(d)

$\frac{4}{4}=1$

(e)

$\frac{2005}{2005}= 1$

NCERT Solutions for Class 6 Maths Chapter 7 Fractions Exercise: 7.2

Q1 (a) Draw number lines and locate the points on them : $\frac{1}{2},\frac{1}{4},\frac{3}{4},\frac{4}{4}$

Answer: The number line is given below:-

Q1 (b) Draw number lines and locate the points on them : $\frac{1}{8},\frac{2}{8},\frac{3}{8},\frac{7}{8}$

Answer: The number line is shown below with the required points marked.

Q1 (c) Draw number lines and locate the points on them : $\frac{2}{5},\frac{3}{5},\frac{8}{5},\frac{4}{5}$

Answer: The number line locating the given fraction is shown below:-

Q2 Express the following as mixed fractions :

(a) $\frac{20}{3}$

(b) $\frac{11}{5}$

(c) $\frac{17}{7}$

(d) $\frac{28}{5}$

(e) $\frac{19}{6}$

(f) $\frac{35}{9}$

Answer: (a) $\frac{20}{3}\ =\ \frac{18\ +\ 2}{3}\ =\ 6\frac{2}{3}$

(b) $\frac{11}{5}\ =\ \frac{10\ +\ 1}{5}\ =\ 2\frac{1}{5}$

(c) $\frac{17}{7}\ =\ \frac{14\ +\ 3}{7}\ =\ 2\frac{3}{7}$

(d) $\frac{28}{5}\ =\ \frac{25\ +\ 3}{5}\ =\ 5\frac{3}{5}$

(e) $\frac{19}{6}\ =\ \frac{18\ +\ 1}{6}\ =\ 3\frac{1}{6}$

(f) $\frac{35}{9}\ =\ \frac{27\ +\ 8}{9}\ =\ 3\frac{8}{9}$

Q3 Express the following as improper fractions :

(a) $7\frac{3}{4}$

(b) $5\frac{6}{7}$

(c) $2\frac{5}{6}$

(d) $10\frac{3}{5}$

(e) $9\frac{3}{7}$

(f) $8\frac{4}{9}$

Answer: The improper fractions of the mixed fractions are given below :-

(a) $7\frac{3}{4}\ =\ \frac{28\ +\ 3}{4}\ =\ \frac{31}{4}$

(b) $5\frac{6}{7}\ =\ \frac{35\ +\ 6}{7}\ =\ \frac{41}{7}$

(c) $2\frac{5}{6}\ =\ \frac{12\ +\ 5}{6}\ =\ \frac{17}{6}$

(d) $10\frac{3}{5}\ =\ \frac{50\ +\ 3}{5}\ =\ \frac{53}{5}$

(e) $9\frac{3}{7}\ =\ \frac{63\ +\ 3}{7}\ =\ \frac{66}{7}$

(f) $8\frac{4}{9}\ =\ \frac{72\ +\ 4}{9}\ =\ \frac{76}{9}$

NCERT Solutions for Class 6 Maths Topic: Simplest Form of a Fraction

Q1 Write the simplest form of :

(i) $\frac{15}{75}$

(ii) $\frac{16}{72}$

(iii) $\frac{17}{51}$

(iv) $\frac{42}{28}$

(v) $\frac{80}{24}$

Answer: (i) $\frac{15}{75}=\frac{5}{25}=\frac{1}{5}$

(ii) $\frac{16}{72}=\frac{8}{36}=\frac{4}{18}=\frac{2}{9}$

(iii) $\frac{17}{51}=\frac{1}{3}$

(iv) $\frac{42}{28}=\frac{21}{14}=\frac{3}{2}$

(v) $\frac{80}{24}=\frac{40}{12}=\frac{20}{6}=\frac{10}{3}$

Q2 Is $\frac{49}{64}$ in its simplest form?

Answer: Yes, $\frac{49}{64}$ is in its simplest form because 49 and 64 has no common divisor.

NCERT Solutions for Class 6 Maths Topic: Equivalent Fractions

Q1 Are $\frac{1}{3}$ and $\frac{2}{7}$ ; $\frac{2}{5}$ and $\frac{2}{7}$ ; $\frac{2}{9}$ and $\frac{6}{27}$ and equivalent? Give reason

Answer: $\frac{1}{3}$ and $\frac{2}{7}$ ; $\frac{2}{5}$ and $\frac{2}{7}$ are not equivalent because

$\frac{1}{3}> \frac{2}{7}$ and

$\frac{2}{5}> \frac{2}{7}$

but

$\frac{2}{9}= \frac{6}{27}=0.222$

Q2 Give example of four equivalent fractions.

Answer: Four example of equivalent fractions are :

$\frac{2}{4}=\frac{4}{8};\frac{1}{3}=\frac{3}{9};\frac{8}{4}=\frac{12}{6};\frac{1}{5}=\frac{5}{25}$

Q3 Identify the fractions in each. Are these fractions equivalent?

Answer:

(i) $\frac{6}{8}$ (ii) $\frac{9}{12}$ (iii) $\frac{12}{16}$ (iv) $\frac{15}{20}$

all fractions in it simplest form is

$\frac{3}{4}$

So all fractions are equivalent

Q1 Find five equivalent fractions of each of the following:

(i) $\frac{2}{3}$

(ii) $\frac{1}{5}$

(iii) $\frac{3}{5}$

(iv) $\frac{5}{9}$

Answer: (i) $\frac{2}{3}=\frac{8}{12}$

(ii) $\frac{1}{5}=\frac{5}{25}$

(iii) $\frac{3}{5}=\frac{15}{25}$

(iv) $\frac{5}{9}=\frac{50}{90}$

NCERT Solutions for Class 6 Maths Exercise: 7.3

Q1 Write the fractions. Are all these fractions equivalent?

Answer: In the case of (a), we have:-

(i) $f_1\ =\ \frac{1}{2}$

(ii) $f_2\ =\ \frac{2}{4} =\ \frac{1}{2}$

(iii) $f_3\ =\ \frac{3}{6} =\ \frac{1}{2}$

(iv) $f_4\ =\ \frac{4}{8} =\ \frac{1}{2}$

Hence all fractions are equal in this case.

In the case of (b), we have:-

(i) $f_1\ =\ \frac{4}{12}\ =\ \frac{1}{3}$

(ii) $f_2\ =\ \frac{3}{9} =\ \frac{1}{3}$

(iii) $f_3\ =\ \frac{2}{6} =\ \frac{1}{3}$

(iv) $f_4\ =\ \frac{1}{3}$

(v) $f_5\ =\ \frac{6}{15}\ =\ \frac{2}{5}$

Q2 Write the fractions and pair up the equivalent fractions from each row.

Answer: The fractions of each are given below :-

(a) $f_a\ =\ \frac{1}{2}$

(b) $f_b\ =\ \frac{4}{6}\ =\ \frac{2}{3}$

(c) $f_c\ =\ \frac{3}{9}\ =\ \frac{1}{3}$

(d) $f_d\ =\ \frac{2}{8}\ =\ \frac{1}{4}$

(e) $f_e\ =\ \frac{3}{4}$

Similarly,

(i) $f_1\ =\ \frac{6}{18}\ =\ \frac{1}{3}$

(ii) $f_2\ =\ \frac{4}{8}\ =\ \frac{1}{2}$

(iii) $f_3\ =\ \frac{12}{16}\ =\ \frac{3}{4}$

(iv) $f_4\ =\ \frac{8}{12}\ =\ \frac{2}{3}$

(v) $f_5\ =\ \frac{4}{16}\ =\ \frac{1}{4}$

Q3 (a) Replace box in each of the following by the correct number : $\frac{2}{7}=\frac{8}{\square }$

Answer: The correct number is 28.

$\frac{2}{7}\times \frac{4}{4} =\ \frac{8}{28}\ =\frac{8}{\square }$

Thus $\square\ =\ 28$ .

Q3 (b) Replace $\square$ in each of the following by the correct number : $\frac{5}{8}=\frac{10}{\square }$

Answer: (b) The correct answer is 16.

$\frac{5}{8}\times \frac{2}{2}=\frac{10}{16}$

Q3 (c) Replace $\square$ in each of the following by the correct number : $\frac{3}{5}=\frac{\square }{20}$

Answer: The required value is 12.

$\frac{3}{5}\times \frac{4}{4}=\frac{12 }{20}$

Q3 (d) Replace in each of the following by the correct number : $\frac{45}{60}=\frac{15}{\square }$

Answer: The required value is 20.

$\frac{45}{60}\times \frac{\frac{1}{3}}{\frac{1}{3}}=\frac{15}{20 }$

Q3 (e) Replace $\square$ in each of the following by the correct number : $\frac{18}{24}=\frac{4}{\square }$

Answer: The correct number is $\frac{48}{9}$ .

Multiplying numerator and denomenator by $\frac{4}{18}$ .

We have :- $\frac{18}{24}\times \frac {\frac{4}{18}}{\frac{4}{18}}\ =\ \frac{4}{\frac{96}{18}}\ =\ \frac{4}{\frac{48}{9}}$

Hence $\square\ =\ \frac{48}{9}$

Q4 Find the equivalent fraction of $\frac{3}{5}$ having

(a) denominator $20$

(b) numerator $9$

(c) denominator $30$

(d) numerator $27$

Answer: (a) Multiply numerator and denominator by 4, we have :

$\frac{3}{5}\times \frac{4}{4}\ =\ \frac{12}{20}$

(b) Multiply numerator and denominator by 3, we have :

$\frac{3}{5}\times \frac{3}{3}\ =\ \frac{9}{15}$

(c) Multiply numerator and denominator by 6, we have :

$\frac{3}{5}\times \frac{6}{6}\ =\ \frac{18}{30}$

(d) Multiply numerator and denominator by 9, we have :

$\frac{3}{5}\times \frac{9}{9}\ =\ \frac{27}{45}$

Q5 Find the equivalent fraction of $\frac{36}{48}$ with

(a) numerator $9$

(b) denominator $4$

Answer: The required equivalent fractions are given below :-

(a) Divide both numerator and denomenator by 4.

$\frac{36}{48}\times \frac{\frac{1}{4}}{\frac{1}{4}}\ =\ \frac{9}{12}$

(b) Divide both numerator and denomenator by 12.

$\frac{36}{48}\times \frac{\frac{1}{12}}{\frac{1}{12}}\ =\ \frac{3}{4}$

Q6 (a) Check whether the given fractions are equivalent : $\frac{5}{9},\frac{30}{35}$

Answer: Multiply both numerator and denominator by 6.

$\frac{5}{9}\times \frac{6}{6}\ =\ \frac{30}{54}\ \neq \frac{30}{35}$

Q6 (b) Check whether the given fractions are equivalent : $\frac{3}{10},\frac{12}{50}$

Answer:

Multiply both numerator and denominator by 4, we get :

$\frac{3}{10}\times \frac{4}{4}\ =\ \frac{12}{40}\ \neq \ \frac{12}{50}$

Q6 (c) Check whether the given fractions are equivalent : $\frac{7}{13},\frac{5}{11}$

Answer: Multiply both numerator and denominator by $\frac{5}{7}$ , we get :

$\frac{7}{13}\times \frac{\frac{5}{7}}{\frac{5}{7}}\ =\ \frac{5}{\frac{65}{7}}\ \neq \ \frac{5}{11}$

Hence these two fractions are not the same.

Q7 Reduce the following fractions to simplest form :

(a) $\frac{48}{60}$

(b) $\frac{150}{60}$

(c) $\frac{84}{98}$

(d) $\frac{12}{52}$

(e) $\frac{7}{28}$

Answer: (a) $\frac{48}{60}\ =\ \frac{24}{30}\ =\ \frac{12}{15}\ =\frac{4}{5}$

(b) $\frac{150}{60}\ =\ \frac{15}{6}\ =\ \frac{5}{2}$

(c) $\frac{84}{98}\ =\ \frac{42}{49}\ =\ \frac{6}{7}$

(d) $\frac{12}{52}\ =\ \frac{6}{26}\ =\ \frac{3}{13}$

(e) $\frac{7}{28}\ =\ \frac{1}{4}$

Q8 Ramesh had $20$ pencils, Sheelu had $50$ pencils and Jamaal had $80$ pencils. After $4$ months, Ramesh used up $10$ pencils, Sheelu used up $25$ pencils and Jamaal used up $40$ pencils. What fraction did each use up? Check if each has used up an equal fraction of her/his pencils?

Answer: The fraction of pencils used by Ramesh is:-

$=\ \frac{10}{20}\ =\ \frac{1}{2}$

The fraction of pencils used by Sheelu is:-

$=\ \frac{25}{50}\ =\ \frac{1}{2}$

The fraction of pencils used by Jamaal is:-

$=\ \frac{40}{80}\ =\ \frac{1}{2}$

Thus, the fractions of pencils used by each are the same.

Q9 Match the equivalent fractions and write two more for each.

(i) $\frac{250}{400}$ (a) $\frac{2}{3}$

(ii) $\frac{180}{200}$ (b) $\frac{2}{5}$

(iii) $\frac{660}{990}$ (c) $\frac{1}{2}$

(iv) $\frac{180}{360}$ (d) $\frac{5}{8}$

(v) $\frac{220}{550}$ (e) $\frac{9}{10}$

Answer: (i) $\frac{250}{400}\ =\ \frac{25}{40}\ =\ \frac{5}{8}$

(ii) $\frac{180}{200}\ =\ \frac{18}{20}\ =\ \frac{9}{10}$

(iii) $\frac{660}{990}\ =\ \frac{66}{99}\ =\ \frac{22}{33}\ =\ \frac{2}{3}$

(iv) $\frac{180}{360}\ =\ \frac{18}{36}\ =\ \frac{2}{4}\ =\ \frac{1}{2}$

(v) $\frac{220}{550}\ =\ \frac{22}{55}\ =\ \frac{2}{5}$

NCERT Solutions for Class 6 Maths Topic: Comparing Fractions

Q1 You get one-fifth of a bottle of juice and your sister gets one-third of the same size of a bottle of juice. Who gets more?

Answer: My sister gets more because $\frac{1}{3}> \frac{1}{5}$

NCERT Solutions for Class Maths Topic: Comparing Like Fractions

Q1 Which is the larger fraction?

(i) $\frac{7}{10}$ or $\frac{8}{10}$

(ii) $\frac{11}{24}$ or $\frac{13}{24}$

(iii) $\frac{17}{102}$ or $\frac{12}{102}$

Answer: The fractions are shown below using greater than or less than sign

(i) $\frac{7}{10}$ $<$ $\frac{8}{10}$

(ii) $\frac{11}{24}$ $<$ $\frac{13}{24}$

(iii) $\frac{17}{102}$ $>$ $\frac{12}{102}$

Q2 Write these in ascending and also in descending order.

(a) $\frac{1}{8},\frac{5}{8},\frac{3}{8}$

(b) $\frac{1}{5},\frac{11}{5},\frac{4}{5},\frac{3}{5},\frac{7}{5}$

(c) $\frac{1}{7},\frac{3}{7},\frac{13}{7},\frac{11}{7},\frac{7}{7}$

Answer: (a) $\frac{1}{8}< \frac{3}{8}< \frac{5}{8}$

$\frac{5}{8}>\frac{3}{8}> \frac{1}{8}$

(b) $\frac{1}{5}< \frac{3}{5}< \frac{4}{5}< \frac{7}{5}< \frac{11}{5}$

$\frac{11}{5}> \frac{7}{5}> \frac{4}{5}> \frac{3}{5}> \frac{1}{5}$

(c) $\frac{1}{7}< \frac{3}{7}< \frac{7}{7}< \frac{11}{7}< \frac{13}{7}$

$\frac{13}{7}> \frac{11}{7}> \frac{7}{7}> \frac{3}{7}> \frac{1}{7}$

NCERT Class 6 Maths Chapter 7 Fractions Topic: Arrangement of Fractions

Q1 (1) Arrange the following in ascending and descending order :

$\frac{1}{12},\frac{1}{23},\frac{1}{5},\frac{1}{7},\frac{1}{50},\frac{1}{9},\frac{1}{17}$

Answer: (a) $\frac{1}{5}> \frac{1}{7}> \frac{1}{9}> \frac{1}{12}> \frac{1}{17}> \frac{1}{23}> \frac{1}{50}$

and $\frac{1}{50}< \frac{1}{23}< \frac{1}{17}< \frac{1}{12}< \frac{1}{9}< \frac{1}{7}< \frac{1}{5}$

Q1 (b) Arrange the following in ascending and descending order :

$\frac{3}{7},\frac{3}{11},\frac{3}{5},\frac{3}{2},\frac{3}{13},\frac{3}{4},\frac{3}{17}$

Answer: The following in ascending and descending order are :

(b) $\frac{3}{2}>\frac{3}{4}> \frac{3}{5}>\frac{3}{7}>\frac{3}{11}>\frac{3}{13}>\frac{3}{17}$

$\frac{3}{17}<\frac{3}{13}<\frac{3}{11}<\frac{3}{7}<\frac{3}{5}<\frac{3}{2}<\frac{3}{3}$

Q1 (c) Arrange the following in ascending and descending order :

Write 3 more similar examples and arrange them in ascending and descending order.

Answer: The following in ascending and descending order are:

(i) $\frac{3}{5},\frac{7}{5},\frac{4}{5}$

$\frac{3}{5}<\frac{4}{5}<\frac{7}{5}$

and $\frac{7}{5}>\frac{4}{5}>\frac{3}{5}$

(ii) $\frac{3}{11},\frac{7}{11},\frac{4}{11}$

$\frac{3}{11}<\frac{4}{11}<\frac{7}{11}$

and $\frac{7}{11}>\frac{4}{11}>\frac{3}{11}$

(iii) $\frac{3}{11},\frac{3}{7},\frac{3}{5}$

$\frac{3}{11}<\frac{3}{7}<\frac{3}{5}$

and $\frac{3}{5}>\frac{3}{7}>\frac{3}{11}$

NCERT Solutions for Class 6 Maths Chapter 7 Fractions Exercise: 7.4

Q1 Write shaded portion as fraction. Arrange them in ascending and descending order using correct sign $'<'\; '='\; '> '$ between the fractions:

(c) Show $\frac{2}{6},\frac{4}{6},\frac{8}{6}\; and\; \frac{6}{6}$ on the number line. Put appropriate signs between the fractions given

$\frac{5}{6}\square \frac{2}{6},$ $\frac{3}{6}\square 0,$ $\frac{1}{6}\square \frac{6}{6},$ $\frac{8}{6}\square \frac{5}{6},$

Answer: (a) $f_1\ =\ \frac{3}{8}$

$f_2\ =\ \frac{6}{8}\ =\ \frac{3}{4}$

$f_3\ =\ \frac{4}{8}\ =\ \frac{1}{2}$

$f_4\ =\ \frac{1}{8}$

$f_2\ >\ f_3\ >\ f_1\ >\ f_4$

(b) $f_1\ =\ \frac{8}{9}$

$f_2\ =\ \frac{4}{9}$

$f_3\ =\ \frac{3}{9}\ =\ \frac{1}{3}$

$f_4\ =\ \frac{6}{9}\ =\ \frac{2}{3}$

(c)

From the above number line we can compare the given numbers easily.

$\frac{5}{6}\ >\ \frac{2}{6},$ $\frac{3}{6}\ >\ 0,$ $\frac{1}{6}\ <\ \frac{6}{6},$ $\frac{8}{6}\ >\ \frac{5}{6}$

Q2 Compare the fractions and put an appropriate sign.

(a) $\frac{3}{6}\square \frac{2}{6}$

(b) $\frac{1}{7}\square \frac{1}{4}$

(c) $\frac{4}{5}\square \frac{5}{5}$

(d) $\frac{3}{5}\square \frac{3}{7}$

Answer: The comparison is given below :-

(a) $\frac{3}{6}\ >\ \frac{2}{6}$

(b) $\frac{1}{7}\ <\ \frac{1}{4}$

(c) $\frac{4}{5}\ <\ \frac{5}{5}$

(d) $\frac{3}{5}\ >\ \frac{3}{7}$

Q3 Make five more such pairs and put appropriate signs.

Answer: The five pairs can be :-

$\frac{2}{3}\ > \frac{1}{3}$ , $\frac{5}{3}\ > \frac{2}{3}$ $\frac{5}{9}\ < \frac{4}{3}$ $\frac{2}{7}\ < \frac{5}{7}$ $\frac{1}{2}\ >\ \frac{1}{3}$

Q4 (a) Look at the figures and write $'< ' or '> ','='$ between the given pairs of fractions.

(a) $\frac{1}{6}\square \frac{1}{3}$

Answer: With the help of given diagram :

$\frac{1}{6}\ <\ \frac{2}{6}$

Thus $\frac{1}{6}\ <\ \frac{1}{3}$

Q4 (b) Look at the figures and write $'< ' or '> ','='$ between the given pairs of fractions.

(b) $\frac{3}{4}\square \frac{2}{6}$

Answer: From the diagram it is cleat that :

$\frac{3}{4}\ >\ \frac{2}{6}$

Q4 (c) Look at the figures and write $'< ' or '> ','='$ between the given pairs of fractions.

(c) $\frac{2}{3}\square \frac{2}{4}$

Answer: From the given diagram, we can clearly say that :-

$\frac{2}{3}\ >\ \frac{2}{4}$

Q4 (d) Look at the figures and write ‘<’ or ‘>’, ‘=’ between the given pairs of fractions.

(d) $\frac{6}{6}\ \square\ \frac{3}{3}$

Answer: From the diagram it is clear that :-

$\frac{6}{6}\ =\ \frac{3}{3}\ =\ 1$

Q5 How quickly can you do this? Fill appropriate sign.

(a) $\frac{1}{2}\square \frac{1}{5}$

(b) $\frac{2}{4}\square \frac{3}{6}$

(c) $\frac{3}{5}\square \frac{2}{3}$

(d) $\frac{3}{4}\square \frac{2}{8}$

(e) $\frac{3}{5}\square \frac{6}{5}$

(f) $\frac{7}{9}\square \frac{3}{9}$

(g) $\frac{1}{4}\square \frac{2}{8}$

(h) $\frac{6}{10}\square \frac{4}{5}$

(i) $\frac{3}{4}\square \frac{7}{8}$

(j) $\frac{6}{10}\square \frac{3}{5}$

(k) $\frac{5}{7}\square \frac{15}{21}$

Answer: (a) $\frac{1}{2}\ >\ \frac{1}{5}$

(b) $\frac{2}{4}\ =\ \frac{3}{6}$

(c) $\frac{3}{5}\ <\ \frac{2}{3}$

(d) $\frac{3}{4}\ >\ \frac{2}{8}$

(e) $\frac{3}{5}\ <\ \frac{6}{5}$

(f) $\frac{7}{9}\ >\ \frac{3}{9}$

(g) $\frac{1}{4}\ =\ \frac{2}{8}$

(h) $\frac{6}{10}\ <\ \frac{4}{5}$

(i) $\frac{3}{4}\ <\ \frac{7}{8}$

(j) $\frac{6}{10}\ =\ \frac{3}{5}$

(k) $\frac{5}{7}\ =\ \frac{15}{21}$

Q6 The following fractions represent just three different numbers. Separate them into three groups of equivalent fractions, by changing each one to its simplest form.

(a) $\frac{2}{12}$

(b) $\frac{3}{15}$

(c) $\frac{8}{50}$

(d) $\frac{16}{100}$

(e) $\frac{10}{16}$

(f) $\frac{15}{75}$

(g) $\frac{12}{60}$

(h) $\frac{16}{96}$

(i) $\frac{12}{75}$

( j) $\frac{12}{72}$

(k) $\frac{3}{18}$

(l) $\frac{4}{25}$

Answer: (i) $\frac{2}{12}\times \frac{\frac{1}{2}}{\frac{1}{2}}\ =\ \frac{1}{6}$

(ii) $\frac{3}{15}\times \frac{\frac{1}{3}}{\frac{1}{3}}\ =\ \frac{1}{5}$

(iii) $\frac{8}{50}\times \frac{\frac{1}{2}}{\frac{1}{2}}\ =\ \frac{4}{25}$

(iv) $\frac{16}{100}\times \frac{\frac{1}{4}}{\frac{1}{4}}\ =\ \frac{4}{25}$

(v) $\frac{10}{16}\times \frac{\frac{1}{2}}{\frac{1}{2}}\ =\ \frac{5}{8}$

(vi) $\frac{15}{75}\times \frac{\frac{1}{15}}{\frac{1}{15}}\ =\ \frac{1}{5}$

(vii) $\frac{12}{60}\times \frac{\frac{1}{12}}{\frac{1}{12}}\ =\ \frac{1}{5}$

(viii) $\frac{16}{96}\times \frac{\frac{1}{16}}{\frac{1}{16}}\ =\ \frac{1}{6}$

(ix) $\frac{12}{75}\times \frac{\frac{1}{3}}{\frac{1}{3}}\ =\ \frac{4}{25}$

(x) $\frac{12}{72}\times \frac{\frac{1}{12}}{\frac{1}{12}}\ =\ \frac{1}{6}$

(xi) $\frac{3}{18}\times \frac{\frac{1}{3}}{\frac{1}{3}}\ =\ \frac{1}{6}$

(xii) $\frac{4}{25}$

Q7 (a) Find answers to the following. Write and indicate how you solved them.

Is $\frac{5}{9}$ equal to $\frac{4}{5}?$

Answer: No.

Multiply numerator and denomenator by $\frac{4}{5}$ .

We have : $\frac{5}{9}\times \frac{\frac{4}{5}}{\frac{4}{5}}\ =\ \frac{4}{\frac{36}{5}}$

Hence $\frac{5}{9}\ \neq \ \frac{4}{5}$

Q7 (b) Find answers to the following. Write and indicate how you solved them.

Is $\frac{9}{16}$ equal to $\frac{5}{9}$ ?

Answer: We have $\frac{9}{16}$ .

$\frac{9}{16}\ =\ \frac{9}{16}\times \frac{\frac{5}{9}}{\frac{5}{9}}\ =\ \frac{5}{\frac{80}{9}}\ \neq\ \frac{5}{9}$

Q7 (c) Find answers to the following. Write and indicate how you solved them.

Is $\frac{4}{5}$ equal to $\frac{16}{20}?$

Answer: Yes.

By multiplying numerator and denominator by 5, we get :

$\frac{4}{5}\times \frac{5}{5}\ =\ \frac{16}{20}$

Q7 (d) Find answers to the following. Write and indicate how you solved them.

Is $\frac{1}{15}$ equal to $\frac{4}{30}$ ?

Answer: No.

Multiply both numerator and denomenator by 2, we get :-

$\frac{1}{15}\times \frac{2}{2}\ =\ \frac{2}{30}\ \neq\ \frac{4}{30}$

Q8 Ila read $25$ pages of a book containing $100$ pages. Lalita read $\frac{2}{5}$ of the same book. Who read less?

Answer: The fraction of the book read by Ila is:-

$=\ \frac{25}{100}\ =\ \frac{1}{4}$

So we can compare the fraction now:-

$\frac{1}{4}\ <\ \frac{2}{5}$

Hence Ila reads less.

Q9 Rafiq exercised for $\frac{3}{6}$ of an hour, while Rohit exercised for $\frac{3}{4}$ of an hour. Who exercised for a longer time?

Answer: Who exercised for a longer time can be found by comparing the fraction of their work time.

$\frac{3}{6}\ <\ \frac{3}{4}$

Hence Rohit exercised for a longer time.

Q10 In a class A of $25$ students, $20$ passed with $60^{o}/_{o}$ or more marks; in another class B of $30$ students, $24$ passed with $60^{o}/_{o}$ or more marks. In which class was a greater fraction of students getting with $60^{o}/_{o}$ or more marks?

Answer: In class A, the fraction of students passed with $60 \%$ or above marks :

$=\ \frac{20}{25}\ =\ \frac{4}{5}$

And, in class B, the fraction is :

$=\ \frac{24}{30}\ =\ \frac{4}{5}$

Hence the required fraction is same in both the classes.

NCERT Class 6 Maths Chapter 7 Fractions Topic: Addition and Subtraction of Fractions

Q1 My mother divided an apple into $4$ equal parts. She gave me two parts and my brother one part. How much apple did she give to both of us together?

Answer: mother gave to me $\frac{1}{2}$ part

mother gave to my brother $\frac{1}{4}$ part

She gave both off us

$\frac{1}{2}+\frac{1}{4}=\frac{3}{4}$ part

Q2 Mother asked Neelu and her brother to pick stones from the wheat. Neelu picked one-fourth of the total stones in it and her brother also picked up one-fourth of the stones. What fraction of the stones did both pick up together?

Answer: Neelu picked stones

$=\frac{1}{4}$

brother picked up the stones

$=\frac{1}{4}$

The total fraction of the stones they both pick up together

$=\frac{1}{4}+\frac{1}{4}=\frac{1}{2}$ of total stones.

Q3 Sohan was putting covers on his note books. He put one fourth of the covers on Monday. He put another one fourth on Tuesday and the remaining on Wednesday. What fraction of the covers did he put on Wednesday?

Answer: He put covers on Monday= $\frac{1}{4}$

He put the cover on Tuesday = $\frac{1}{4}$

and the remaining on Wednesday.

Thus, the fraction of the covers he put on Wednesday = $1-(\frac{1}{4}+\frac{1}{4})$

$=1-(\frac{1}{2})$

$=\frac{1}{2}$

NCERT Class 6 Maths Chapter 7 Fractions Topic: Adding or Substracting like Fractions

Q1 Find the difference between $\frac{7}{8}$ and $\frac{3}{8}$ .

Answer: The difference between $\frac{7}{8}$ and $\frac{3}{8}$ is given by

$\frac{7}{8}-\frac{3}{8}=\frac{4}{8}=\frac{1}{2}$

Q2 Mother made a gud patti in a round shape. She divided it into $5$ parts. Seema ate one piece from it. If I eat another piece then how much would be left?

Answer: Seema ate = $\frac{1}{5}$

I eat = $\frac{1}{5}$

Total part eaten is

$\frac{1}{5}+\frac{1}{5}=\frac{2}{5}$

The left part would be

$=1-\frac{2}{5}=\frac{5-2}{5}=\frac{3}{5}$

Q3 My elder sister divided the watermelon into $16$ parts. I ate $7$ out of them. My friend ate $4$ . How much did we eat between us? How much more of the watermelon did I eat than my friend? What portion of the watermelon remained?

Answer: I ate= $\frac{7}{16}$

My friend ate = $\frac{4}{16}$

we both eat

$\frac{7}{16}+\frac{4}{16}=\frac{7+4}{16}=\frac{11}{16}$

the watermelon more I eat than my friend is

$\frac{7}{16}-\frac{4}{16}=\frac{7-4}{16}=\frac{3}{16}$

The portion of the watermelon remained

$1-\frac{11}{16}=\frac{16-11}{16}=\frac{5}{16}$

NCERT Solutions for Class 6 Maths Chapter 7 Fractions Exercise: 7.5

Q1 Write these fractions appropriately as additions or subtractions :

Answer: In case (a) - Addition

case (b) - Subtraction

case (c) - Addition

Q2 Solve :

(a) $\frac{1}{18} +\frac{1}{18}$

(b) $\frac{8}{15} +\frac{3}{15}$

(c) $\frac{7}{7} -\frac{5}{7}$

(d) $\frac{1}{22} +\frac{21}{22}$

(e) $\frac{12}{15} -\frac{7}{15}$

(f) $\frac{5}{8} +\frac{3}{8}$

(g) $1-\frac{2}{3}\left ( 1=\frac{3}{3} \right )$

( h) $\frac{1}{4}+\frac{0}{4}$

(i) $3-\frac{12}{5}$

Answer: (a) $\frac{1}{18} +\frac{1}{18}\ =\ \frac{1+1}{18}\ =\ \frac{2}{18}\ =\ \frac{1}{9}$

(b) $\frac{8}{15} +\frac{3}{15}\ =\ \frac{8+3}{15}\ =\ \frac{11}{15}$

(c) $\frac{7}{7} -\frac{5}{7}\ =\ \frac{7-5}{7}\ =\ \frac{2}{7}$

(d) $\frac{1}{22} +\frac{21}{22}\ =\ \frac{1+21}{22}\ =\ \frac{22}{22}\ =\ 1$

(e) $\frac{12}{15} -\frac{7}{15}\ =\ \frac{12-7}{15}\ =\ \frac{5}{15}\ =\ \frac{1}{ 3}$

(f) $\frac{5}{8} +\frac{3}{8}\ =\ \frac{5+3}{8}\ =\ \frac{8}{8}\ =\ 1$

(g) $1-\frac{2}{3}\ =\ \frac{3}{3}\ -\ \frac{2}{3}\ =\ \frac{3-2}{3}\ =\ \frac{1}{3}$

( h) $\frac{1}{4}+\frac{0}{4}\ =\ \frac{1+0}{4}\ =\ \frac{1}{4}$

(i) $3-\frac{12}{5}\ =\ \frac{15}{5}\ -\ \frac{12}{5}\ =\ \frac{15-12}{5}\ =\ \frac{3}{5}$

Q3 Shubham painted $\frac{2}{3}$ of the wall space in his room. His sister Madhavi helped and painted $\frac{1}{3}$ of the wall space. How much did they paint together?

Answer: Total wall painted = Wall painted by Subham + Wall pained by Madhavi

$=\ \frac{2}{3}\ +\ \frac{1}{3}\ =\ \frac{3}{3}\ =\ 1$

Hence the whole wall is painted by them.

Q4 Fill in the missing fractions.

(a) $\frac{7}{10}-\square =\frac{3}{10}$

(b) $-\square \frac{3}{21}=\frac{5}{21}$

(c) $\square- \frac{3}{6}=\frac{3}{6}$

(d) $\square+ \frac{5}{27}=\frac{12}{27}$

Answer: (a) $\frac{7}{10}-\square =\frac{3}{10}$

$\square\ =\ \frac{7}{10}\ -\ \frac{3}{10}$

or $\square\ =\ \frac{5}{10}\ =\ \frac{1}{2}$

(b) $-\square \frac{3}{21}=\frac{5}{21}$

$-\square =\frac{5}{3}$

or $\square\ =\ -\ \frac{5}{3}$

(c) $\square- \frac{3}{6}=\frac{3}{6}$

$\square\ =\ \frac{3}{6}\ +\ \frac{3}{6}\ =\ \frac{6}{6}\ =\ 1$

(d) $\square+ \frac{5}{27}=\frac{12}{27}$

$\square\ =\ \frac{12}{27}\ -\ \frac{5}{27}$

or $=\ \frac{7}{27}$

Q5 Javed was given $\frac{5}{7}$ of a basket of oranges. What fraction of oranges was left in the basket?

Answer: The total fraction of oranges in the basket are $\frac{7}{7}$ .

Thus the fraction of oranges left is :

$\frac{7}{7}\ -\ \frac{5}{7}\ =\ \frac{2}{7}$

NCERT Class 6 Maths Chapter 7 Fractions Topic: Addition and Subtraction of Fractions

Q1 Add $\frac{2}{5}$ and $\frac{3}{7}$ .

Answer: Addition of $\frac{2}{5}$ and $\frac{3}{7}$ is given by

$\frac{2}{5}+\frac{3}{7}=\frac{14+15}{35}=\frac{29}{35}$

Q2 Subtract $\frac{2}{5}$ from $\frac{5}{7}$ .

Answer: Subtraction of $\frac{2}{5}$ from $\frac{5}{7}$ is given by

$\frac{5}{7}-\frac{2}{5}=\frac{25-14}{35}=\frac{11}{35}$

NCERT Solutions for Class 6 Maths Chapter 7 Fractions Exercise: 7.6

Q1 Solve

(a) $\frac{2}{3}+\frac{1}{7}$ (b) $\frac{3}{10}+\frac{7}{15}$ (c) $\frac{4}{9}+\frac{2}{7}$

(d) $\frac{5}{7}+\frac{1}{3}$ (e) $\frac{2}{5}+\frac{1}{6}$ (f) $\frac{4}{5}+\frac{2}{3}$

Answer: (a) $\frac{2}{3}+\frac{1}{7}\ =\ \frac{2\times 7\ +\ 1\times 3}{21}\ =\ \frac{17}{21}$

(b) $\frac{3}{10}+\frac{7}{15}\ =\ \frac{3\times 15\ +\ 7\times 10}{150}\ =\ \frac{115}{150}\ =\ \frac{23}{30}$

(c) $\frac{4}{9}+\frac{2}{7}\ =\ \frac{4\times 3\ +\ 2\times 9}{63}\ =\ \frac{46}{63}$

(d) $\frac{5}{7}+\frac{1}{3}\ =\ \frac{5\times 3\ +\ 1\times 7}{21}\ =\ \frac{22}{21}$

(e) $\frac{2}{5}+\frac{1}{6}\ =\ \frac{2\times 6\ +\ 1\times 5}{30}\ =\ \frac{17}{30}$

(f) $\frac{4}{5}+\frac{2}{3}\ =\ \frac{4\times 3\ +\ 2\times 5}{15}\ =\ \frac{22}{15}$

Q1 Solve

(g) $\frac{3}{4}-\frac{1}{3}$ (h) $\frac{5}{5}-\frac{1}{3}$ (i) $\frac{2}{3}+\frac{3}{4}+\frac{1}{2}$

(j) $\frac{1}{2}+\frac{1}{3}+\frac{1}{6}$ (k) $1\frac{1}{3}+3\frac{2}{3}$ (l) $4\frac{2}{3}+3\frac{1}{4}$

(m) $\frac{16}{5}-\frac{7}{5}$ (n) $\frac{4}{3}-\frac{1}{2}$

Answer: (g) $\frac{3}{4}-\frac{1}{3}\ =\ \frac{3\times 3\ -\ 1\times 4}{12}\ =\ \frac{5}{12}$

(h) $\frac{5}{5}-\frac{1}{3}\ =\ \frac{5\times 3\ -\ 1\times 5}{15}\ =\ \frac{10}{15}\ =\ \frac{2}{3}$

(i) $\frac{2}{3}+\frac{3}{4}+\frac{1}{2}\ =\ \frac{2\times 4\ +\ 3\times 3}{12}\ +\ \frac{1}{2}\ =\ \frac{17}{12}\ +\ \frac{1}{2}\ =\ \frac{17\times 2\ +\ 1\times 12}{24}$

$=\ \frac{46}{24}\ =\ \frac{23}{12}$

(j) $\frac{1}{2}+\frac{1}{3}+\frac{1}{6}\ =\ \frac{1\times 3\ +\ 1\times 2}{6}\ +\ \frac{1}{6}\ =\ \frac{5}{6}\ +\ \frac{1}{6}\ =\ \frac{6}{6}\ =\ 1$

(k) $1\frac{1}{3}+3\frac{2}{3}\ =\ \frac{4}{3}\ +\ \frac{11}{3}\ =\ \frac{15}{3}\ =\ 5$

(l) $4\frac{2}{3}+3\frac{1}{4}\ =\ \frac{14}{3}\ +\ \frac{13}{4}\ =\ \frac{14\times 4\ +\ 13\times 3}{12}\ =\ \frac{95}{12}$ \

(m) $\frac{16}{5}-\frac{7}{5}\ =\ \frac{16\ -\ 7}{5}\ =\ \frac{9}{5}$

(n) $\frac{4}{3}-\frac{1}{2}\ =\ \frac{4\times2\ -\ 1\times3}{6}\ =\ \frac{5}{6}$

Q2 Sarita bought $\frac{2}{5}$ metre of ribbon and Lalita $\frac{3}{4}$ metre of ribbon. What is the total length of the ribbon they bought?

Answer: The total length of ribbon is given :-

$=\ \frac{2}{5}\ +\ \frac{3}{4}\ =\ \frac{2\times 4\ +\ 3\times 5}{20}\ =\ \frac{23}{20}$

Thus total length of ribbon is _{$\frac{23}{20}\ m$} .

Q3 Naina was given $1\frac{1}{2}$ piece of cake and Najma was given $1\frac{1}{3}$ piece of cake. Find the total amount of cake was given to both of them.

Answer: Total amount of cake given to both = Cake given to Naina + Cake given to Najma

$=\ 1\frac{1}{2}\ +\ 1\frac{1}{3}$

$=\ \frac{3}{2}\ +\ \frac{4}{3}$

$=\ \frac{3\times 3\ +\ 4\times 2 }{6}$

$=\ \frac{17 }{6}$

Q4 Fill in the boxes :

(a) $\square-\frac{5}{8}=\frac{1}{4}$

(b) $\square-\frac{1}{5}=\frac{1}{2}$

(c) $\frac{1}{2}-\square =\frac{1}{6}$

Answer: (a) $\square-\frac{5}{8}=\frac{1}{4}$ :-

$\square\ =\ \frac{1}{4}\ +\ \frac{5}{8}\ =\ \frac{1\times 8\ +\ 5\times 4}{32}\ =\ \frac{28}{32}\ =\ \frac{7}{8}$

(b) $\square-\frac{1}{5}=\frac{1}{2}$ :-

$\square\ =\ \frac{1}{2}\ +\ \frac{1}{5}\ =\ \frac{1\times 5\ +\ 1\times 2}{10}\ =\ \frac{7}{10}$

(c) $\frac{1}{2}-\square =\frac{1}{6}$ :-

$\square\ =\ \frac{1}{2}\ -\ \frac{1}{6}\ =\ \frac{1\times 6\ -\ 1\times 2}{12}\ =\ \frac{4}{12}\ =\ \frac{1}{3}$

Q5 Complete the addition-subtraction box.

Answer: The required table is shown below:-

Q5 Complete the addition-subtraction box.

Answer: The required box is given below :-

Q6 A piece of wire $\frac{7}{8}$ metre long broke into two pieces. One piece was $\frac{1}{4}$ metre long. How long is the other piece?

Answer: Let the length of another piece of wire be x.

Thus, $x\ +\ \frac{1}{4}\ =\ \frac{7}{8}$

$x\ =\ \frac{7}{8}\ -\ \frac{1}{4}$

$=\ \frac{7\times 4\ -\ 1\times 8}{32}\ =\ \frac{20}{32}$

$=\ \frac{10}{16}\ =\ \frac{5}{8}$

Hence the length of other part is _{$\frac{5}{8}\ m$} .

Q7 Nandini’s house is $\frac{9}{10}\; km$ from her school. She walked some distance and then took a bus for $\frac{1}{2}\; km$ to reach the school. How far did she walk?

Answer: The distance Nandini walked is given by :-

$\frac{9}{10}\ -\ \frac{1}{2}\ =\ \frac{9\times 2\ -\ 1\times 10 }{20}\ =\ \frac{8}{20}\ =\ \frac{2}{5}$

Hence she walked _{$\frac{2}{5}\ Km$} .

Q8 Asha and Samuel have bookshelves of the same size partly filled with books. Asha’s shelf is $\frac{5}{6}th$ full and Samuel’s shelf is $\frac{2}{5}th$ full. Whose bookshelf is more full? By what fraction?

Answer: If we compare the bookshelves of both, we obtain that :

$\frac{5}{6}\ >\ \frac{2}{5}$

Also, $\frac{5}{6}\ -\ \frac{2}{5}\ =\ \frac{25-12}{30}\ =\ \frac{13}{30}$

Hence the bookshelf of Asha is more full and by $\frac{13}{30}$ fraction.

Q9 Jaidev takes $2\frac{1}{5}$ minutes to walk across the school ground. Rahul takes $\frac{7}{4}$ minutes to do the same. Who takes less time and by what fraction?

Answer: Firstly, let us convert the time taken by Jaidev in the improper fraction from mixed fraction.

$2\frac{1}{5}\ =\ \frac{10\ +\ 1}{5}\ =\ \frac{11}{5}$

Now, comparing both, we have :

$\frac{11}{5}\ >\ \frac{7}{4}$

Also, $\frac{11}{5}\ -\ \frac{7}{4}\ =\ \frac{11\times 4\ -\ 7\times 5}{20}\ =\ \frac{9}{20}$

Hence Rahul takes less time as compared to Jaidev by _{$\frac{9}{20}\ minute$} a fraction.