NCERT Solutions Class 6 Maths Chapter 7

Q.1 Write the fraction representing the shaded portion.

Ans-

$\begin{array}{l}\left(\text{i}\right)\frac{2}{4}\left(\text{ii}\right)\frac{8}{9}\left(\text{iii}\right)\frac{4}{8}\left(\text{iv}\right)\frac{1}{4}\\ \left(\text{v}\right)\frac{3}{7}\left(\text{vi}\right)\frac{3}{12}\left(\text{vii}\right)\frac{10}{10}\\ \left(\text{viii}\right)\frac{4}{9}\left(\text{ix}\right)\frac{4}{8}\left(\text{x}\right)\frac{1}{2}\end{array}$

Q.2 Colour the part according to the given fraction.

(a) (b)

(c)

(e)

Ans-

(a) (b)

(c) (d)

(e)

Q.3 Identify the error, if any
(a)

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

(b)

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

(c)

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

Ans-

(a)

This is

$\frac{1}{2}$

This is incorrect as the shaded portion does not represent the required fraction.
(b)

This is

$\frac{1}{4}$

This is incorrect as the shaded portion does not represent the required fraction.
(c)

This is

$\frac{3}{4}$

This is incorrect as the shaded portion does not represent the required fraction.

Q.4 What fraction of a day is 8 hours?

Ans-

Number of hours in a day = 24 hours

Fraction =

$\frac{8}{24}$

Q.5 What fraction of an hour is 40 minutes?

Ans- 

Number of minutes in an hour = 60 minutes

Fraction =

$\frac{40}{60}$

Q.6 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.
(a) How can Arya divide his sandwiches so that each person has an equal share?
(b) What part of a sandwich will each boy receive?

Ans-

(a) each sandwich will be divided into 3 equal parts, so that each one of them get equal share.

(b) Number of parts of sandwich = 6
Every one of them will get 2 pieces each, out of 6 pieces. Each boy will get part =

$\frac{2}{6}=\frac{1}{3}$

Q.7 Kanchan dyes dresses. She had to dye 30 dresses. She has so far finished 20 dresses. What fraction of dresses has she finished?

Ans-

Total dresses to dye = 30

Dresses done dying = 20

Fraction

$=\frac{20}{30}$

Q.8 Write the natural numbers from 2 to 12. What fraction of them are prime numbers?

Ans-

Natural numbers from 2 to 12 = 11

Prime numbers = 2, 3, 5, 7, 11

Fraction

$=\frac{5}{11}$

Q.9 Write the natural numbers from 102 to 113. What fraction of them are prime numbers?

Ans-

Natural numbers from 102 to 113 = 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113.

Prime numbers among them = 103, 107, 109, 113

Fraction =

$\frac{4}{12}$

Q.10 What fraction of these circles have X’s in them?

Ans-

Number of circles having X’s in them = 4

Fraction =

$\frac{4}{8}$

Q.11 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?

Ans-

CDs bought by Kristin = 3

CDs received as gifts = 5

Total = 8

Fraction of CDs she buy =

$\frac{3}{8}$

Fraction of CDs gifted =

$\frac{5}{8}$

Q.12 Draw number lines and locate the points on them :

$\begin{array}{l}\left(\mathrm{a}\right)\frac{1}{2},\frac{1}{4},\frac{3}{4},\frac{4}{4}\end{array}$ $\begin{array}{l}\left(\mathrm{b}\right)\frac{1}{8},\frac{2}{8},\frac{3}{8},\frac{7}{8}\end{array}$ $\begin{array}{l}\left(\mathrm{c}\right)\frac{2}{5},\frac{3}{5},\frac{8}{5},\frac{4}{5}\end{array}$

Ans-

(a)

$\frac{1}{2},\frac{1}{4},\frac{3}{4},\frac{4}{4}$

(b)

$\frac{1}{8},\frac{2}{8},\frac{3}{8},\frac{7}{8}$

(c)

$\frac{2}{5},\frac{3}{5},\frac{8}{5},\frac{4}{5}$

Q.13 Express the following as mixed fractions :

$\begin{array}{l}\left(\mathrm{a}\right)\frac{20}{3}\left(\mathrm{b}\right)\frac{11}{5}\\ \left(\mathrm{c}\right)\frac{17}{7}\left(\mathrm{d}\right)\frac{28}{5}\\ \left(\mathrm{e}\right)\frac{19}{6}\left(\mathrm{f}\right)\frac{35}{9}\end{array}$

Ans-

\begin{array}{l}(a)\frac{20}{3}=3\begin{array}{c}\hfill 6\\ \hfill \overline{)\begin{array}{l}20\\ \underset{¯}{-18}\\ \underset{¯}{2}\end{array}}\end{array}\\ \text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}=6\frac{2}{3}\\ (b)\frac{11}{5}=5\begin{array}{c}\hfill 2\\ \hfill \overline{)\begin{array}{l}\text{11}\\ \underset{¯}{-10}\\ \underset{¯}{\text{1}}\end{array}}\end{array}\\ =2\frac{1}{5}\\ (c)\frac{17}{7}=7\begin{array}{c}\hfill 2\\ \hfill \overline{)\begin{array}{l}\text{17}\\ \underset{¯}{-14}\\ \underset{¯}{\text{3}}\end{array}}\end{array}\\ =2\frac{3}{7}\\ (d)\frac{28}{5}=5\begin{array}{c}\hfill 5\\ \hfill \overline{)\begin{array}{l}\text{28}\\ \underset{¯}{-25}\\ \underset{¯}{\text{3}}\end{array}}\end{array}\\ =5\frac{3}{5}\\ (e)\frac{19}{6}=6\begin{array}{c}\hfill 3\\ \hfill \overline{)\begin{array}{l}\text{19}\\ \underset{¯}{-18}\\ \underset{¯}{\text{1}}\end{array}}\end{array}\\ =3\frac{1}{6}\\ (f)\frac{35}{9}=9\begin{array}{c}\hfill 3\\ \hfill \overline{)\begin{array}{l}\text{35}\\ \underset{¯}{-27}\\ \underset{¯}{\text{8}}\end{array}}\end{array}\\ =3\frac{8}{9}\end{array}

Q.14 Express the following as improper fractions :

$\begin{array}{l}\left(\mathrm{a}\right)7\frac{3}{4}\left(\mathrm{b}\right)5\frac{6}{7}\\ \left(\mathrm{c}\right)2\frac{5}{6}\left(\mathrm{d}\right)10\frac{3}{5}\\ \left(\mathrm{e}\right)9\frac{3}{7}\left(\mathrm{f}\right)8\frac{4}{9}\end{array}$

Ans-

$\begin{array}{l}\left(\mathrm{a}\right)7\frac{3}{4}=7+\frac{3}{4}=\frac{7\times 4+3}{4}=\frac{31}{4}\\ \left(\mathrm{b}\right)5\frac{6}{7}=5+\frac{6}{7}=\frac{5\times 7+6}{7}=\frac{41}{7}\\ \left(\mathrm{c}\right)2\frac{5}{6}=2+\frac{5}{6}=\frac{2\times 6+5}{6}=\frac{17}{6}\\ \left(\mathrm{d}\right)10\frac{3}{5}=10+\frac{3}{5}=\frac{10\times 5+3}{5}=\frac{53}{5}\\ \left(\mathrm{e}\right)9\frac{3}{7}=9+\frac{3}{7}=\frac{9\times 7+3}{7}=\frac{66}{7}\\ \left(\mathrm{f}\right)8\frac{4}{9}=8+\frac{4}{9}=\frac{8\times 9+4}{9}=\frac{76}{9}\end{array}$

Q.15 Write the fractions. Are all these fractions equivalent ?
(a)

(b)

Ans-

(a)

$\text{Here,}\frac{1}{2},\frac{\cancel{2}}{\cancel{4}}=\frac{1}{2},\frac{\cancel{3}}{\cancel{6}}=\frac{1}{2},\frac{\cancel{4}}{\cancel{8}}=\frac{1}{2}$

So, all these fractions are equivalent.

(b)

$\text{Here,}\frac{4}{12}=\frac{1}{3},\frac{3}{9}=\frac{1}{3},\frac{2}{6}=\frac{1}{3},\frac{6}{15}=\frac{2}{5}.$

Q.16 Write the fractions and pair up the equivalent fractions from each row.

Ans-

Equivalent fractions are shown below :

Q.17 Write the fractions and pair up the equivalent fractions from each row.

Ans-

Equivalent fractions are shown below :

Q.18 Write the fractions and pair up the equivalent fractions from each row.

Ans-

Equivalent fractions are shown below :

Q.19 Replace in each of the following by the correct number :

$\left(\text{a}\right)\frac{2}{7}=\frac{8}{}\left(\text{b}\right)\frac{5}{8}=\frac{10}{}\left(\text{c}\right)\frac{3}{5}=\frac{}{20}\left(\text{d}\right)\frac{45}{60}=\frac{15}{}\left(\text{e}\right)\frac{18}{24}=\frac{}{4}$

Ans-

\begin{array}{l}\text{(a)}\frac{2}{7}=\frac{8}{}\\ \Rightarrow \frac{2}{7}=\frac{2\times 4}{7\times 4}=\frac{8}{28}\\ \text{(b)}\frac{5}{8}=\frac{10}{}\\ \Rightarrow \frac{5}{8}=\frac{2\times 5}{8\times 2}=\frac{10}{16}\\ (c)\frac{3}{5}=\frac{}{20}\\ \Rightarrow \frac{3}{5}=\frac{3\times 4}{5\times 4}=\frac{12}{20}\\ (d)\frac{45}{60}=\frac{15}{}\\ \Rightarrow \frac{45÷3}{60÷3}=\frac{15}{20}\\ (e)\frac{18}{24}=\frac{}{4}\\ \Rightarrow \frac{18÷6}{24÷6}=\frac{3}{4}\end{array}

Q.20 Find the equivalent fraction of having
(a) denominator 20 (b) numerator 9
(c) denominator 30 (d) numerator 27

Ans-

$\begin{array}{l}\left(\text{a}\right)\text{Denominator 2}0\\ \frac{3}{5}=\frac{}{20}\\ \Rightarrow \frac{3}{5}=\frac{3\times 4}{5\times 4}=\frac{12}{20}\\ \left(\text{b}\right)\text{Numerator 9}\\ \frac{3}{5}=\frac{9}{}\\ \Rightarrow \frac{3}{5}=\frac{3\times 3}{5\times 3}=\frac{9}{15}\\ \left(\text{c}\right)\text{Denominator 3}0\\ \frac{3}{5}=\frac{}{30}\\ \Rightarrow \frac{3}{5}=\frac{3\times 6}{5\times 6}=\frac{18}{30}\\ \left(\text{d}\right)\text{Numerator 27}\\ \frac{3}{5}=\frac{27}{}\\ \Rightarrow \frac{3}{5}=\frac{3\times 9}{5\times 9}=\frac{27}{45}\end{array}$

Q.21 Find the equivalent fraction of

$\frac{36}{48}$

having
(a) numerator 9 (b) denominator 4

Ans-

$\begin{array}{l}\left(\text{a}\right)\text{Numerator 9}\\ \frac{36}{48}=\frac{9}{}\\ \Rightarrow \frac{36÷4}{48÷4}=\frac{9}{12}\\ \left(\text{b}\right)\text{Denominator 4}\\ \frac{36}{48}=\frac{}{4}\\ \Rightarrow \frac{36÷12}{48÷12}=\frac{3}{4}\end{array}$

Q.22 Check whether the given fractions are equivalent :

$\begin{array}{l}\left(\text{a}\right)\frac{5}{9},\frac{30}{54}\\ \left(\text{b}\right)\frac{3}{10},\frac{12}{50}\\ \left(\text{c}\right)\frac{7}{13},\frac{5}{11}\end{array}$

Ans-

(a)

$\frac{5}{9},\frac{30}{54}$

The given fractions will be equivalent if the product of numerator of one fraction with denominator of another fraction is equal.

Here, 5 × 54 = 9 × 30. So, the fractions are equivalent.

(b)

$\frac{3}{10},\frac{12}{50}$

The given fractions will be equivalent if the product of numerator of one fraction with denominator of another fraction is equal.

$\text{Here,}50\times 3\ne 12\times 10\text{So},\text{these fractions are not equivalent}.$ $(c)$ $\frac{7}{13},\frac{5}{11}$ $$\begin{gathered} \text{The given fractions will be equivalent if the product of numerator of one fraction with denominator of another fraction is equal}. \\ \text{Here, 11}\times 7\ne 13\times 5\text{So},\text{these fractions are not equivalent}. \end{gathered}$$

Q.23 Reduce the following fractions to simplest form :

$\begin{array}{l}\left(\mathrm{a}\right)\frac{48}{60}\left(\mathrm{b}\right)\frac{150}{60}\\ \left(\mathrm{c}\right)\frac{84}{98}\left(\mathrm{d}\right)\frac{12}{52}\\ \left(\mathrm{e}\right)\frac{7}{28}\end{array}$

Ans-

$\begin{array}{l}\left(\mathrm{a}\right)\frac{48}{60}=\frac{12\times 4}{12\times 5}=\frac{4}{5}\\ \left(\mathrm{b}\right)\frac{150}{60}=\frac{15\times 10}{6\times 10}=\frac{15}{6}=\frac{5}{2}\\ \left(\mathrm{c}\right)\frac{84}{98}=\frac{14\times 6}{14\times 7}=\frac{6}{7}\\ \left(\mathrm{d}\right)\frac{12}{52}=\frac{4\times 3}{4\times 13}=\frac{3}{13}\\ \left(\mathrm{e}\right)\frac{7}{28}=\frac{1\times 7}{4\times 7}=\frac{1}{4}\end{array}$

Q.24 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 ?

Here, we can see that Ramesh, Sheelu and Jamaal has used up an equal fraction of his/her pencils.

Ans-

Here, we can see that Ramesh, Sheelu and Jamaal has used up an equal fraction of his/her pencils.

Q.25 Match the equivalent fractions and write two more for each :

Ans-

Q.26 Write shaded portions as fraction. Arrange them in ascending or descending order using the correct sign ‘<’ ‘=’ ‘>’ between the fractions.

$\begin{array}{l}\text{(c)}\\ \text{Show}\frac{2}{6},\frac{4}{6},\frac{8}{6}\text{and}\frac{6}{6}\text{on the number line}\text{. Put appropriate}\\ \text{signs between the fractions given :}\\ \frac{5}{6}\_\_\frac{2}{6},\frac{3}{6}\_\_0,\frac{1}{6}\_\_\frac{6}{6},\frac{8}{6}\_\_\frac{5}{6}\end{array}$

Ans-

Since, they all are like fractions. They can be arranged in increasing order by observing numerator only.

So,

$\frac{1}{8}<\frac{3}{8}<\frac{4}{8}<\frac{6}{8}$

(b)

Since, they all are like fractions. They can be arranged in increasing order by observing numerator only.

So,

$\frac{3}{9}<\frac{4}{9}<\frac{6}{9}<\frac{8}{9}$

(c)

$\frac{5}{6}\begin{array}{|c|}\hline >\\ \hline\end{array}\frac{2}{6},\frac{3}{6}\begin{array}{|c|}\hline >\\ \hline\end{array}0,\frac{1}{6}\begin{array}{|c|}\hline <\\ \hline\end{array}\frac{6}{6},\frac{8}{6}\begin{array}{|c|}\hline >\\ \hline\end{array}\frac{5}{6}$

Q.27 Write shaded portions as fraction. Arrange them in ascending or descending order using the correct sign ‘<’ ‘=’ ‘>’ between the fractions.

$\begin{array}{l}\text{(c)}\\ \text{Show}\frac{2}{6},\frac{4}{6},\frac{8}{6}\text{and}\frac{6}{6}\text{on the number line}\text{. Put appropriate}\\ \text{signs between the fractions given :}\\ \frac{5}{6}\_\_\frac{2}{6},\frac{3}{6}\_\_0,\frac{1}{6}\_\_\frac{6}{6},\frac{8}{6}\_\_\frac{5}{6}\end{array}$

Ans-

Since, they all are like fractions. They can be arranged in increasing order by observing numerator only.

So,

$\frac{1}{8}<\frac{3}{8}<\frac{4}{8}<\frac{6}{8}$

(b)

Since, they all are like fractions. They can be arranged in increasing order by observing numerator only.

So,

$\frac{3}{9}<\frac{4}{9}<\frac{6}{9}<\frac{8}{9}$

(c)

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

Q.28 Compare the fractions and put an appropriate sign.

$\begin{array}{l}\left(\mathrm{a}\right)\frac{3}{6}\left[\right]\frac{5}{6}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}(b)\hspace{0.17em}}\frac{1}{7}\left[\right]\frac{1}{4}\\ \text{(c)\hspace{0.17em}}\frac{4}{5}\left[\right]\frac{5}{5}\left(\mathrm{d}\right)\frac{3}{5}\left[\right]\frac{3}{7}\end{array}$

Ans-

$$\begin{gathered} \begin{array}{l}\left(\mathrm{a}\right)\frac{3}{6}\left[\right]\frac{5}{6}\\ \text{Since},\text{these are like fractions and 3}<\text{5}.\text{So},\frac{3}{6}[<]\frac{5}{6}\\ \text{(b)\hspace{0.17em}}\frac{1}{7}\left[\right]\frac{1}{4}\\ \text{Here},\text{numerator of both the fractions are same}. \\ \text{So},\text{larger the denominator is},\text{smaller is the value of the fraction}.\\ \mathrm{So},\frac{1}{7}[<]\frac{1}{4}\\ \left(\mathrm{c}\right)\frac{4}{5}\left[\right]\frac{5}{5}\\ \text{Since},\text{these are like fractions and 4}<\text{5}.\text{So},\frac{4}{5}[<]\frac{5}{5}\\ \text{(d)\hspace{0.17em}}\frac{3}{5}\left[\right]\frac{3}{7}\\ \text{Here},\text{numerator of both the fractions are same}. \\ \text{So},\text{larger the denominator is},\text{smaller is the value of the fraction}.\\ \mathrm{So},\frac{3}{5}[>]\frac{3}{7}\end{array} \end{gathered}$$

Q.29 Compare the fractions and put an appropriate sign.

$$\begin{gathered} \begin{array}{l}\left(\mathrm{a}\right)\frac{3}{6}\left[\right]\frac{5}{6} \\ \left(\text{b}\right)\frac{1}{7}\left[\right]\frac{1}{4}\\ \left(\text{c}\right)\frac{4}{5}\left[\right]\frac{5}{5} \\ \left(\mathrm{d}\right)\frac{3}{5}\left[\right]\frac{3}{7}\end{array} \end{gathered}$$

Ans-

$$\begin{gathered} \begin{array}{l}\left(\mathrm{a}\right)\frac{3}{6}\left[\right]\frac{5}{6}\\ \text{Since},\text{these are like fractions and 3}<\text{5}.\text{So},\frac{3}{6}[<]\frac{5}{6}\\ \left(\text{b}\right)\frac{1}{7}\left[\right]\frac{1}{4}\\ \text{Here},\text{numerator of both the fractions are same}.\text{So},\text{larger the denominator is}, \\ \text{smaller is the value of the fraction}.\\ \\ \mathrm{So},\frac{1}{7}[<]\frac{1}{4}\\ \left(\mathrm{c}\right)\frac{4}{5}\left[\right]\frac{5}{5}\\ \text{Since},\text{these are like fractions and 4}<\text{5}.\text{So},\frac{4}{5}[<]\frac{5}{5}\\ \text{(d)\hspace{0.17em}}\frac{3}{5}\left[\right]\frac{3}{7}\\ \text{Here},\text{numerator of both the fractions are same}.\text{So},\text{larger the denominator is}, \\ \text{smaller is the value of the fraction}.\\ \mathrm{So},\frac{3}{5}[>]\frac{3}{7}\end{array} \end{gathered}$$

Q.30 et the pairs of fractions to compare is

$\begin{array}{l}(a)\frac{3}{7}[]\frac{5}{7}\text{(b)}\frac{2}{7}[]\frac{2}{4}\\ (c)\frac{4}{9}[]\frac{5}{9}(d)\frac{1}{5}[]\frac{1}{7}\\ (e)\frac{13}{15}[]\frac{23}{15}\end{array}$

Ans-

$$\begin{gathered} \begin{array}{l}\left(\mathrm{a}\right)\frac{3}{7}\left[\right]\frac{5}{7}\\ \text{Since},\text{these are like fractions and 3}<\text{5}.\text{So},\\ \frac{3}{7}[<]\frac{5}{7}\\ \text{(b)}\frac{2}{7}\left[\right]\frac{2}{4}\\ \text{Here},\text{numerator of both the fractions are same}. \\ \text{So},\text{larger the denominator is},\text{smaller is the value of the fraction}.\\ \mathrm{So},\frac{2}{7}[<]\frac{2}{4}\\ \left(\mathrm{c}\right)\frac{4}{9}\left[\right]\frac{5}{9}\\ \text{Since},\text{these are like fractions and 4}<\text{5}.\text{So},\\ \frac{4}{9}[<]\frac{5}{9}\\ \text{(d)\hspace{0.17em}}\frac{1}{5}\left[\right]\frac{1}{7}\\ \text{Here},\text{numerators of both the fractions are same}. \\ \text{So},\text{larger the denominator is},\text{smaller is the value of the fraction}.\\ \mathrm{So},\frac{1}{5}[>]\frac{1}{7}\\ \text{(e)\hspace{0.17em}}\frac{13}{15}\left[\right]\frac{23}{15}\\ \text{Since},\text{these are like fractions and 13}<\text{23}.\text{So},\\ \frac{13}{23}[<]\frac{15}{23}\end{array} \end{gathered}$$

Q.31 Look at the figures and write ‘<’ or ‘>’, ‘=’ between the given pairs of fractions.

$$\begin{gathered} \left(\text{a}\right)\frac{1}{6}\left[\right]\frac{1}{3} \\ \left(\text{b}\right)\frac{3}{4}\left[\right]\frac{2}{6} \\ \left(\text{c}\right)\frac{2}{3}\left[\right]\frac{2}{4} \\ \left(\text{d}\right)\frac{5}{6}\left[\right]\frac{5}{5} \end{gathered}$$

Ans-

$$\begin{gathered} \left(\text{a}\right)\frac{1}{6}[<]\frac{1}{3} \\ \left(\text{b}\right)\frac{3}{4}[>]\frac{2}{6} \\ \left(\text{c}\right)\frac{2}{3}[>]\frac{2}{4} \\ \left(\text{d}\right)\frac{5}{6}[<]\frac{5}{5} \end{gathered}$$

Q.32 How quickly can you do this ? Fill appropriate sign. ( ‘<’, ‘=’, ‘>’)

$\begin{array}{l}\left(\text{a}\right)\frac{1}{2}\begin{array}{|c|}\hline \\ \hline\end{array}\frac{1}{5}\left(\text{b}\right)\frac{2}{4}\begin{array}{|c|}\hline \\ \hline\end{array}\frac{3}{6}\left(\text{c}\right)\frac{3}{5}\begin{array}{|c|}\hline \\ \hline\end{array}\frac{2}{3}\\ \left(\text{d}\right)\frac{3}{4}\begin{array}{|c|}\hline \\ \hline\end{array}\frac{2}{8}\left(\text{e}\right)\frac{3}{5}\begin{array}{|c|}\hline \\ \hline\end{array}\frac{6}{5}\left(\text{f}\right)\frac{7}{9}\begin{array}{|c|}\hline \\ \hline\end{array}\frac{3}{9}\\ \left(\text{g}\right)\frac{1}{4}\begin{array}{|c|}\hline \\ \hline\end{array}\frac{2}{8}\left(\text{h}\right)\frac{6}{10}\begin{array}{|c|}\hline \\ \hline\end{array}\frac{4}{5}\left(\text{i}\right)\frac{3}{4}\begin{array}{|c|}\hline \\ \hline\end{array}\frac{7}{8}\\ \left(\text{j}\right)\frac{6}{10}\begin{array}{|c|}\hline \\ \hline\end{array}\frac{4}{5}\left(\text{k}\right)\frac{5}{7}\begin{array}{|c|}\hline \\ \hline\end{array}\frac{15}{21}\end{array}$

Ans-

$\begin{array}{l}\left(\text{a}\right)\frac{1}{2}\begin{array}{|c|}\hline >\\ \hline\end{array}\frac{1}{5}\left(\text{b}\right)\frac{2}{4}\begin{array}{|c|}\hline =\\ \hline\end{array}\frac{3}{6}\left(\text{c}\right)\frac{3}{5}\begin{array}{|c|}\hline <\\ \hline\end{array}\frac{2}{3}\\ \left(\text{d}\right)\frac{3}{4}\begin{array}{|c|}\hline >\\ \hline\end{array}\frac{2}{8}\left(\text{e}\right)\frac{3}{5}\begin{array}{|c|}\hline <\\ \hline\end{array}\frac{6}{5}\left(\text{f}\right)\frac{7}{9}\begin{array}{|c|}\hline >\\ \hline\end{array}\frac{3}{9}\\ \left(\text{g}\right)\frac{1}{4}\begin{array}{|c|}\hline =\\ \hline\end{array}\frac{2}{8}\left(\text{h}\right)\frac{6}{10}\begin{array}{|c|}\hline <\\ \hline\end{array}\frac{4}{5}\left(\text{i}\right)\frac{3}{4}\begin{array}{|c|}\hline <\\ \hline\end{array}\frac{7}{8}\\ \left(\text{j}\right)\frac{6}{10}\begin{array}{|c|}\hline <\\ \hline\end{array}\frac{4}{5}\left(\text{k}\right)\frac{5}{7}\begin{array}{|c|}\hline =\\ \hline\end{array}\frac{15}{21}\end{array}$

Q.33 How quickly can you do this ? Fill appropriate sign. ( ‘<’, ‘=’, ‘>’)

$\begin{array}{l}\left(\mathrm{a}\right)\frac{1}{2}\boxed{}\frac{1}{5}\left(\mathrm{b}\right)\frac{2}{4}\boxed{}\frac{3}{6}\left(\mathrm{c}\right)\frac{3}{5}\boxed{}\frac{2}{3}\\ \left(\mathrm{d}\right)\frac{3}{4}\boxed{}\frac{2}{8}\left(\mathrm{e}\right)\frac{3}{5}\boxed{}\frac{6}{5}\left(\mathrm{f}\right)\frac{7}{9}\boxed{}\frac{3}{9}\\ \left(\mathrm{g}\right)\frac{1}{4}\boxed{}\frac{2}{8}\left(\mathrm{h}\right)\frac{6}{10}\boxed{}\frac{4}{5}\left(\mathrm{i}\right)\frac{3}{4}\boxed{}\frac{7}{8}\\ \left(\mathrm{j}\right)\frac{6}{10}\boxed{}\frac{4}{5}\left(\mathrm{k}\right)\frac{5}{7}\boxed{}\frac{15}{21}\end{array}$

Ans-

$\begin{array}{l}\left(\mathrm{a}\right)\frac{1}{2}\boxed{>}\frac{1}{5}\left(\mathrm{b}\right)\frac{2}{4}\boxed{=}\frac{3}{6}\left(\mathrm{c}\right)\frac{3}{5}\boxed{<}\frac{2}{3}\\ \left(\mathrm{d}\right)\frac{3}{4}\boxed{>}\frac{2}{8}\left(\mathrm{e}\right)\frac{3}{5}\boxed{<}\frac{6}{5}\left(\mathrm{f}\right)\frac{7}{9}\boxed{>}\frac{3}{9}\\ \left(\mathrm{g}\right)\frac{1}{4}\boxed{=}\frac{2}{8}\left(\mathrm{h}\right)\frac{6}{10}\boxed{<}\frac{4}{5}\left(\mathrm{i}\right)\frac{3}{4}\boxed{<}\frac{7}{8}\\ \left(\mathrm{j}\right)\frac{6}{10}\boxed{<}\frac{4}{5}\left(\mathrm{k}\right)\frac{5}{7}\boxed{=}\frac{15}{21}\end{array}$

Q.34 The following fractions represent just three different numbers. Separate them into three groups of equivalent fractions, by changing each one to its simplest form.

$\begin{array}{l}\left(\mathrm{a}\right)\frac{2}{12}\left(\mathrm{b}\right)\frac{3}{15}\left(\mathrm{c}\right)\frac{8}{50}\\ \left(\mathrm{d}\right)\frac{16}{100}\left(\mathrm{e}\right)\frac{10}{60}\left(\mathrm{f}\right)\frac{15}{75}\\ \left(\mathrm{g}\right)\frac{12}{60}\left(\mathrm{h}\right)\frac{16}{96}\left(\mathrm{i}\right)\frac{12}{75}\\ \left(\mathrm{j}\right)\frac{12}{72}\left(\mathrm{k}\right)\frac{3}{18}\left(\mathrm{l}\right)\frac{4}{25}\end{array}$

Ans-

$\begin{array}{l}\left(\mathrm{a}\right)\frac{2}{12}=\frac{1\times 2}{6\times 2}=\frac{1}{6}\left(\mathrm{b}\right)\frac{3}{15}=\frac{1\times 3}{5\times 3}=\frac{1}{5}\left(\mathrm{c}\right)\frac{8}{50}=\frac{4\times 2}{25\times 2}=\frac{4}{25}\\ \left(\mathrm{d}\right)\frac{16}{100}=\frac{4\times 4}{25\times 4}=\frac{4}{25}\left(\mathrm{e}\right)\frac{10}{60}=\frac{1\times 10}{6\times 10}=\frac{1}{6}\left(\mathrm{f}\right)\frac{15}{75}=\frac{1\times 15}{5\times 15}=\frac{1}{5}\\ \left(\mathrm{g}\right)\frac{12}{60}=\frac{1\times 12}{5\times 12}=\frac{1}{5}\left(\mathrm{h}\right)\frac{16}{96}=\frac{1\times 16}{6\times 16}=\frac{1}{6}\left(\mathrm{i}\right)\frac{12}{75}=\frac{3\times 4}{3\times 25}=\frac{4}{25}\\ \left(\mathrm{j}\right)\frac{12}{72}=\frac{1\times 12}{6\times 12}=\frac{1}{6}\left(\mathrm{k}\right)\frac{3}{18}=\frac{1\times 3}{6\times 3}=\frac{1}{6}\left(\mathrm{l}\right)\frac{4}{25}=\frac{1\times 4}{1\times 25}=\frac{4}{25}\end{array}$

The three different groups representing same fraction are
Fractions representing

$\frac{1}{6}$

:

$\frac{2}{12},\frac{10}{60},\frac{16}{96},\frac{12}{72},\frac{3}{18}$

Fractions representing

$\frac{1}{5}$

:

$\frac{3}{15},\frac{15}{75},\frac{12}{60}$

Fractions representing

$\frac{4}{25}$

:

$\frac{8}{50},\frac{16}{100},\frac{12}{75},\frac{4}{25}$

Q.35 Find answers to the following. Write and indicate how you solved them.

$\begin{array}{l}\left(\mathrm{a}\right)\mathrm{Is}\frac{5}{9}\mathrm{equal}\mathrm{to}\frac{4}{5}?\end{array}$ $$\begin{gathered} \begin{array}{l} \\ \left(\mathrm{b}\right)\mathrm{Is}\frac{9}{16}\mathrm{equal}\mathrm{to}\frac{5}{9}?\end{array} \end{gathered}$$ $\begin{array}{l}\left(\mathrm{c}\right)\mathrm{Is}\frac{4}{5}\mathrm{equal}\mathrm{to}\frac{16}{20}?\end{array}$ $$\begin{gathered} \begin{array}{l} \\ \left(\mathrm{d}\right)\mathrm{Is}\frac{1}{15}\mathrm{equal}\mathrm{to}\frac{4}{30}?\end{array} \end{gathered}$$

Ans-

(a) Let us convert both the fractions into like fractions.

$\begin{array}{l}\frac{5}{9}\text{and}\frac{4}{5}\\ \frac{5\times 5}{9\times 5}\text{and}\frac{4\times 9}{5\times 9}\\ \frac{25}{45}\text{and}\frac{36}{45}\\ \text{Since, 25 < 36}\text{. So,}\frac{5}{9}<\frac{4}{5}.\end{array}$

The fractions are not equal.
(b)
Let us convert both the fractions into like fractions.

$\begin{array}{l}\frac{9}{16}\text{and}\frac{5}{9}\\ \frac{9\times 9}{16\times 9}\text{and}\frac{5\times 16}{16\times 9}\\ \frac{81}{144}\text{and}\frac{80}{144}\\ \text{Since, 81>80}\text{. So,}\frac{9}{16}>\frac{5}{9}.\end{array}$

The fractions are not equal.
(c)
Let us convert both the fractions into like fractions.

\begin{array}{l}\frac{16}{20}\text{and}\frac{4}{5}\\ \frac{16}{20}\text{and}\frac{4\times 4}{5\times 4}\\ \frac{16}{20}\text{and}\frac{16}{20}\\ \text{Since, 16 = 16}\text{. So,}\frac{16}{20}=\frac{4}{5}.\end{array}

The fractions are equal.
(d)
Let us convert both the fractions into like fractions.

$\begin{array}{l}\frac{1}{15}\text{and}\frac{4}{30}\\ \frac{1\times 2}{15\times 2}\text{and}\frac{4}{30}\\ \frac{2}{30}\text{and}\frac{4}{30}\\ \text{Since, 2 < 4}\text{. So,}\frac{1}{15}<\frac{4}{30}.\end{array}$

Q.36  Ila read 25 pages of a book containing 100 pages. Lalita read

$\frac{2}{5}$

of the same book. Who read less?

Ans-

Pages read by Ila = 25

Fraction of pages read by Ila =

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

Fraction of pages read by Lalita =

$\frac{2}{5}$

Comparing both the fractions :

$\begin{array}{l}\frac{1}{4}\text{and}\frac{2}{5}\\ \frac{1\times 5}{4\times 5}\text{and}\frac{2\times 4}{4\times 5}\\ \frac{5}{20}\text{and}\frac{8}{20}\\ \text{Since, 5 < 8}\text{.}\\ \end{array}$

So, Ila read less.

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?

Ans-

Rafiq exercised for

$\frac{3}{6}$

of an hour
Rohit exercised for

$\frac{3}{4}$

of an hour
Comparing both the fractions :
Since, numerator of both the fractions are same and denominators 4 < 6.
So, Rohit exercised longer.

In a class A of 25 students, 20 passed in first class. In another class B of 30 students, 24 passes in first class. In which class was a greater fraction of students getting first class?

Ans-

Fraction of students of class A who passed in first class =

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

Fraction of students of class B who passed in first class =

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

So, equal fraction of students got first class.

Write these fractions appropriately as additions or subtractions :

Answer

Solve :

$\begin{array}{l}\left(\text{a}\right)\frac{\text{1}}{\text{18}}\text{+}\frac{\text{1}}{\text{18}}\\ \left(\text{b}\right)\frac{\text{8}}{\text{15}}\text{+}\frac{\text{3}}{\text{15}}\\ \left(\mathrm{c}\right)\frac{7}{5}-\frac{7}{5}\\ \left(\mathrm{d}\right)\frac{1}{22}+\frac{21}{22}\\ \left(\mathrm{e}\right)\frac{12}{15}-\frac{7}{15}\\ \left(\mathrm{f}\right)\frac{5}{8}+\frac{3}{8}\\ \left(\mathrm{g}\right)1-\frac{2}{3}\left(1=\frac{3}{3}\right)\\ \left(\mathrm{h}\right)\frac{1}{4}+\frac{0}{4}\\ \left(\mathrm{i}\right)3-\frac{12}{5}\end{array}$

Ans- 

$\begin{array}{l}\text{(a)}\frac{1}{18}+\frac{1}{18}\\ =\frac{1+1}{18}\\ =\frac{2}{18}\end{array}$ $\begin{array}{l}\text{(b)}\frac{8}{15}+\frac{3}{15}\\ =\frac{8+3}{15}\\ =\frac{11}{15}\end{array}$ $\begin{array}{l}\end{array}$

$\begin{array}{l}\text{(c)}\frac{7}{7}-\frac{5}{7}\\ =\frac{7-5}{7}\\ =\frac{2}{7}\end{array}$ $\begin{array}{l}\end{array}$ $\begin{array}{l}\text{(d)}\frac{1}{22}+\frac{21}{22}\\ =\frac{1+21}{22}\\ =\frac{22}{22}=1\end{array}$ $\begin{array}{l}\end{array}$ $\begin{array}{l}\text{(e)}\frac{12}{15}-\frac{7}{15}\\ =\frac{12-7}{15}\\ =\frac{5}{15}=\frac{1}{3}\end{array}$

$\begin{array}{l}\begin{array}{l}\text{(f)}\frac{5}{8}+\frac{3}{8}\\ =\frac{8}{8}=1\end{array}\\ \text{}\left(\text{g}\right)1–\frac{2}{3}\text{}\\ =\frac{3}{3}–\frac{1}{3}\text{}\\ =\frac{2}{3}\end{array}$ $\begin{array}{l}\end{array}$ $\begin{array}{l}\text{(h)}\frac{1}{4}+\frac{0}{4}\\ =\frac{1}{4}+0\\ =\frac{1}{4}\end{array}$ $\begin{array}{l}\end{array}$ $\begin{array}{l}(\text{i) 3}-\frac{12}{5}\\ =\frac{3\times 5}{5}-\frac{12}{5}\\ =\frac{15}{5}-\frac{12}{5}\\ =\frac{3}{5}\end{array}$

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?

Ans-

$\begin{array}{l}\text{Space painted by shubham =}\frac{2}{3}\text{of the room}\\ \text{Space painted by Madhvi =}\frac{1}{3}\text{of the room}\\ \text{Hence, together they painted =}\frac{2}{3}+\frac{1}{3}=1\\ \mathrm{i}.\mathrm{e}.\text{the complete wall.}\end{array}$

Fill in the missing fractions :

$\begin{array}{l}\left(\text{a}\right)\frac{\text{7}}{\text{10}}-\boxed{}\text{\hspace{0.33em}=\hspace{0.33em}}\frac{\text{3}}{\text{10}}\\ \left(\text{b}\right)\boxed{}-\frac{\text{3}}{\text{21}}\text{=}\frac{\text{5}}{\text{21}}\\ \left(\text{c}\right)\boxed{}-\frac{\text{3}}{\text{6}}\text{\hspace{0.33em}=\hspace{0.33em}}\frac{\text{3}}{\text{6}}\\ \left(\text{d}\right)\boxed{}\text{\hspace{0.33em}+\hspace{0.33em}}\frac{\text{5}}{\text{27}}\text{\hspace{0.33em}=\hspace{0.33em}}\frac{\text{12}}{\text{27}}\end{array}$

Ans-

$\begin{array}{l}(\text{a)}\frac{7}{10}-\boxed{}=\frac{3}{10}\\ \Rightarrow \boxed{}=\frac{7}{10}-\frac{3}{10}\\ \Rightarrow \boxed{}=\frac{4}{10}\\ (\text{b)}\boxed{}-\frac{3}{21}=\frac{5}{21}\\ \Rightarrow \boxed{}=\frac{3}{21}+\frac{5}{21}\\ \Rightarrow \boxed{}=\frac{8}{21}\\ \text{(c)}\boxed{}-\frac{3}{6}=\frac{3}{6}\\ \Rightarrow \boxed{}=\frac{3}{6}+\frac{3}{6}\\ \Rightarrow \boxed{}=\frac{6}{6}=1\\ \text{(d)}\boxed{}+\frac{5}{27}=\frac{12}{27}\\ \Rightarrow \boxed{}=\frac{12}{27}-\frac{5}{27}\\ \Rightarrow \boxed{}=\frac{12-5}{27}=\frac{7}{27}\end{array}$

Javed was given

$\frac{5}{7}$

of a basket of oranges. What fraction of oranges was left in the basket?

Ans-

Fractions given to Javed =

$\frac{5}{7}$

Fractions left in basket

$$\begin{gathered} =1-\frac{5}{7} \\ =\frac{7}{7}-\frac{5}{7} \\ =\frac{2}{7} \end{gathered}$$