NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals (EX 2.3) Exercise 2.3

Q.1

\begin{array}{l}Find:\\ (i)\frac{1}{4}of\left(a\right)\frac{1}{4}\left(b\right)\frac{3}{5}\left(c\right)\frac{4}{3}\\ (ii)\frac{1}{7}of\left(a\right)\frac{2}{9}\left(b\right)\text{}\frac{6}{5}\left(c\right)\text{}\frac{3}{10}\end{array}

Ans.

\begin{array}{l}\left(i\right)\\ \left(a\right)\frac{1}{4}\text{of}\frac{1}{4}=\frac{1}{4}\times \frac{1}{4}=\boxed{\frac{1}{16}}\\ \left(b\right)\frac{1}{4}\text{of}\frac{3}{5}=\frac{1}{4}\times \frac{3}{5}=\boxed{\frac{3}{20}}\\ \left(c\right)\frac{1}{4}\text{of}\frac{4}{3}=\frac{1}{\cancel{4}}\times \frac{\cancel{4}}{3}=\boxed{\frac{1}{3}}\\ (ii)\\ (a)\frac{1}{7}\text{of}\frac{2}{9}=\frac{1}{7}\times \frac{2}{9}=\boxed{\frac{2}{63}}\\ (b)\frac{1}{7}\text{of}\frac{6}{5}=\frac{1}{7}\times \frac{6}{5}=\boxed{\frac{6}{35}}\\ (c)\frac{1}{7}\text{of}\frac{3}{10}=\frac{1}{7}\times \frac{3}{10}=\boxed{\frac{3}{70}}\end{array}

Q.2

$\begin{array}{l}\mathrm{Multiply}\mathrm{and}\mathrm{reduce}\mathrm{to}\mathrm{lowest}\mathrm{form}(\mathrm{if}\mathrm{possible}).\\ \left(\mathrm{i}\right)\frac{2}{3}\times 2\frac{2}{3}\left(\mathrm{ii}\right)\frac{2}{7}\times \frac{7}{9}\left(\mathrm{iii}\right)\frac{3}{8}\times \frac{6}{4}\\ \left(\mathrm{iv}\right)\frac{9}{5}\times \frac{3}{5}\left(\mathrm{v}\right)\frac{1}{3}\times \frac{15}{8}\left(\mathrm{vi}\right)\frac{11}{2}\times \frac{3}{10}\\ \left(\mathrm{vii}\right)\frac{4}{5}\times \frac{12}{7}\end{array}$

Ans.

$\begin{array}{l}\left(\mathrm{i}\right)\frac{2}{3}\times 2\frac{2}{3}=\frac{2}{3}\times \frac{8}{3}=\boxed{\frac{16}{9}}\\ \left(\mathrm{ii}\right)\frac{2}{7}\times \frac{7}{9}=\frac{2}{\cancel{7}}\times \frac{\cancel{7}}{9}=\boxed{\frac{2}{9}}\\ \left(\mathrm{iii}\right)\frac{3}{8}\times \frac{6}{4}=\frac{3}{\cancel{2}\times 4}\times \frac{\cancel{2}\times 3}{4}=\boxed{\frac{9}{16}}\\ \left(\mathrm{iv}\right)\frac{9}{5}\times \frac{3}{5}=\boxed{\frac{27}{25}}\\ \left(\mathrm{v}\right)\frac{1}{3}\times \frac{15}{8}=\frac{1}{\cancel{3}}\times \frac{\cancel{3}\times 5}{8}=\boxed{\frac{5}{8}}\\ \left(\mathrm{vi}\right)\frac{11}{2}\times \frac{3}{10}=\boxed{\frac{33}{20}}\\ \left(\mathrm{vii}\right)\frac{4}{5}\times \frac{12}{7}=\boxed{\frac{48}{35}}\end{array}$

Q.3

$\begin{array}{l}\mathrm{For}\mathrm{the}\mathrm{fractions}\mathrm{given}\mathrm{below}:\\ \left(\mathrm{a}\right)\mathrm{Multiply}\mathrm{and}\mathrm{reduce}\mathrm{the}\mathrm{product}\mathrm{to}\mathrm{lowest}\\ \mathrm{form}\left(\mathrm{if}\mathrm{possible}\right)\\ \left(\mathrm{b}\right)\mathrm{Tell}\mathrm{whether}\mathrm{the}\mathrm{fraction}\mathrm{obtained}\mathrm{is}\mathrm{proper}\\ \mathrm{or}\mathrm{improper}.\\ \left(\mathrm{c}\right)\mathrm{If}\mathrm{the}\mathrm{fraction}\mathrm{obtained}\mathrm{is}\mathrm{improper}\mathrm{then}\\ \mathrm{convert}\mathrm{it}\mathrm{into}\mathrm{a}\mathrm{mixed}\mathrm{fraction}.\\ \text{(i)}\frac{2}{5}\times 5\frac{1}{4}\\ \text{(ii)}6\frac{2}{5}\times \frac{7}{9}\\ \text{(iii)}\frac{3}{2}\times 5\frac{1}{3}\\ \text{(iv)}\frac{5}{6}\times 2\frac{3}{7}\\ \left(\mathrm{v}\right)3\frac{2}{5}\times \frac{4}{7}\\ \text{(vi)}2\frac{3}{5}\times 3\\ \text{(vii)}3\frac{4}{7}\times \frac{3}{5}\end{array}$

Ans.

$\begin{array}{l}\left(\text{i}\right)\\ \left(\text{a}\right)\frac{2}{5}\times 5\frac{1}{4}=\frac{2}{5}\times \frac{21}{4}=\frac{\cancel{2}}{5}\times \frac{21}{\cancel{2}\times 2}=\boxed{\frac{21}{10}}\\ \left(\text{b}\right)\text{It is an improper fraction}.\\ \left(\text{c}\right)\frac{21}{10}=\boxed{2\frac{1}{10}}\\ \left(\mathrm{ii}\right)\\ \left(\mathrm{a}\right)6\frac{2}{5}\times \frac{7}{9}=\frac{32}{5}\times \frac{7}{9}=\boxed{\frac{224}{45}}\\ \left(\mathrm{b}\right)\text{It is an improper fraction}.\\ \left(\mathrm{c}\right)\frac{224}{45}=\boxed{4\frac{44}{45}}\\ \left(\mathrm{iii}\right)\\ \left(\mathrm{a}\right)\frac{3}{2}\times 5\frac{1}{3}=\frac{3}{2}\times \frac{16}{3}=\frac{\cancel{3}}{\cancel{2}}\times \frac{\cancel{2}\times 8}{\cancel{3}}=\frac{8}{1}=\boxed{8}\\ \left(\mathrm{b}\right)\text{\hspace{0.17em}It\hspace{0.17em}is whole number.}\\ \text{(iv)}\\ \text{(a)\hspace{0.17em}}\frac{5}{6}\times 2\frac{3}{7}\\ =\frac{5}{6}\times \frac{17}{7}\\ =\boxed{\frac{85}{42}}\\ \left(\mathrm{b}\right)\text{\hspace{0.17em}It is an improper fraction}.\\ \left(\mathrm{c}\right)\frac{85}{42}=\boxed{2\frac{1}{42}}\\ \left(\mathrm{v}\right)\\ \left(\mathrm{a}\right)\text{\hspace{0.17em}}3\frac{2}{5}\times \frac{4}{7}\\ =\frac{17}{5}\times \frac{4}{7}\\ =\frac{68}{35}\\ \left(\mathrm{b}\right)\text{\hspace{0.17em}It is an improper fraction}.\\ \left(\mathrm{c}\right)\frac{68}{35}=\boxed{1\frac{33}{35}}\\ \left(\mathrm{vi}\right)\\ \left(\mathrm{a}\right)2\frac{3}{5}\times 3\\ =\frac{13}{5}\times \frac{3}{1}\\ =\frac{39}{5}\\ \left(\text{b}\right)\text{It is an improper fraction}.\\ \left(\text{c}\right)\frac{39}{5}=\boxed{7\frac{4}{5}}\\ \left(\mathrm{vii}\right)\\ \left(\mathrm{a}\right)3\frac{4}{7}\times \frac{3}{5}\\ =\frac{25}{7}\times \frac{3}{5}\\ =\frac{5\times \cancel{5}}{7}\times \frac{3}{\cancel{5}}\\ =\frac{15}{7}\\ \text{(b)\hspace{0.17em}It is an improper fraction}.\\ \left(\mathrm{c}\right)\frac{15}{7}=\boxed{2\frac{1}{7}}\end{array}$

Q.4

$\begin{array}{l}\mathrm{Which}\mathrm{is}\mathrm{greater}:\\ \left(i\right)\frac{2}{7}of\frac{3}{4}\mathrm{or}\frac{3}{5}of\frac{5}{8}\\ \left(ii\right)\frac{1}{2}of\frac{6}{7}\mathrm{or}\frac{2}{3}of\frac{3}{7}\end{array}$

Ans.

\begin{array}{l}\left(\text{i}\right)\\ \frac{2}{7}\text{of}\frac{3}{4}\text{or}\frac{3}{5}\text{of}\frac{5}{8}\\ \frac{2}{7}\times \frac{3}{4}or\frac{3}{5}\times \frac{5}{8}\\ =\frac{\cancel{2}}{7}\times \frac{3}{\cancel{2}\times 2}\text{or}\frac{3}{\cancel{5}}\times \frac{\cancel{5}}{8}\\ =\frac{3}{14}\text{or}\frac{3}{8}\\ \text{Now},\text{the LCM of 14 and 8 is 56}.\text{So},\text{we get}\\ \frac{3}{14}=\frac{3\times 4}{14\times 4}=\frac{12}{56}\text{or}\frac{3}{8}=\frac{3\times 7}{8\times 7}=\frac{21}{56}\\ \text{Since},\text{21}>\text{12},\text{so}\frac{3}{8}>\frac{3}{14}\\ \text{Hence},\boxed{\frac{3}{5}\text{of}\frac{5}{8}>\frac{2}{7}\text{of}\frac{3}{4}}\\ \left(\text{ii}\right)\\ \frac{1}{2}\text{of}\frac{6}{7}or\text{}\frac{2}{3}\text{of}\frac{3}{7}\\ \frac{1}{2}\text{of}\frac{6}{7}or\frac{2}{3}\text{of}\frac{3}{7}\\ =\frac{1}{\cancel{2}}\times \frac{\cancel{2}\times 3}{7}\text{or}\frac{2}{\cancel{3}}\times \frac{\cancel{3}}{7}\\ =\frac{3}{7}\text{or}\frac{2}{7}\\ \text{Since},\text{3}>\text{2},\text{so},\frac{3}{7}>\frac{2}{7}\\ \text{Hence},\boxed{\frac{1}{2}\text{of}\frac{6}{7}>\frac{2}{3}\text{of}\frac{3}{7}}\end{array}

Q.5

$$\begin{gathered} \mathrm{Saili}\mathrm{plants}4\mathrm{saplings},\mathrm{in}\mathrm{a}\mathrm{row},\mathrm{in}\mathrm{her}\mathrm{garden}.\mathrm{The}\mathrm{distance}\mathrm{between}\mathrm{two}\mathrm{adjacent}\mathrm{}\mathrm{saplings}\mathrm{}\mathrm{is}\frac{3}{4}m. \\ \mathrm{Find}\mathrm{the}\mathrm{distance}\mathrm{between}\mathrm{the}\mathrm{first}\mathrm{and}\mathrm{the}\mathrm{last}\mathrm{sapling}. \end{gathered}$$

Ans.

\begin{array}{l}\text{Here},\text{the distance between the two saplings is given as}\frac{3}{4}\text{m}\\ \text{So},\text{the distance between first and the last sapling is}\\ \frac{3}{4}\text{m}\times \text{3=}\frac{9}{4}\text{m}\\ \text{=}\boxed{\text{2}\frac{1}{4}\text{m}}\end{array}

Q.6

$\begin{array}{l}\mathrm{Lipika}\mathrm{}\mathrm{reads}\mathrm{}\mathrm{a}\mathrm{}\mathrm{book}\mathrm{}\mathrm{for}\mathrm{\hspace{0.17em}}1\frac{3}{4}\mathrm{\hspace{0.17em}}\mathrm{hours}\mathrm{}\mathrm{every}\mathrm{}\mathrm{day}.\mathrm{}\mathrm{She}\\ \mathrm{reads}\mathrm{}\mathrm{the}\mathrm{}\mathrm{entire}\mathrm{}\mathrm{book}\mathrm{}\mathrm{in}\mathrm{}6\mathrm{}\mathrm{days}.\mathrm{}\mathrm{How}\mathrm{}\mathrm{many}\mathrm{}\mathrm{hours}\\ \mathrm{in}\mathrm{}\mathrm{all}\mathrm{}\mathrm{were}\mathrm{}\mathrm{required}\mathrm{}\mathrm{by}\mathrm{}\mathrm{her}\mathrm{}\mathrm{to}\mathrm{}\mathrm{read}\mathrm{}\mathrm{the}\mathrm{}\mathrm{book}?\end{array}$

Ans.

\begin{array}{l}\text{Lipika reads}1\frac{3}{4}=\frac{7}{4}\text{hours a day}.\\ \text{So},\text{Number of hours required by her to read the book}\\ \text{in 6 days is}\text{}\frac{7}{4}\text{hour}\times 6=\frac{7}{2\times \cancel{2}}\text{hour}\times \left(\cancel{2}\times 3\right)\\ =\frac{21}{2}\text{hour}\\ \text{=}\boxed{\text{10}\frac{1}{2}\text{hour}}\end{array}

Q.7

$\begin{array}{l}\mathrm{A}\mathrm{}\mathrm{car}\mathrm{}\mathrm{runs}\mathrm{}16\mathrm{}\mathrm{km}\mathrm{}\mathrm{using}\mathrm{}1\mathrm{}\mathrm{litre}\mathrm{}\mathrm{of}\mathrm{}\mathrm{petrol}.\mathrm{}\mathrm{How}\\ \mathrm{much}\mathrm{}\mathrm{distance}\mathrm{}\mathrm{will}\mathrm{}\mathrm{it}\mathrm{}\mathrm{cover}\mathrm{}\mathrm{using}\mathrm{\hspace{0.17em}}2\frac{3}{4}\mathrm{litres}\mathrm{}\mathrm{of}\mathrm{}\mathrm{petrol}?\end{array}$

Ans.

\begin{array}{c}\text{In 1 litre of petrol},\text{car runs 16 km}.\\ \text{So},\text{in}2\frac{3}{4}\text{litres of petrol},\text{distance covered by car is}\\ 2\frac{3}{4}\times 16\text{km}\\ =\frac{11}{\cancel{4}}\times \left(\cancel{4}\times 4\right)\text{km}\\ =\boxed{\text{44}\text{km}}\end{array}

Q.8

$\begin{array}{l}\left(\mathrm{a}\right)\\ \left(\mathrm{i}\right)\text{}\mathrm{Provide}\mathrm{the}\mathrm{number}\mathrm{in}\mathrm{the}\mathrm{box}\text{\hspace{0.17em}}\boxed{},\mathrm{such}\mathrm{that}\frac{2}{3}\times \boxed{}=\frac{10}{30}\\ \left(\mathrm{ii}\right)\mathrm{The}\mathrm{simplest}\mathrm{form}\mathrm{of}\mathrm{the}\mathrm{number}\mathrm{obtained}\mathrm{in}\boxed{}\mathrm{is}\_\_\_\_\\ \left(\mathrm{b}\right)\\ \left(\mathrm{i}\right)\mathrm{Provide}\mathrm{the}\mathrm{number}\mathrm{in}\mathrm{the}\mathrm{box}\boxed{},\mathrm{such}\mathrm{that}\frac{3}{5}\times \boxed{}=\frac{24}{75}\\ \left(\mathrm{ii}\right)\\ \mathrm{The}\mathrm{simplest}\mathrm{form}\mathrm{of}\mathrm{the}\mathrm{number}\mathrm{obtained}\mathrm{in}\boxed{}\mathrm{is}\_\_\_\_\end{array}$

Ans.

$\begin{array}{l}\left(\text{a}\right)\\ \left(\text{i}\right)\frac{\text{2}}{\text{3}}\times \boxed{}\text{=}\frac{\text{10}}{\text{30}}\\ =\frac{\text{2×5}}{\text{3×10}}=\frac{\text{2}}{\text{3}}\text{×}\frac{\text{5}}{\text{10}}\\ \text{So,}\frac{\text{2}}{\text{3}}\times \frac{\text{5}}{\text{10}}=\frac{\text{10}}{\text{30}}\\ \text{Therefore, the number in}\boxed{}\text{is}\frac{\text{5}}{\text{10}}\text{.}\\ \text{(ii)}\\ \text{The simplest form of}\frac{\text{5}}{\text{10}}\text{is}\frac{\text{5}}{\text{10}}=\frac{}{}=\boxed{\frac{\text{1}}{\text{2}}}\\ \text{(b)}\\ \left(\text{i}\right)\frac{\text{3}}{\text{5}}\times \boxed{}\text{=}\frac{\text{24}}{\text{75}}\\ =\frac{\text{3×8}}{\text{5×15}}=\frac{\text{3}}{\text{5}}\text{×}\frac{\text{8}}{\text{15}}\\ \text{So,}\frac{\text{3}}{\text{5}}\text{×}\frac{\text{8}}{\text{15}}=\frac{\text{24}}{\text{75}}\\ \text{Therefore, the number in}\boxed{}\text{is}\frac{\text{8}}{\text{15}}\text{.}\\ \text{(ii)}\\ \text{The simplest form of}\frac{\text{8}}{\text{15}}\text{is}\boxed{\frac{\text{8}}{\text{15}}}\end{array}$