NCERT Solutions for Class 7 Maths Exercise 2.3

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NCERT solutions for Maths Fractions and Decimals Download as PDF

NCERT Solutions for Class 7 Maths Exercise 2.3

NCERT Solutions for Class 7 Maths Fractions and Decimals

Class –VII Mathematics (Ex. 2.3)
Question 1.Find:

(i) {tex}\frac{1}{4}{/tex} of

(a) {tex}\frac{1}{4}{/tex}

(b) {tex}\frac{3}{5}{/tex}

(c) {tex}\frac{4}{3}{/tex}

(ii) {tex}\frac{1}{7}{/tex} of

(a) {tex}\frac{2}{9}{/tex}

(b) {tex}\frac{6}{5}{/tex}

(c) {tex}\frac{3}{{10}}{/tex}

Answer:

(i)

(a) {tex}\frac{1}{4}{/tex} of {tex}\frac{1}{4}{/tex} = {tex}\frac{1}{4} \times \frac{1}{4} = \frac{{1 \times 1}}{{4 \times 4}} = \frac{1}{{16}}{/tex}

(b) {tex}\frac{1}{4}{/tex} of {tex}\frac{3}{5}{/tex} = {tex}\frac{1}{4} \times \frac{3}{4} = \frac{{1 \times 3}}{{4 \times 4}} = \frac{3}{{16}}{/tex}

(c) {tex}\frac{1}{4}{/tex} of {tex}\frac{4}{3}{/tex} = {tex}\frac{1}{4} \times \frac{4}{3} = \frac{{1 \times 4}}{{4 \times 3}} = \frac{1}{3}{/tex}

(ii)

(a) {tex}\frac{1}{7}{/tex} of {tex}\frac{2}{9}{/tex} = {tex}\frac{1}{7} \times \frac{2}{9} = \frac{{1 \times 2}}{{7 \times 9}} = \frac{2}{{63}}{/tex}

(b) {tex}\frac{1}{7}{/tex} of {tex}\frac{2}{9}{/tex} = {tex}\frac{1}{7} \times \frac{6}{5} = \frac{{1 \times 6}}{{7 \times 5}} = \frac{6}{{35}}{/tex}

(c) {tex}\frac{1}{7}{/tex} of {tex}\frac{2}{9}{/tex} = {tex}\frac{1}{7} \times \frac{3}{{10}} = \frac{{1 \times 3}}{{7 \times 10}} = \frac{3}{{70}}{/tex}


NCERT Solutions for Class 7 Maths Exercise 2.3

Question 2.Multiply and reduce to lowest form (if possible):

(i) {tex}\frac{2}{3} \times 2\frac{2}{3}{/tex}

(ii) {tex}\frac{2}{7} \times \frac{7}{9}{/tex}

(iii) {tex}\frac{3}{8} \times \frac{6}{4}{/tex}

(iv) {tex}\frac{9}{5} \times \frac{3}{5}{/tex}

(v) {tex}\frac{1}{3} \times \frac{{15}}{8}{/tex}

(vi) {tex}\frac{{11}}{2} \times \frac{3}{{10}}{/tex}

(vii) {tex}\frac{4}{5} \times \frac{{12}}{7}{/tex}

Answer:

(i) {tex}\frac{2}{3} \times 2\frac{2}{3} = \frac{2}{3} \times \frac{8}{3} = \frac{{2 \times 8}}{{3 \times 3}} = \frac{{16}}{9} = 1\frac{7}{9}{/tex}

(ii) {tex}\frac{2}{7} \times \frac{7}{9} = \frac{{2 \times 7}}{{7 \times 9}} = \frac{2}{9}{/tex}

(iii) {tex}\frac{3}{8} \times \frac{6}{4} = \frac{{3 \times 6}}{{8 \times 4}} = \frac{{3 \times 3}}{{8 \times 2}} = \frac{9}{{16}}{/tex}

(iv) {tex}\frac{9}{5} \times \frac{3}{5} = \frac{{9 \times 3}}{{5 \times 5}} = \frac{{27}}{{25}} = 1\frac{2}{{25}}{/tex}

(v) {tex}\frac{1}{3} \times \frac{{15}}{8} = \frac{{1 \times 15}}{{3 \times 8}} = \frac{{1 \times 5}}{{1 \times 8}} = \frac{5}{8}{/tex}

(vi) {tex}\frac{{11}}{2} \times \frac{3}{{10}} = \frac{{11 \times 3}}{{2 \times 10}} = \frac{{33}}{{20}} = 1\frac{3}{{20}}{/tex}

(vii) {tex}\frac{4}{5} \times \frac{{12}}{7} = \frac{{4 \times 12}}{{5 \times 7}} = \frac{{48}}{{35}} = 1\frac{{13}}{{35}}{/tex}


NCERT Solutions for Class 7 Maths Exercise 2.3

Question 3.Multiply the following fractions:

(i) {tex}\frac{2}{5} \times 5\frac{1}{4}{/tex}

(ii) {tex}6\frac{2}{5} \times \frac{7}{9}{/tex}

(iii) {tex}\frac{3}{2} \times 5\frac{1}{3}{/tex}

(iv) {tex}\frac{5}{6} \times 2\frac{3}{7}{/tex}

(v) {tex}3\frac{2}{5} \times \frac{4}{7}{/tex}

(vi) {tex}2\frac{3}{5} \times 3{/tex}

(vii) {tex}3\frac{4}{7} \times \frac{3}{5}{/tex}

Answer:

(i) {tex}\frac{2}{5} \times 5\frac{1}{4} = \frac{2}{5} \times \frac{{21}}{4} = \frac{{2 \times 21}}{{5 \times 4}} = \frac{{1 \times 21}}{{5 \times 2}} = \frac{{21}}{{10}} = 2\frac{1}{{10}}{/tex}

(ii) {tex}6\frac{2}{5} \times \frac{7}{9} = \frac{{32}}{5} \times \frac{7}{9} = \frac{{32 \times 7}}{{5 \times 9}} = \frac{{224}}{{45}} = 4\frac{{44}}{{45}}{/tex}

(iii) {tex}\frac{3}{2} \times 5\frac{1}{3} = \frac{3}{2} \times \frac{{16}}{3} = \frac{{48}}{6} = 8{/tex}

(iv) {tex}\frac{5}{6} \times 2\frac{3}{7} = \frac{5}{6} \times \frac{{17}}{7} = \frac{{85}}{{42}} = 2\frac{1}{{42}}{/tex}

(v) {tex}3\frac{2}{5} \times \frac{4}{7} = \frac{{17}}{7} \times \frac{4}{7} = \frac{{68}}{{35}} = 1\frac{{33}}{{35}}{/tex}

(vi) {tex}2\frac{3}{5} \times 3 = \frac{{13}}{5} \times \frac{3}{1} = \frac{{13 \times 3}}{{5 \times 1}} = \frac{{39}}{5} = 7\frac{4}{5}{/tex}

(vii) {tex}3\frac{4}{7} \times \frac{3}{5} = \frac{{25}}{7} \times \frac{3}{5} = \frac{{5 \times 3}}{{7 \times 1}} = \frac{{15}}{7} = 2\frac{1}{7}{/tex}


NCERT Solutions for Class 7 Maths Exercise 2.3

Question 4.Which is greater:

(i){tex}\frac{2}{7}{/tex} of {tex}\frac{3}{4}{/tex} or {tex}\frac{3}{5}{/tex} of {tex}\frac{5}{8}{/tex}

(ii){tex}\frac{1}{2}{/tex} of {tex}\frac{6}{7}{/tex} or {tex}\frac{2}{3}{/tex} of {tex}\frac{3}{7}{/tex}

Answer:

(i) {tex}\frac{2}{7}{/tex} of {tex}\frac{3}{4}{/tex} or {tex}\frac{3}{5}{/tex} of {tex}\frac{5}{8}{/tex} {tex} \Rightarrow {/tex} {tex}\frac{2}{7}{/tex} x {tex}\frac{3}{4}{/tex} or {tex}\frac{3}{5}{/tex} x {tex}\frac{5}{8}{/tex}

{tex} \Rightarrow {/tex} {tex}\frac{3}{{14}}{/tex} or {tex}\frac{3}{8}{/tex} {tex} \Rightarrow {/tex} {tex}\frac{3}{{14}} < \frac{3}{8}{/tex}

Thus, {tex}\frac{3}{5}{/tex} of {tex}\frac{5}{8}{/tex} is greater.

(ii) {tex}\frac{1}{2}{/tex} of {tex}\frac{6}{7}{/tex} or {tex}\frac{2}{3}{/tex} of {tex}\frac{3}{7}{/tex} {tex} \Rightarrow {/tex} {tex}\frac{1}{2}{/tex} x {tex}\frac{6}{7}{/tex} or {tex}\frac{2}{3}{/tex} x {tex}\frac{3}{7}{/tex}

{tex} \Rightarrow {/tex} {tex}\frac{3}{7}{/tex} or {tex}\frac{2}{7}{/tex} {tex} \Rightarrow {/tex} {tex}\frac{3}{7}{/tex}>{tex}\frac{2}{7}{/tex}

Thus, {tex}\frac{1}{2}{/tex} of {tex}\frac{6}{7}{/tex} is greater.


NCERT Solutions for Class 7 Maths Exercise 2.3

Question 5.Saili plants 4 saplings in a row in her garden. The distance between two adjacent saplings is {tex}\frac{3}{4}{/tex} m. Find the distance between the first and the last sapling.

Answer:

The distance between two adjacent saplings = {tex}\frac{3}{4}{/tex} m

Saili planted 4 saplings in a row, then number of gap in saplings

Therefore, the distance between the first and the last saplings = {tex}3 \times \frac{3}{4}{/tex} = {tex}\frac{9}{4}{/tex} m = {tex}2\frac{1}{4}{/tex} m

Thus the distance between the first and the last saplings is {tex}2\frac{1}{4}{/tex} m.


NCERT Solutions for Class 7 Maths Exercise 2.3

Question 6.Lipika reads a book for {tex}1\frac{3}{4}{/tex} hours everyday. She reads the entire book in 6 days. How many hours in all were required by her to read the book?

Answer:

Time taken by Lipika to read a book = {tex}1\frac{3}{4}{/tex} hours.

She reads entire book in 6 days.

Now, total hours taken by her to read the entire book = {tex}1\frac{3}{4} \times 6{/tex} = {tex}\frac{7}{4} \times 6 = \frac{{21}}{2} = 10\frac{1}{2}{/tex} hours

Thus {tex}10{/tex} hours were required by her to read the book.


NCERT Solutions for Class 7 Maths Exercise 2.3

Question 7.A car runs 16 km using 1 litre of petrol. How much distance will it cover using {tex}2\frac{3}{4}{/tex} litres of petrol?

Answer:

In 1 litre of pertrol, car covers the distance = 16 km

In {tex}2\frac{3}{4}{/tex} litres of petrol, car covers the distance = {tex}2\frac{3}{4}{/tex} of 16 km = {tex}\frac{{11}}{4} \times 16{/tex} = 44 km

Thus, car will cover 44 km distance.


NCERT Solutions for Class 7 Maths Exercise 2.3

Question 8.(a) (i) Provide the number in the box {tex}\boxed{{\text{ }}},{/tex} such that {tex}\frac{2}{3} \times \boxed{{\text{ }}} = \frac{{10}}{{30}}.{/tex}

(ii) The simplest form of the number obtained in {tex}\boxed{{\text{ }}}{/tex} is __________.

(b) (i) Provide the number in the box {tex}\boxed{{\text{ }}},{/tex} such that {tex}\frac{3}{5} \times \boxed{{\text{ }}} = \frac{{24}}{{75}}.{/tex}

(ii) The simplest form of the number obtained in {tex}\boxed{{\text{ }}}{/tex} is __________.

Answer:

(a)

(i) {tex}\frac{2}{3} \times \boxed{\frac{5}{{10}}} = \frac{{10}}{{30}}{/tex}

(ii) The simplest form of {tex}\frac{5}{{10}}{/tex} is {tex}\frac{1}{2}.{/tex}

(b)

(i) {tex}\frac{3}{5} \times \boxed{\frac{8}{{15}}} = \frac{{24}}{{75}}{/tex}

(ii) The simplest form of {tex}\frac{8}{{15}}{/tex} is {tex}\frac{8}{{15}}.{/tex}

NCERT Solutions for Class 7 Maths Exercise 2.3

NCERT Solutions Class 7 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 7 Maths includes text book solutions from Class 7 Maths Book . NCERT Solutions for CBSE Class 7 Maths have total 15 chapters. 7 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 7 solutions PDF and Maths ncert class 7 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide.

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