Fractions and Decimals Ex-2.3

NCERT solutions for Maths Fractions and Decimals 

NCERT Solutions for Class 7 Maths Fractions and Decimals

Class –VII Mathematics (Ex. 2.3)

Question 1.Find:

(i) $\frac{1}{4}$ of

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

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

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

(ii) $\frac{1}{7}$ of

(a) $\frac{2}{9}$

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

(c) $\frac{3}{{10}}$

Answer:

(i)

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

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

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

(ii)

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

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

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

NCERT Solutions for Class 7 Maths Exercise 2.3

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

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

(ii) $\frac{2}{7} \times \frac{7}{9}$

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

(iv) $\frac{9}{5} \times \frac{3}{5}$

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

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

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

Answer:

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

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

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

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

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

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

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

NCERT Solutions for Class 7 Maths Exercise 2.3

Question 3.Multiply the following fractions:

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

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

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

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

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

(vi) $2\frac{3}{5} \times 3$

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

Answer:

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

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

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

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

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

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

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

NCERT Solutions for Class 7 Maths Exercise 2.3

Question 4.Which is greater:

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

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

Answer:

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

$\Rightarrow$ $\frac{3}{{14}}$ or $\frac{3}{8}$ $\Rightarrow$ $\frac{3}{{14}} < \frac{3}{8}$

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

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

$\Rightarrow$ $\frac{3}{7}$ or $\frac{2}{7}$ $\Rightarrow$ $\frac{3}{7}$>$\frac{2}{7}$

Thus, $\frac{1}{2}$ of $\frac{6}{7}$ 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 $\frac{3}{4}$ m. Find the distance between the first and the last sapling.

Answer:

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

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

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

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

NCERT Solutions for Class 7 Maths Exercise 2.3

Question 6.Lipika reads a book for $1\frac{3}{4}$ 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 = $1\frac{3}{4}$ hours.

She reads entire book in 6 days.

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

Thus $10$ 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 $2\frac{3}{4}$ litres of petrol?

Answer:

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

In $2\frac{3}{4}$ litres of petrol, car covers the distance = $2\frac{3}{4}$ of 16 km = $\frac{{11}}{4} \times 16$ = 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 $\boxed{{\text{ }}},$ such that $\frac{2}{3} \times \boxed{{\text{ }}} = \frac{{10}}{{30}}.$

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

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

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

Answer:

(a)

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

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

(b)

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

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