Exercise 2.2 (Revised) - Chapter 2 - Fractions & Decimals - Ncert Solutions class 7 - Maths

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Chapter 2: Fractions & Decimals - NCERT Solutions for Class 7 Maths

Ex 2.2 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 $\frac{3}{4}=\frac{1}{4} \times \frac{3}{4}=\frac{1 \times 3}{4 \times 4}=\frac{3}{16}$
(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 $\frac{2}{9}=\frac{1}{7} \times \frac{3}{10}=\frac{1 \times 3}{7 \times 10}=\frac{3}{70}$

Ex 2.2 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) $\frac{4}{5} \times \frac{12}{7}=\frac{4 \times 12}{5 \times 7}=\frac{48}{35}=1 \frac{13}{35}$

Ex 2.2 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) $3 \frac{4}{7} \times \frac{3}{5}=\frac{25}{7} \times \frac{3}{5}=\frac{5 \times 3}{7 \times 1}=\frac{15}{7}=2 \frac{1}{7}$

Ex 2.2 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 $\frac{5}{8} \Rightarrow \frac{2}{7} \times \frac{3}{4}$ or $\frac{3}{5} \times \frac{5}{8}$
$\Rightarrow \frac{3}{14}$ 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 $\frac{3}{7} \Rightarrow \frac{1}{2} \times \frac{6}{7}$ or $\frac{2}{3} \times \frac{3}{7}$
$\Rightarrow \frac{3}{7}$ or $\frac{2}{7} \Rightarrow \frac{3}{7}>\frac{2}{7}$
Thus, $\frac{1}{2}$ of $\frac{6}{7}$ is greater.

Ex 2.2 Question 5.

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

Answer:

The distance between two adjacent saplings $=\frac{3}{4} \mathrm{~m}$
Saili planted 4 saplings in a row, then number of gap in saplings

Therefore, the distance between the first and the last saplings $=3 \times \frac{3}{4}=\frac{9}{4} \mathrm{~m}=2 \frac{1}{4} \mathrm{~m}$
Thus the distance between the first and the last saplings is $2 \frac{1}{4} \mathrm{~m}$.
Ex 2.2 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.

Ex 2.2 Question 7.

A car runs $16 \mathrm{~km}$ 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 $=16 \mathrm{~km}$
In $2 \frac{3}{4}$ litres of petrol, car covers the distance $=2 \frac{3}{4}$ of $16 \mathrm{~km}=\frac{11}{4} \times 16=44 \mathrm{~km}$
Thus, car will cover $44 \mathrm{~km}$ distance.

Ex 2.2 Question 8.

(a) (i) Provide the number in the box $\square$, such that $\frac{2}{3} \times \square=\frac{10}{30}$.
(ii) The simplest form of the number obtained in $\square$ is $\qquad$ .
(b) (i) Provide the number in the box $\square$, such that $\frac{3}{5} \times \square=\frac{24}{75}$.
(ii) The simplest form of the number obtained in $\square$ is $\qquad$ .

Answer:

(a) (i) $\frac{2}{3} \times \frac{5}{10}=\frac{10}{30}$
(ii) The simplest form of $\frac{5}{10}$ is $\frac{1}{2}$.
(b) (i) $\frac{3}{5} \times \frac{8}{15}=\frac{24}{75}$
(ii) The simplest form of $\frac{8}{15}$ is $\frac{8}{15}$.