# RD Sharma Solutions Class 7 Fractions Exercise 2.2

## RD Sharma Solutions Class 7 Chapter 2 Exercise 2.2

### RD Sharma Class 7 Solutions Chapter 2 Ex 2.2 PDF Free Download

#### Exercise 2.2

Q1. Multiply

$\frac{7}{11}\; by \; \frac{3}{5}$

$\frac{3}{5} \; by \; 25$

$3\frac{4}{15}$ by 24

$3\frac{1}{8} \; by \; 4\frac{10}{11}$

Solution:

We have, $\frac{7}{11}\; by \; \frac{3}{5}$

= $\frac{7}{11}\; \times \; \frac{3}{5} \\ = \frac{21}{55}$

(ii) We have, $\frac{3}{5} \; by \; 25$

= $\frac{3}{5} \; \times \; 25 \\ = 15$

(iii) We have, $3\frac{4}{15}$ by 24

= $3\frac{4}{15} \times 24 \\ = \frac{49}{15} \times 24 \\ = \frac{1176}{24} \\ = 78\frac{2}{5}$

(iv) We have, $3\frac{1}{8} \; by \; 4\frac{10}{11}$

= $3\frac{1}{8} \; by \; 4\frac{10}{11}\\ = \frac{25}{8} \times \frac{54}{11} \\ = \frac{25 \times 54}{88} \\ = 15\frac{15}{44}$

Q2.  Find the product:

$\frac{4}{7} \times \frac{14}{25} \\$

$7\frac{1}{2} \times 2\frac{4}{15}$

$3\frac{6}{7} \times 4\frac{2}{3}$

$6\frac{11}{14} \times 3\frac{1}{2}$

Solution:

We have, $\frac{4}{7} \times \frac{14}{25} \\ = \frac{4 \times 14}{7 \times 25} \\ = \frac{56}{175} \\ = \frac{8}{25}$

We have, $7\frac{1}{2} \times 2\frac{4}{15} \\ = \frac{15}{2} \times \frac{34}{15} \\ = \frac{15 \times 34}{2 \times 15} \\ = \frac{510}{30} \\ = 17$

We have, $3\frac{6}{7} \times 4\frac{2}{3} \\ = \frac{27}{7} \times \frac{14}{3} \\ = 3 \times \frac{14}{3} \\ = 14$

We have, $6\frac{11}{14} \times 3\frac{1}{2} \\ = \frac{95}{14} \times \frac{7}{2} \\ = \frac{95 \times 7}{28} \\ = \frac{665}{28} \\ = 23\frac{3}{4}$

Q3. Simplify:

$\frac{12}{25} \times \frac{15}{28} \times \frac{35}{36}$

$\frac{10}{27} \times \frac{39}{56} \times \frac{28}{65}$

$2\frac{2}{17} \times 7\frac{2}{9} \times 1\frac{33}{52}$

Solution:

We have, $\frac{12}{25} \times \frac{15}{28} \times \frac{35}{36} \\ = \frac{12 \times 15 \times 35}{25 \times 28 \times 36} \\ = \frac{6300}{25200} \\ = \frac{1}{4}$

$\frac{10}{27} \times \frac{39}{56} \times \frac{28}{65} \\ = \frac{10 \times 39 \times 28}{27 \times 56 \times 65} \\ = \frac{10920}{98280} \\ = \frac{1}{9}$

We have, $2\frac{2}{17} \times 7\frac{2}{9} \times 1\frac{33}{52} \\ = \frac{36}{17} \times \frac{65}{9} \times \frac{85}{52} \\ = \frac{36 \times 65 \times 85}{17 \times 9 \times 52} \\ = \frac{198900}{7956} \\ = 25$

Q4. Find:

$\frac{1}{2} of 4\frac{2}{9}$

$\frac{5}{8} \; of \; 9\frac{2}{3}$

$\frac{2}{3} \; of \frac{9}{16}$

Solution:

We have, $\frac{1}{2} of 4\frac{2}{9} \\ = \frac{1}{2} \times \frac{38}{9} \\ = \frac{38}{18}\\ = 2\frac{1}{9}$

$\frac{5}{8} of 9\frac{2}{3} \\ = \frac{5}{8} \times \frac{29}{3} \\ = \frac{5 \times 29}{8 \times 3} \\ = \frac{145}{24} \\ = 6\frac{1}{24}$

We have, $\frac{2}{3} \; of \frac{9}{16} \\ =\frac{2}{3} \times \frac{9}{16}\\=\frac{2 \times 9}{3 \times 16} \\ = \frac{18}{48} \\ = \frac{3}{8}$

Q5. Which is greater ? $\frac{1}{2} \; of \; \frac{6}{7}$ or $\frac{2}{3} \; of \; \frac{3}{7}$.

Solution:

Given, $\frac{1}{2} \; of \; \frac{6}{7}\; or \; \frac{2}{3} \; of \; \frac{3}{7} \\ = \frac{1}{2} \times \frac{6}{7} \; or \; \frac{2}{3} \times \frac{3}{7} \\ = \frac{1 \times 6}{2 \times 7} \times \frac{2 \times 3}{3 \times 7} \\ = \frac{6}{14} \; or \; \frac{6}{21}$

While comparing two fractions, when the numerators of both the fractions are same, then the denominator having higher value shows the fraction has lower value.

So, $\frac{6}{14}$ is greater.

Therefore, $\frac{1}{2} \; of \; \frac{6}{7}$ is greater.

Q6. Find,

$\frac{7}{11} \; of \; 330$

$\frac{5}{9} \; of \; 108 \; meters$

$\frac{3}{7} \; of \; 42 \; litres$

$\frac{1}{12}$ of an hour

$\frac{5}{6}$ of an year

$\frac{3}{20}$ of a Kg

$\frac{7}{20}$ of a litres

$\frac{5}{6}$ of a day

$\frac{2}{7}$ of a week

Solution:

We have, $\frac{7}{11} \; of \; 330 \\ = \frac{7}{11} \times 330 \\ = 7 \times 30 \\ = 210$

We have, $\frac{5}{9} \; of \; 108 \; meters \\ = \frac{5}{9} \times 108 \; meters \\ = 5 \times 12 \; meters \\ = 60 \; meters$

We have, $\frac{3}{7} \; of \; 42 \; litres \\ = \frac{3}{7} \times 42 \; litres \\ = 3 \times 6 \; litres \\ = 18 \; litres$

We have, $\frac{1}{12}$ of an hour

An hour = 60 minutes

Therefore, $\frac{1}{12} \times 6o \; minutes \\ = 5 \; minutes$

(v) We have, $\frac{5}{6}$ of an year

I Year = 12 months

Therefore, $\frac{5}{6} \times 12 \; months \\ = 5 \times 2 \; months \\ = 10 \; months$

(vi) We have, $\frac{3}{20}$

1 Kg = 1000 gms

Therefore, $\frac{3}{20} \times 1000 \; gms \\ = 3 \times 50 \; gms \\ = 150 \; gms$

(vii) We have,  $\frac{7}{20}$ of a litre

1 litre = 1000 ml

Therefore, $\frac{7}{20} \times 1000 \; ml \\ = 7 \times 50 \; ml \\ = 350 \; ml$

(viii) We have, $\frac{5}{6}$ of a day

I day = 24 hours

Therefore, $\frac{5}{6} \times 24 \; hours \\ = 5 \times 4 \; hours \\ = 20 \; hours$

(ix) We have, $\frac{2}{7}$ of a week

I week = 7 days

Therefore, $\frac{2}{7} \times 7 \; days \\ = 2 \; days$

Q7. Shikha plans 5 saplings in a row in her garden. The distance between two adjacent saplings is $\frac{3}{4}$ m. Find the distance between first and last sapling.

Solution:

There are 4 adjacent spacing for 5 saplings.

Given, the distance between two adjacent saplings is $\frac{3}{4}$ m.

4 adjacent spacing for 5 saplings = $\frac{3}{4} \times 4$ = 3 m

Therefore, the distance between first and last sapling is 3 m.

Q8. Ravish reads $\frac{1}{3}$ part of a book in one hour. How much part of the book will he read in $2\frac{1}{5}$ hours?

Solution:

Let x be the full part of book.

Given, Ravish reads $\frac{1}{3}$ part of a book in one hour

1 hour = $\frac{1}{3}$ x

Part of the book will he read in $2\frac{1}{5}$ hours

$2\frac{1}{5} = \frac{11}{5}$ hours = $\frac{1}{3} \times x \times \frac{11}{5}$

$\frac{11}{15}$ x = $\frac{11}{15}$ part of book

Q9. Lipika reads a book for $1\frac{3}{4}$ hours every day. She reads the entire book in 6 days. How many hours in all were required by her to read the book?

Solution:

Given,

Time taken by Lipika to read a book per day = $1\frac{3}{4} = \frac{7}{4}$ hours

Time taken by Lipika to read a book for 6 days  = $\frac{7}{4} \times 6$ = $\frac{42}{4} = 10\frac{1}{2}$ hours.

Q10. Find the area of a rectangular park which is $41\frac{2}{3} \; m$ long and $18\frac{3}{5} \; m$ broad.

Solution:

Given, $41\frac{2}{3} \; m = \frac{145}{3} \; m \\ And, \; 18\frac{3}{5} \; m = \frac{93}{5} \; m \\$

Area of a rectangular park = (length x breadth) = $(\frac{125}{3} \; m \times \frac{93}{5} \; m) \\ = (\frac{125 \times 93}{15}) m^{2} \\ = (\frac{11625}{15}) m^{2} \\ = 775 m^{2}$

Q11. If milk is available at Rs $17\frac{3}{4}$ per litre, find the cost of $7\frac{2}{5}$ litres of milk.

Solution:

Given,

$Rs 17\frac{3}{4} = Rs \frac{71}{4} \\ And, 7\frac{2}{5} \; litres = \frac{37}{5} \; litres \\$

The cost of milk per litre = $Rs \frac{71}{4}$

The cost of milk per $\frac{37}{5} \; litres$ = Rs $\frac{37}{5} \times \frac{71}{4} \\ = Rs \frac{2327}{20} \\ = Rs 131\frac{7}{20}$

Q12. Sharda can walk $8\frac{1}{3}$ km in one hour. How much distance will she cover in $2\frac{2}{5}$ hours.

Solution:

Given,

$8\frac{1}{3} km = \frac{25}{3} km \\ 2\frac{2}{5} hours = \frac{12}{5} hours$

Distance covered by Sharda in one hour = $\frac{25}{3} km$

Distance covered by Sharda in $\frac{12}{5} hours$ = $2\frac{2}{5} \times \frac{25}{3}$ = 20 km

Q13. A sugar bag contains 30 kg of sugar. After consuming $\frac{2}{3}$ of it, how much sugar is left in the bag

Solution:

Given, A sugar bag contains 30 kg of sugar.

After consuming $\frac{2}{3}$ of it, the amount of sugar left in the bag = $30 kg – \frac{2}{3} \times 30 kg \\ = 30 kg – 20 kg \\ = 10 kg$

Q14. Each side of a square is $6\frac{2}{3}$ m long. Find its area.

Solution:

Given,

Each side = $6\frac{2}{3} m = \frac{20}{3} m$

Area = side2 = $(\frac{20}{3})^{2} m^{2}$ = $\frac{400}{9} m^{2} \\ = 44\frac{4}{9} m^{2}$

Q15. There are 45 students in a class and $\frac{3}{5}$ of them are boys. How many girls are there in the class?

Solution:

Given,

There are 45 students in a class,

And $\frac{3}{5}$ of them are boys.

Therefore, no of girls in the class = 45 – $\frac{3}{5}\times 45$

= 45 – 27

= 18

#### Practise This Question

Which of the following is the smallest whole number?