# PSEB 7th Class Maths Solutions Chapter 2 Fractions and Decimals Ex 2.3

Punjab State Board PSEB 7th Class Maths Book Solutions Chapter 2 Fractions and Decimals Ex 2.3 Textbook Exercise Questions and Answers.

## PSEB Solutions for Class 7 Maths Chapter 2 Fractions and Decimals Ex 2.3

1. Solve the following :

Question (i).
$$\frac {1}{3}$$ of
(a) $$\frac {1}{5}$$
(b) $$\frac {2}{7}$$
(c) $$\frac {3}{2}$$

Question (ii).
$$\frac {3}{4}$$ of
(a) $$\frac {2}{9}$$
(b) $$\frac {4}{7}$$
(c) $$\frac {8}{3}$$

2. Multiply the fractions and reduce it to the lowest form (If possible) :

Question (i).
$$\frac{2}{7} \times \frac{7}{9}$$
$$\frac{2}{7} \times \frac{7}{9}$$
= $$\frac {2}{9}$$

Question (ii).
$$\frac{1}{3} \times \frac{15}{8}$$
$$\frac{1}{3} \times \frac{15}{8}$$
= $$\frac {5}{8}$$

Question (iii).
$$\frac{12}{27} \times \frac{3}{9}$$
$$\frac{12}{27} \times \frac{3}{9}$$
= $$\frac {4}{27}$$

Question (iv).
$$\frac{2}{5} \times \frac{6}{4}$$
$$\frac{2}{5} \times \frac{6}{4}$$
= $$\frac {3}{5}$$

Question (v).
$$\frac{81}{100} \times \frac{6}{7}$$
$$\frac{81}{100} \times \frac{6}{7}$$
= $$\frac {243}{350}$$

Question (vi).
$$\frac{3}{5} \times \frac{5}{27}$$
$$\frac{3}{5} \times \frac{5}{27}$$
= $$\frac {1}{9}$$

3. Multiply the following fractions :

Question (i).
$$\frac{3}{2} \times 5 \frac{1}{3}$$
$$\frac{3}{2} \times 5 \frac{1}{3}$$
= $$\frac{3}{2} \times \frac{16}{3}$$
= 8

Question (ii).
$$\frac{1}{7} \times 5 \frac{2}{3}$$
$$\frac{1}{7} \times 5 \frac{2}{3}$$
= $$\frac{1}{7} \times \frac{17}{3}$$
= $$\frac {17}{21}$$

Question (iii).
$$2 \frac{5}{6} \times 4$$
$$2 \frac{5}{6} \times 4$$
= $$\frac {17}{6}$$ × 4
= $$\frac {34}{3}$$
= 11$$\frac {1}{3}$$

Question (iv).
$$4 \frac{1}{3} \times 9 \frac{1}{4}$$
$$4 \frac{1}{3} \times 9 \frac{1}{4}$$
= $$\frac{13}{3} \times \frac{37}{4}$$
= $$\frac {481}{12}$$

Question (v).
$$2 \frac{2}{3} \times 3 \frac{5}{8}$$
$$2 \frac{2}{3} \times 3 \frac{5}{8}$$
= $$\frac{8}{3} \times \frac{29}{8}$$
= 9$$\frac {2}{3}$$

Question (vi).
$$3 \frac{1}{5} \times 2 \frac{1}{4}$$
$$3 \frac{1}{5} \times 2 \frac{1}{4}$$
= $$\frac{16}{5} \times \frac{9}{4}$$
= $$\frac {36}{5}$$
= 7$$\frac {1}{5}$$

4. Which fraction is greater in the following fractions ?

Question (i).
$$\frac {3}{2}$$ of $$\frac {2}{7}$$ or $$\frac {5}{2}$$ of $$\frac {3}{8}$$
$$\frac {3}{2}$$ of $$\frac {2}{7}$$
= $$\frac{3}{2} \times \frac{2}{7}$$
= $$\frac {3}{7}$$
or
$$\frac {5}{2}$$ of $$\frac {3}{8}$$
= $$\frac{5}{2} \times \frac{3}{8}$$
= $$\frac {15}{16}$$
Since, $$\frac {15}{16}$$ > $$\frac {3}{7}$$
So, $$\frac {5}{2}$$ of $$\frac {3}{8}$$ is greater.

Question (ii).
$$\frac {1}{2}$$ of $$\frac {6}{5}$$ or $$\frac {1}{3}$$ of $$\frac {4}{5}$$
$$\frac {1}{2}$$ of $$\frac {6}{5}$$
= $$\frac {1}{2}$$ × $$\frac {6}{5}$$
= $$\frac {3}{5}$$
or
$$\frac {1}{3}$$ of $$\frac {4}{5}$$
= $$\frac {1}{3}$$ × $$\frac {4}{5}$$
= $$\frac {4}{15}$$
Since, $$\frac {3}{5}$$ > $$\frac {4}{15}$$
So, $$\frac {1}{2}$$ of $$\frac {6}{5}$$ is greater.

5. If the speed of a car is 105 $$\frac {1}{3}$$ km/hr, find the distance covered by it m 3$$\frac {2}{3}$$ hours.
Distance travelled in 1 hour= 105$$\frac {1}{3}$$ km
= $$\frac {316}{3}$$ km
Distance travelled in 3$$\frac {2}{3}$$ hours i.e. in $$\frac {11}{3}$$ hours
= $$\frac {11}{3}$$ × $$\frac {316}{3}$$ km
= $$\frac {3476}{9}$$ km
= 386$$\frac {2}{9}$$km

6. The length of a rctangular plot of land is 29$$\frac {3}{7}$$ m. If its breadth is 12$$\frac {8}{11}$$m, find its area.
Length of rectangular plot (l)
= 29$$\frac {3}{7}$$m = $$\frac {206}{7}$$m
Breadth of rectangular plot (b)
= 12$$\frac {8}{11}$$m = $$\frac {140}{11}$$m
Area of rectangular plot
= l × b = $$\frac{206}{7} \mathrm{~m} \times \frac{140}{11} \mathrm{~m}$$
= $$\frac{4120}{11}$$ sq.m
= 374$$\frac{6}{11}$$ sq.m

7. If a cloth costs ₹ 120 $$\frac {1}{4}$$ per metre, find the cost of 4$$\frac {1}{3}$$ metre of this cloth.
Per m cost of cloth = ₹ 120$$\frac {1}{4}$$
= ₹ $$\frac {481}{4}$$
Cost of 4$$\frac {1}{3}$$ metre of this cloth
= $$\frac {1}{3}$$ × ₹ $$\frac {481}{4}$$
= ₹ $$\frac {6253}{12}$$
= ₹ 521$$\frac {1}{12}$$

8. Multiple choice questions :

Question (i).
$$\frac {1}{4}$$ of $$\frac {8}{3}$$ is :
(a) $$\frac {9}{7}$$
(b) $$\frac {8}{4}$$
(c) $$\frac {2}{3}$$
(d) 1
(c) $$\frac {2}{3}$$

Question (ii).
$$\frac {3}{2}$$ × $$\frac {2}{3}$$ = ?
(a) 1
(b) $$\frac {5}{6}$$
(c) 3
(d) $$\frac {6}{5}$$
(a) 1

Question (iii).
The value of the product of two proper fractions is :
(a) greater than both of the proper fractions.
(b) lesser than both of the proper fractions.
(c) lie between the given two fractions.
(d) none of these.
$$1 \frac{2}{3} \times 4 \frac{5}{7}=4 \frac{10}{21} ?$$ (True/False)
$$\frac{3}{4} \times \frac{2}{3}=\frac{2}{3} \times \frac{3}{4} ?$$ (True/False)