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) \(\frac {3}{2}\)

Answer:

Question (ii).

\(\frac {3}{4}\) of

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

(b) \(\frac {4}{7}\)

(c) \(\frac {8}{3}\)

Answer:

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

Question (i).

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

Answer:

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

= \(\frac {2}{9}\)

Question (ii).

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

Answer:

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

= \(\frac {5}{8}\)

Question (iii).

\(\frac{12}{27} \times \frac{3}{9}\)

Answer:

\(\frac{12}{27} \times \frac{3}{9}\)

= \(\frac {4}{27}\)

Question (iv).

\(\frac{2}{5} \times \frac{6}{4}\)

Answer:

\(\frac{2}{5} \times \frac{6}{4}\)

= \(\frac {3}{5}\)

Question (v).

\(\frac{81}{100} \times \frac{6}{7}\)

Answer:

\(\frac{81}{100} \times \frac{6}{7}\)

= \(\frac {243}{350}\)

Question (vi).

\(\frac{3}{5} \times \frac{5}{27}\)

Answer:

\(\frac{3}{5} \times \frac{5}{27}\)

= \(\frac {1}{9}\)

3. Multiply the following fractions :

Question (i).

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

Answer:

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

= \(\frac{3}{2} \times \frac{16}{3}\)

= 8

Question (ii).

\(\frac{1}{7} \times 5 \frac{2}{3}\)

Answer:

\(\frac{1}{7} \times 5 \frac{2}{3}\)

= \(\frac{1}{7} \times \frac{17}{3}\)

= \(\frac {17}{21}\)

Question (iii).

\(2 \frac{5}{6} \times 4\)

Answer:

\(2 \frac{5}{6} \times 4\)

= \(\frac {17}{6}\) × 4

= \(\frac {34}{3}\)

= 11\(\frac {1}{3}\)

Question (iv).

\(4 \frac{1}{3} \times 9 \frac{1}{4}\)

Answer:

\(4 \frac{1}{3} \times 9 \frac{1}{4}\)

= \(\frac{13}{3} \times \frac{37}{4}\)

= \(\frac {481}{12}\)

Question (v).

\(2 \frac{2}{3} \times 3 \frac{5}{8}\)

Answer:

\(2 \frac{2}{3} \times 3 \frac{5}{8}\)

= \(\frac{8}{3} \times \frac{29}{8}\)

= 9\(\frac {2}{3}\)

Question (vi).

\(3 \frac{1}{5} \times 2 \frac{1}{4}\)

Answer:

\(3 \frac{1}{5} \times 2 \frac{1}{4}\)

= \(\frac{16}{5} \times \frac{9}{4}\)

= \(\frac {36}{5}\)

= 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 \(\frac {3}{8}\)

Answer:

\(\frac {3}{2}\) 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 \(\frac {4}{5}\)

Answer:

\(\frac {1}{2}\) 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.

Answer:

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.

Answer:

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.

Answer:

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

Answer:

(c) \(\frac {2}{3}\)

Question (ii).

\(\frac {3}{2}\) × \(\frac {2}{3}\) = ?

(a) 1

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

(c) 3

(d) \(\frac {6}{5}\)

Answer:

(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.

Answer:

(b) lesser than both of the proper fractions.

9. Check if the following equations are ‘True’ or ‘False’ :

Question (i).

\(1 \frac{2}{3} \times 4 \frac{5}{7}=4 \frac{10}{21} ?\) (True/False)

Answer:

False

Question (ii).

\(\frac{3}{4} \times \frac{2}{3}=\frac{2}{3} \times \frac{3}{4} ?\) (True/False)

Answer:

True