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

Rajasthan Board RBSE Solutions for Class 7 Maths Chapter 2 Fractions and Decimals Ex 2.3 Textbook Exercise Questions and Answers.

RBSE Class 7 Maths Solutions Chapter 2 Fractions and Decimals 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:

Question 2.
Multiply and reduce to lowest form (if possible):
(i) \(\frac{2}{3} \times 2 \frac{2}{3}\)
(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:

Question 3.
Multiply the following functions:
(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:

Question 4.
Which is greater?
(i) \(\frac{2}{7}\) of \(\frac{3}{4}\) or \(\frac{3}{5}\) of \(\frac{5}{8}\).
Answer:

(ii) \(\frac{1}{2}\) of \(\frac{6}{7}\) or \(\frac{2}{3}\) of \(\frac{3}{7}\).
Answer:

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:
Let P, Q, R and S be the four saplings planted in a row.

∵ Distance between two saplings = m
∴ Distance between first and last sapling
= PS = 3 × PQ
= 3 × \(\frac{3}{4}\) = \(\frac{9}{4}\)m = 2\(\frac{1}{4}\)m

Question 6.
Lipika reads a book for hours every day. She reads the entire book in 6 days. How many hours in all were required by her to read the book?
Answer:
∵ Hours given by Lipika in one day
= 1\(\frac{3}{4}\) = \(\frac{7}{4}\)hours
∴ Total hours required by her in 6 days
= \(\frac{7}{4} \times 6=\frac{7 \times 6}{4}=\frac{42}{4}\)
= \(\frac{42 \div 2}{4 \div 2}=\frac{21}{2}=10 \frac{1}{2}\) hours

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 petrol, the car runs =16km
∴ In 2\(\frac{3}{4}\) litres of petrol, the car runs
= 16 \(\times 2 \frac{3}{4}=16 \times \frac{11}{4}=\frac{16 \times 11}{4}\)
= \(\frac{176}{4}=\frac{176 \div 4}{4 \div 4}\) = 44 km

Question 8.
(a) (i) Provide the number in the box ________, such that \(\frac{2}{3}\) × ________ = \(\frac{10}{30}\).
(ii) The simplest forth of the number obtained in _________ is ________ .
Answer:
(i) \(\frac{2}{3}\) × \(\frac{5}{10}\) = \(\frac{10}{30}\)
(ii) \(\frac{5}{10}\) is = \(\frac{5 \div 5}{10 \div 5}=\frac{1}{2}\)

(b) (i) Provide the number in the box _______ ,such that \(\frac{3}{5}\) × _________ = \(\frac{24}{75}\).
(ii) The simplest form of the number obtained in _________ is _______ .
Answer:
(i) \(\frac{3}{5}\) × \(\frac{8}{15}\) = \(\frac{24}{75}\)
(ii) \(\frac{8}{15}\) is = \(\frac{8}{15}\)