The DAV Class 7 Maths Book Solutions Pdf and **DAV Class 7 Maths Chapter 1 Worksheet 2** Solutions of Rational Numbers offer comprehensive answers to textbook questions.

## DAV Class 7 Maths Ch 1 WS 2 Solutions

Question 1.

In each of the following cases, show that the rational numbers are equivalent.

(i) \(\frac{4}{9}\) and \(\frac{44}{99}\)

Answer:

\(\frac{4}{9}\) and \(\frac{44}{99}\)

\(\frac{4}{9}\) = \(\frac{4}{9}\) hence they are equivalent rational numbers.

(ii) \(\frac{7}{-3}\) and \(\frac{35}{-15}\)

Answer:

\(\frac{7}{-3}\) and \(\frac{35}{-15}\)

\(\frac{7}{-3}\) = \(\frac{7}{-3}\), So, they are equivalent rational numbers.

(iii) \(\frac{-3}{5}\) and \(\frac{-12}{20}\)

Answer:

\(\frac{-3}{5}\) and \(\frac{-12}{20}\)

\(\frac{-3}{5}\) = \(\frac{-3}{5}\) So, they are not equivalent rational numbers.

Question 2.

In each of the following cases, show that the rational numbers are not equivalent.

(i) \(\frac{4}{9}\) and \(\frac{16}{27}\)

Answer:

\(\frac{4}{9}\) and \(\frac{16}{27}\)

⇒ 4 × 27 and 16 × 9

⇒ 108 ≠ 144

(ii) \(\frac{-100}{3}\) and \(\frac{300}{9}\)

Answer:

\(\frac{-100}{3}\) and \(\frac{300}{9}\)

⇒ -100 × 9 and 300 × 3

⇒ -900 ≠ 900

(iii) \(\frac{3}{-17}\) and \(\frac{8}{-51}\)

Answer:

\(\frac{3}{-17}\) and \(\frac{8}{-51}\)

⇒ 3 × (-51) and 8 × (-17)

⇒ -153 ≠ -136

So, they are not equivalent rational numbers.

Question 3.

Write three rational numbers equivalent to each of the following:

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

Answer:

\(\frac{4}{7}=\frac{4 \times 2}{7 \times 2}=\frac{8}{14}\)

and \(\frac{4}{7}=\frac{4 \times 3}{7 \times 3}=\frac{12}{21}\) and \(\frac{4 \times 4}{7 \times 4}=\frac{16}{28}\)

Hence, the three equivalent fractions are

\(\frac{8}{14}=\frac{12}{21}=\frac{16}{28}\)

(ii) \(\frac{36}{108}\)

Answer:

\(\frac{36}{108}=\frac{36 \div 2}{108 \div 2}=\frac{18}{54}\)

and \(\frac{36 \div 3}{108 \div 3}=\frac{12}{36}\) and \(\frac{36 \div 4}{108 \div 4}=\frac{9}{27}\)

Hence, the equivalent fractions are

\(\frac{18}{54}, \frac{12}{36}\) and \(\)

(iii) \(\frac{-5}{-7}\)

Answer:

\(\frac{-5}{-7}=\frac{-5 \times 2}{-7 \times 2}=\frac{-10}{-14}\)

and \(\frac{-5 x-2}{-7 x-2}=\frac{10}{14}\) and \(-\frac{5 \times 3}{-7 \times 3}=\frac{-15}{-21}\)

Hence, the equivalent fractions are

\(\frac{-10}{-14}, \frac{10}{14}\) and \(\frac{-15}{-21}\)

(iv) \(\frac{-72}{180}\)

Answer:

\(\frac{-72}{180}=\frac{-72 \div 2}{180 \div 2}=\frac{-36}{90}\)

and \(\frac{-72 \div 3}{180 \div 3}=\frac{-24}{60}\) and \(\frac{-72 \div 4}{180 \div 4}=\frac{-18}{45}\)

Hence the equivalent rational numbers are

\(\frac{-36}{90}, \frac{-24}{60}\) and \(\frac{-18}{45}\)

Question 4.

Express \(\frac{3}{5}\) as rational number with numerator,

(i) -21

Answer:

\(\frac{3}{5}=\frac{3 \times-7}{5 \times-7}\)

= \(\frac{-21}{-35}\)

(ii) 150

Answer:

\(\frac{3}{5}=\frac{3 \times 50}{5 \times 50}\)

= \(\frac{150}{250}\)

Question 5.

Express \(\frac{4}{-7}\) as a rational number with denominator

(i) 84

Answer:

\(\frac{4}{-7}=\frac{4 \times-12}{-7 x-12}\)

= \(\frac{-48}{84}\)

(ii) -28

Answer:

\(\frac{4}{-7}=\frac{4 \times 4}{-7 \times 4}\)

= \(\frac{16}{-28}\)

Question 6.

Express \(\frac{90}{216}\) as a rational number with numerator 5.

Answer:

\(\frac{90}{216}=\frac{90 \div 18}{216 \div 18}\)

= \(\frac{5}{12}\)

Question 7.

Express \(\frac{-64}{256}\) as a rational number with denominator 8.

Answer:

\(\frac{-64}{256}=\frac{-64 \div 32}{256 \div 32}\)

= \(\frac{-2}{8}\)

Question 8.

Find the equivalent forms of the rational numbers having a common denominator in each of the following collections of rational numbers:

(i) \(\frac{2}{5}, \frac{6}{13}\)

Answer:

The L.C.M of 5 and 13 = 5 × 13 = 65

= \(\frac{2 \times 13}{5 \times 13}, \frac{6 \times 5}{13 \times 5}\)

⇒ \(\frac{26}{65}, \frac{30}{65}\)

(ii) \(\frac{1}{7}, \frac{2}{8}, \frac{3}{14}\)

Answer:

The L.C.M of 7, 8, 14 = 56

= \(\frac{1}{7} \times \frac{8}{8}, \frac{2 \times 7}{8 \times 7}, \frac{3 \times 4}{14 \times 4}\)

⇒ \(\frac{8}{56}, \frac{14}{56}, \frac{12}{56}\)

(iii) \(\frac{5}{12}, \frac{7}{4}, \frac{9}{60}, \frac{11}{3}\)

Answer:

The L.C.M of 12, 4, 60 and 3 = 60

= \(\frac{5}{12} \times \frac{5}{5}, \frac{7}{4} \times \frac{15}{15}, \frac{9}{60} \times \frac{1}{1}, \frac{11}{3} \times \frac{20}{20}\)

= \(\frac{25}{60}, \frac{105}{60}, \frac{9}{60}, \frac{220}{60}\)