The DAV Class 7 Maths Book Solutions Pdf and **DAV Class 7 Maths Chapter 2 Worksheet 5 **Solutions of Operations on Rational Numbers offer comprehensive answers to textbook questions.

## DAV Class 7 Maths Ch 2 WS 5 Solutions

Question 1.

Divide:

(i) \(\frac{2}{5}\) by \(\frac{-1}{3}\)

Answer:

\(\frac{2}{5} \div \frac{-1}{3}\)

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

= \(\frac{-6}{5}\)

(ii) \(\frac{-7}{4}\) by \(\frac{1}{8}\)

Answer:

\(\frac{-7}{4} \div \frac{1}{8}\)

= \(\frac{-7}{4} \times \frac{8}{1}=\frac{-7 \times 8}{4 \times 1}\)

= \(\frac{-56}{4}\)

(iii) -10 by \(\frac{1}{5}\)

Answer:

-1 ÷ \(\frac{1}{5}\)

= -1 × 5

= -5

(iv) \(\frac{1}{13}\) by -2

Answer:

\(\frac{1}{13}\) ÷ -2

= \(\frac{1}{13} \times \frac{-1}{2}=\frac{1 \times-1}{13 \times 2}\)

= \(\frac{-1}{26}\)

Question 2.

By taking x = \(\frac{3}{4}\) and y = \(\frac{-5}{6}\) verify that x ÷ y ≠ y ÷ x

Answer:

L.H.S = x ÷ y = \(\frac{3}{4} \div \frac{-5}{6}\)

= \(\frac{3}{4} \times \frac{6}{-5}\)

= \(\frac{3 \times 6}{4 \times-5}\)

= \(\frac{18}{-20}=\frac{-18}{20}\)

R.H.S = y ÷ x = \(\frac{-5}{6} \div \frac{3}{4}\)

= \(\frac{-5}{6} \times \frac{4}{3}\)

= \(\frac{-5 \times 4}{6 \times 3}=\frac{-20}{18}\)

They are not same but reciprocal to each other. Hence x ÷ y ≠ y ÷ x

Question 3.

The product of two rational numbers is \(\frac{-3}{7}\). If one of the number is \(\frac{5}{21}\), find the other.

Answer:

Let the other number be x and the given number is \(\frac{5}{21}\)

∴ \(\frac{5}{21}\) × x = \(\frac{-3}{7}\)

x = \(\frac{-3}{7} \div \frac{5}{21}\)

= \(\frac{-3}{7} \times \frac{21}{5}\)

= \(\frac{-63}{35}=\frac{-9}{5}\)

Hence the other number = \(\frac{-9}{5}\)

Question 4.

With what number should we multiply \(\frac{-36}{35}\), so that the product be \(\frac{-6}{5}\) ?

Solution:

Let the required number be x

∴ x × \(\frac{-36}{25}=\frac{-6}{5}\)

⇒ x = \(\frac{-6}{5} \div \frac{-36}{25}\)

= \(\frac{-6}{5} \times \frac{25}{-36}=\frac{5}{6}\)

Hence the required number = \(\frac{5}{6}\).

Question 5.

By taking x = \(\frac{-5}{3}\), y = \(\frac{2}{7}\) and z = \(\frac{1}{-4}\) verify that:

(i) x ÷ (y + z) ≠ x ÷ y + x ÷ z

Answer:

L.H.S

(ii) x ÷ (y – z) ≠ x ÷ y – x ÷ z

Answer:

L.H.S

L.H.S ≠ R.H.S

Hence verified

(iii) (x + y) ÷ z = x ÷ z + y ÷ z

Answer:

L.H.S

L.H.S = R.H.S

Hence verified

Question 6.

From a rope of length 40 metres, a man cuts some equal sized pieces. How many pieces can he cut if each piece is of \(\frac{4}{9}\) metres of length?

Answer:

Let the number of pieces required be n

∴ n × \(\frac{4}{9}\) = 40

⇒ n = 40 ÷ \(\frac{4}{9}\)

⇒ n = 40 × \(\frac{9}{4}\)

n = 90

Hence the required number of pieces = 90.