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.