These NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.1 Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Exercise 1.1

Question 1.

Using appropriate properties, find:

(i) \(\frac{-2}{3} \times \frac{3}{5}+\frac{5}{2}-\frac{3}{5} \times \frac{1}{6}\)

(ii) \(\frac{2}{5} \times\left(\frac{-3}{7}\right)-\frac{1}{6} \times \frac{3}{2}+\frac{1}{14} \times \frac{2}{5}\)

Solution:

Question 2.

Write the additive inverse of each of the following:

(i) \(\frac{2}{8}\)

(ii) \(\frac{-5}{9}\)

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

(iv) \(\frac{2}{-9}\)

(v) \(\frac{19}{-6}\)

Solution:

(i) Additive inverse of \(\frac{2}{8}\) is \(\frac{-2}{8}\)

(ii) Additive inverse of \(\frac{-5}{9}\) is \(\frac{5}{9}\)

(iii) Additive inverse of \(\frac{-6}{-5}\) is \(\frac{-6}{5}\)

(iv) Additive inverse of \(\frac{2}{-9}=\left(\frac{-2}{9}\right)\) is \(\frac{2}{9}\)

(v) Additive inverse of \(\frac{19}{-6}=\left(\frac{-19}{6}\right)\) is \(\frac{19}{6}\)

Question 3.

Verify that -(-x) = x for:

(i) x = \(\frac{11}{15}\)

(ii) x = \(\frac{-13}{17}\)

Solution:

Question 4.

Find the multiplicative inverse of the following:

(i) -13

(ii) \(\frac{-13}{19}\)

(iii) \(\frac{1}{5}\)

(iv) \(\frac{-5}{8} \times \frac{-3}{7}\)

(v) \(-1 \times \frac{-2}{5}\)

(vi) -1

Solution:

(i) Multiplicative inverse of -13 is \(\frac{-1}{13}\)

(ii) Multiplicative inverse of \(\frac{-13}{19}\) is \(\frac{-19}{13}\)

(iii) Multiplicative inverse of \(\frac{1}{5}\) is 5.

(iv) \(\left(\frac{-5}{8} \times \frac{-3}{7}\right)=\frac{(-5) \times(-3)}{8 \times 7}=\frac{56}{15}\)

Multiplicative inverse of \(\frac{-5}{8} \times \frac{-3}{7}\) is \(\frac{15}{56}\)

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

Multiplicative inverse of \(-1 \times \frac{-2}{5}\) is \(\frac{5}{2}\)

(vi) Multiplicative inverse of -1 is -1.

Question 5.

Name the property under multiplication used in each of the following:

(i) \(\frac{-4}{5} \times 1=1 \times \frac{-4}{5}=\frac{-4}{5}\)

(ii) \(\frac{-13}{17} \times \frac{-2}{7}=\frac{-2}{7} \times \frac{-13}{17}\)

(iii) \(\frac{-19}{29} \times \frac{29}{-19}=1\)

Solution:

(i) \(\frac{-4}{5} \times 1=1 \times \frac{-4}{5}=\frac{-4}{5}\)

1 is the multiplicative identity.

(ii) \(\frac{-13}{17} \times \frac{-2}{7}=\frac{-2}{7} \times \frac{-13}{17}\)

Multiplication is commutative.

(iii) \(\frac{-19}{29} \times \frac{29}{-19}=1\)

Multiplicative inverse.

Question 6.

Multiply \(\frac{6}{13}\) by the reciprocal of \(\frac{-7}{16}\).

Solution:

Question 7.

Tell what property allows you to compute \(\frac{1}{3} \times\left(6 \times \frac{4}{3}\right) \text { as }\left(\frac{1}{3} \times 6\right) \times \frac{4}{3}\)

Solution:

\(\frac{1}{3} \times\left(6 \times \frac{4}{3}\right) \text { as }\left(\frac{1}{3} \times 6\right) \times \frac{4}{3}\)

In the given question, we use the associative property.

Question 8.

Is \(\frac{8}{9}\) the multiplicative inverse of -1\(\frac{1}{8}\)? Why or why not?

Solution:

\(\frac{8}{9} \times-\frac{9}{8}=-1\) but is not equal to 1.

So, \(\frac{8}{9}\) is not the multiplicative inverse of -1\(\frac{1}{8}\)

Question 9.

Is 0.3 the multiplicative inverse of 3\(\frac{1}{3}\)? Why or why not?

Solution:

0.3 = \(\frac{3}{10}\)

3\(\frac{1}{3}\) = \(\frac{10}{3}\)

\(\frac{3}{10} \times \frac{10}{3}=1\)

∴ Multiplicative inverse of 3\(\frac{1}{3}\) is 0.3.

Question 10.

Write:

(i) The rational number that does not have a reciprocal.

(ii) The rational numbers that are equal to their reciprocals.

(iii) The rational number that is equal to its negative.

Solution:

(i) The rational number ‘0’ does not have a reciprocal.

(ii) The rational numbers 1 and (-1) are equal to their reciprocal.

(iii) The rational number ‘0’ is equal to its negative [(0) + (0) = 0]

∴ The negative of 0 is 0.

Question 11.

Fill in the blanks:

(i) Zero has ________ reciprocal.

(ii) The numbers ________ and ________ are their own reciprocals.

(iii) The reciprocal of -5 is ________

(iv) Reciprocal of \(\frac{1}{\mathrm{x}}\) when x ≠ 0 is ________

(v) The product of two rational numbers is always a ________

(vi) The reciprocal of a positive rational number is ________

Solution:

(i) no

(ii) 1 and -1

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

(iv) x

(v) rational number

(vi) positive