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

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

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