You can Download KSEEB Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.1 Questions and Answers to help you to revise the complete syllabus.

## KSEEB Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 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) The additive inverse of \(\frac{2}{8}\) is \(\frac{-2}{8}\).

(ii) The additive inverse of \(\frac{-5}{9}\) is \(-\left(\frac{-5}{9}\right)\) = \(\frac{5}{9}\)

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

∴ The additive inverse of \(\frac{6}{5}\) is \(\frac{-6}{5}\).

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

∴ The additive inverse of \(\frac{-2}{9}\) is \(\frac{2}{9}\).

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

∴ The additive inverse of \(\frac{-19}{6}\) 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) The multiplicative inverse of -13 is \(\frac{1}{-13}\).

(ii) The multiplicative inverse of \(\frac{-13}{19}\) is \(\frac{1}{\frac{-13}{19}}=\frac{19}{-13}\).

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

(iv) The multiplicative inverse of \(\frac{-5}{8} \times \frac{-3}{7}=\frac{15}{56}\) is \(\frac{56}{15}\).

(v) The multiplicative inverse of \(-1 \times \frac{-2}{5}=\frac{2}{5}\) is \(\frac{5}{2}\).

(vi) The multiplicative inverse of -1 is \(\frac{1}{-1}\) = -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) Multiplicative inverse.

(ii) Commutative.

(iii) 1, is the multiplicative identity.

Question 6.

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

Solution:

The reciprocal of \(\frac{-7}{16}\) is \(\frac{16}{-7}=\frac{6}{13} \times \frac{16}{-7}=\frac{96}{-91}\)

Question 7.

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

Solution:

For any three rational numbers a, b and c

a × (b × c) = (a × b) × c

The multiplication is associative for rational numbers.

Question 8.

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

Solution:

Multiplicative inverse of \(\frac{8}{9}\) is \(\frac{9}{8}\) or \(1 \frac{1}{8}\)

But, here \(-1 \frac{1}{8}\) is negative.

∴ \(\frac{8}{9}\) is not 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 = \(\frac{3}{10}\)

Multiplicative inverse of \(\frac{3}{10}\) is \(\frac{10}{3}\) = \(3 \frac{1}{3}\)

Hence, 0.3 is multiplicative inverse of \(3 \frac{1}{3}\)

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

If product of a number and its multiplicative inverse is 1.

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) Zero is the rational number, that does not have reciprocal.

(ii) 1 is such a rational number, which is equal to its reciprocal. (-1) is also such a rational number.

(iii) 0 is a number which is equal to its negative.

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 \(\frac{1}{x}\), where 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, -1

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

(iv) x

(v) Rational number

(vi) Positive