Haryana State Board HBSE 8th Class Maths Solutions Chapter 1 Rational Numbers Ex 1.1 Textbook Exercise Questions and Answers.

## Haryana Board 8th Class Maths Solutions 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:

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

2nd Method

3rd Method

(ii) 1st Method

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

2nd Method

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:

\(\frac{-2}{8}\) is the additive inverse of \(\frac{2}{8}\) because

\(\frac{-6}{5}\) is the additive inverse of \(\frac{6}{5}\) because

Question 3.

Verify that – (-x) = x for

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

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

Solution:

(i) We have, x = \(\frac{11}{15}\)

The additive inverse of

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 × \(\frac{-2}{5}\)

(vi) -1

Solution:

(i) Let the multiplicative inverse of -13 be x.

∴ -13 × x = 1

(v) Let the multiplicative inverse of -1 × \(\frac{-2}{5}\) be x.

∴ -1 × \(\frac{-2}{5}\) × x = 1

⇒ x = \(\frac{1 \times 5}{-1 \times(-2)}\) = \(\frac{5}{2}\) or \(\frac{-5}{-2}\)

(vi) The multiplicative inverse of -1 is -1 because -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) 1 is the multiplicative identity. (ii) Commutativity, (iii) Multiplicative inverse.

Question 6.

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

Solution:

The reciprocal of \(\frac{-7}{16}\) is \(\frac{16}{-7}\)

The Product of \(\frac{6}{13}\) and \(\frac{16}{-7}\)

= \(\frac{6}{13}\) × \(\frac{16}{-7}\) = \(\frac{96}{-91}\)

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:

We know 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:

No, the multiplicative inverse of \(\frac{8}{9}\) is \(\frac{9}{8}\) or 1\(\frac{1}{8}\).

Here, -1\(\frac{1}{8}\) is negative. Therefore, \(\frac{8}{9}\) 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 = \(\frac{3}{10}\)

Here, 0.3 × 3\(\frac{1}{3}\) = \(\frac{3}{10}\) × \(\frac{10}{3}\) = 1

We say that a rational number \(\frac{c}{d}\) is called the reciprocal or multiplicative inverse of another a rational number \(\frac{a}{b}\) if \(\frac{a}{b}\) × \(\frac{c}{d}\) = 1

∴ The result will be yes.

Question 10.

Write :

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

Solution:

Zero has no reciprocal.

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

Solution:

1 is equal to its reciprocal, because the reciprical of 1 is 1.

-1 is also equal to its reciprocal because the reciprocal of-1 is -1.

-1 × (-1) = 1

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

Solution:

Its value 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 number is always a ……………..

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

Answer:

(i) no

(ii) 1.1

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

(iv) x

(v) rational number

(vi) positive