Punjab State Board PSEB 8th Class Maths Book Solutions Chapter 1 Rational Numbers Ex 1.1 Textbook Exercise Questions and Answers.

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

1. Using appropriate properties find.

Question (i).

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

Solution:

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

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

= \(\frac{3}{5} \times\left[-\frac{2}{3}-\frac{1}{6}\right]+\frac{5}{2}\) (Distributive)

= \(\frac{3}{5}\left[\frac{-4-1}{6}\right]+\frac{5}{2}\)

= \(\frac{3}{5}\left[\frac{-5}{6}\right]+\frac{5}{2}\)

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

= \(-\frac{1}{2}+\frac{5}{2}\)

= \(\frac{-1+5}{2}\)

= \(\frac {4}{2}\)

= 2

Question (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:

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

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

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

= \(\frac{2}{5} \times\left[\frac{-6+1}{14}\right]-\frac{1}{4}\)

= \(\frac{2}{5} \times \frac{-5}{14}-\frac{1}{4}\)

= \(-\frac{1}{7}-\frac{1}{4}=\frac{-4-7}{28}\)

= \(\frac{-11}{28}\)

2. Write the additive inverse of each of the following:

Question (i).

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

Solution:

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

Question (ii).

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

Solution:

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

Question (iii).

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

Solution:

Additive inverse of \(\frac{-6}{-5}\) means \(\frac{6}{5}\) = \(\frac{-6}{5}\)

Question (iv).

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

Solution:

Additive inverse of \(\frac{2}{-9}\) = \(\frac{2}{9}\)

Question (v).

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

Solution:

Additive inverse of \(\frac{19}{-6}\) = \(\frac{19}{6}\)

3. Verify that – (- x) = x for

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

Solution:

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

∴ (-x) = \(\left(\frac{-11}{15}\right)\)

-(-x) = –\(\left(\frac{-11}{15}\right)\)

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

∴ -(-x) = x

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

Solution:

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

∴ (-x) = \(\left(\frac{-13}{17}\right)\)

= \(\frac {13}{17}\)

-(-x) = –\(\left(\frac{-13}{17}\right)\)

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

∴ -(-x) = x

4. Find the multiplicative inverse of the following:

Question (i).

-13

Solution:

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

Question (ii).

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

Solution:

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

Question (iii).

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

Solution:

Multiplicative inverse of \(\frac {1}{5}\) = 5

Question (iv).

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

Solution:

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

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

= \(\frac {15}{56}\)

Multiplicative inverse of \(\frac {15}{56}\) = \(\frac {56}{15}\)

Question (v) .

1 × \(\frac {-2}{5}\)

Solution:

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

= \(\frac {2}{5}\)

Multiplicative inverse of \(\frac {2}{5}\) = \(\frac {5}{2}\)

Question (vi).

-1

Solution:

Multiplicative inverse of -1 = (-1)

(∵ \(\frac{1}{(-1)}\) = (-1))

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

Question (i).

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

Solution:

1 is the multiplicative identity.

Question (ii).

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

Solution:

Commutative property of multiplication.

Question (iii).

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

Solution:

Existence of multiplicative inverse.

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

Solution:

Reciprocal of \(\frac{-7}{16}=\frac{-16}{7}\)

∴ \(\frac{6}{13} \times \frac{-16}{7}\)

= \(\frac{6 \times(-16)}{13 \times 7}\)

= \(\frac {-96}{91}\)

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:

In computing

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

we use the associativity.

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

Solution:

\(-1 \frac{1}{8}=\frac{-9}{8}\)

\(\frac{8}{9} \times \frac{-9}{8}\) = (-1)

∴ \(\frac {8}{9}\) is is not the multiplicative inverse of -1 \(\frac {1}{8}\) as product of two multiplicative inverse is always 1.

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

Solution:

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

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

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

10. Write:

Question (i).

The rational number that does not have a reciprocal.

Solution:

The rational number that does not have a reciprocal is 0.

Question (ii).

The rational numbers that are equal to their reciprocals.

Solution:

The rational numbers that are equal to their reciprocals are 1 and (-1).

Question (iii).

The rational number that is equal to its negative.

Solution:

The rational number that is equal to its negative is zero (0).

11. Fill in the blanks:

Question (i).

Zero has ……………. reciprocal.

Solution:

Zero has no reciprocal.

Question (ii).

The numbers ……………. and ……………. are their own reciprocals.

Solution:

The numbers 1 and -1 are their own reciprocals.

Question (iii).

The reciprocal of – 5 is …………….

Solution:

The reciprocal of – 5 is \(\frac {-1}{5}\)

Question (iv).

Reciprocal of \(\frac{1}{x}\), where x ≠ 0 is …………….

Solution:

Reciprocal of \(\frac{1}{x}\), where x ≠ 0 is x

Question (v) .

The product of two rational numbers is always a …………….

Solution:

The product of two rational numbers is always a rational number.

Question (vi).

The reciprocal of a positive rational number is …………….

Solution:

The reciprocal of a positive rational number is positive.