## MP Board Class 8th Maths Solutions Chapter 1 Rational Numbers Ex 1.1

**Mp Board Class 8 Maths Chapter 1 Question 1.**

Using appropriate properties, find.

Solution:

**Mp Board Class 8th Maths Chapter 1 Question 2.**

Write the additive inverse of each of the following

Solution:

(iv) We have given \(\frac{2}{-9}\)

Multiplying numerator and denominator by -1, we get \(\frac{2}{-9}\)

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

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

Multiplying numerator and denominator by -1, we get \(\frac{-19}{6}\)

**Class 8 Maths Chapter 1 Mp Board Question 3.**

Verify that -(-x) = x for

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

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

Solution:

**Mp Board Solution Class 8 Maths Chapter 1 Question 4.**

Find the multiplicative inverse of the following.

Solution:

(i) We have given, -13

The multiplicative inverse of -13 is \(\left(\frac{-1}{13}\right)\)

(ii) We have given, \(\frac{-13}{19}\)

The multiplicative inverse of is \(\frac{-13}{19}\) is \(\frac{-19}{13}\)

(iii) We have given, \(\frac{1}{5}\)

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

∵ \(\frac{1}{5} \times 5=1\)

(iv) We have given, \(\frac{-5}{8} \times \frac{-3}{7}\)

The multiplicative inverse of

(v) We have given, \(-1 \times \frac{-2}{5}\)

The multiplicative inverse of

(vi) We have given, -1.

The multiplicative inverse of -1 is -1.

∵ (-1) × (-1) = 1.

**Mp Board Class 8 Maths Solutions English Medium Question 5.**

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

Solution:

(i) We have given, \(\frac{-4}{5} \times 1=1 \times \frac{-4}{5}=\frac{-4}{5}\)

i.e., 1 is the multiplicative identity. Thus, it is a identity property under multiplication

(ii) We have given, \(\frac{-13}{17} \times \frac{-2}{7}=\frac{-2}{7} \times \frac{-13}{17}\), which shows the commutativity.

Thus, it is a commutative property under multiplication.

(iii) We have given \(\frac{-19}{29} \times \frac{29}{-19}=1\), which shows that \(\frac{29}{-19}\) is a multiplicative inverse of \(\left(\frac{-19}{29}\right)\)

Thus, it is a inverse property under multiplication.

**Mp Board Class 8th Maths Solutions English Medium Question 6.**

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

Solution:

**Maths Class 8 Mp Board English Medium 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:

Above property is associativity.

[ ∵ a × (b × c) = (a × b) × c]

**Mp Board Solution Class 8 Maths Question 8.**

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

Solution:

We have given a fraction \(\frac{8}{9}\) and \(-1 \frac{1}{8}=\frac{-9}{8}\)

No, \(\frac{-9}{8}\) is not a multiplicative inverse of \(\frac{8}{9}\) because \(\frac{8}{9} \times\left(\frac{-9}{8}\right)=-1 \neq 1\)

**Mp Board Solution Class 8 Math Question 9.**

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

Solution:

**Mp Board 8th Class Maths Book Solutions 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) 0 is the rational number, which does not have a reciprocal.

(ii) 1 and (-1) are the rational numbers, that are equal to their reciprocals.

(iii) 0 is the rational number that is equal to its negative.

**Class 8 Mp Board Maths Solution Question 11.**

Fill in the blanks.

(i) Zero has …… reciprocal.

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

(iii) The reciprocals 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 positive rational number is …….

Solution:

(i) Zero has no reciprocal.

(ii) The numbers 1 and -1 are their own reciprocals.

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

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

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

(vi) The reciprocal of positive rational number is positive.