## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 1 Rational Numbers Ex 1.3

Question 1.

Multiply and express the result in the lowest form:

Solution:

Question 2.

Verify commutative property of multiplication for the following pairs of rational numbers:

(i) \(\frac { 4 }{ 5 }\) and \(\frac { -7 }{ 8 }\)

(ii) 13\(\frac { 1 }{ 3 }\) and 1\(\frac { 1 }{ 8 }\)

(iii) \(\frac { -7 }{ -20 }\) and \(\frac { 5 }{ -14 }\)

Solution:

Question 3.

Verify the following and name the property also:

Solution:

Question 4.

Find the multiplication inverse of the following:

Solution:

Multiplication inverse of:

Question 5.

Using the appropriate properties of operations of rational numbers, evaluate the following:

Solution:

Question 6.

If p = \(\frac { -8 }{ 27 }\), q = \(\frac { 3 }{ 4 }\) and r = \(\frac { -12 }{ 15 }\), then verify that

(i) p × (q × r) = (p × q) × r

(ii) p × (q – r) = p × q – p × r

Solution:

Question 7.

Fill in the following blanks:

(ix) The reciprocal of 0 is …….

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

(xi) If y be the reciprocal of x, then the reciprocal of y^{2} in terms of x will be ………

(xii) The product of a non-zero rational number and its reciprocal is ………

(xiii) The reciprocal of a negative rational number is ………..

Solution:

(ix) The reciprocal of 0 is not defined.

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

(xi) If y be the reciprocal of x, then the reciprocal of y2 in terms of x will be x2.

(xii) The product of a non-zero rational number and its reciprocal is 1.

(xiii) The reciprocal of a negative rational number is a negative rational number.

Question 8.

If \(\frac { 4 }{ 5 }\) the multiplicative inverse of -1\(\frac { 1 }{ 4 }\) ? Why or why not?

Solution:

No, multiplication inverse of \(\frac { 4 }{ 5 }\) is \(\frac { 5 }{ 4 }\) not \(\frac { -5 }{ 4 }\)

Question 9.

Using distributivity, find

Solution:

Question 10.

Find the sum of additive inverse and multiplicative inverse of 9.

Solution:

Additive inverse of 9 = -9

Multiplicative inverse of 9 = \(\frac { 1 }{ 9 }\)

Question 11.

Find the product of additive inverse and multiplicative inverse of \(\frac { -3 }{ 7 }\)

Solution: