## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 1 Rational Numbers Check Your Progress

Question 1.

Evaluate the following:

Solution:

Question 2.

What number should be added to \(\frac { -4 }{ 11 }\) to get \(\frac { -3 }{ 8 }\)?

Solution:

Required number = \(\frac { -3 }{ 8 }\) – (\(\frac { -4 }{ 11 }\))

Question 3.

What rational number should be subtracted from the sum of \(\frac { 3 }{ 14 }\) and \(\frac { -4 }{ 7 }\) to get \(\frac { 13 }{ 21 }\)?

Solution:

Question 4.

If the product of two rational numbers is \(\frac { 25 }{ 42 }\) and one of them -2\(\frac { 6 }{ 7 }\), find the other.

Solution:

Question 5.

Divide the sum of \(\frac { 4 }{ 13 }\) and \(\frac { -3 }{ 2 }\) by their product.

Solution:

Question 6.

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

Solution:

Question 7.

Find the additive inverse of the following:

(i) -13\(\frac { 7 }{ 8 }\)

(ii) 4\(\frac { 3 }{ 6 }\)

Solution:

(i) Additive inverse of -13\(\frac { 7 }{ 8 }\) is 13\(\frac { 7 }{ 8 }\).

(ii) Additive inverse of 4\(\frac { 3 }{ 6 }\) is -4\(\frac { 3 }{ 6 }\).

Question 8.

Find the multiplicative inverse of the following:

(i) \(\frac { -23 }{ 46 }\)

(ii) 0

Solution:

(i) Multiplicative inverse of \(\frac { -23 }{ 46 }\) is \(\frac { -46 }{ 23 }\) = -2.

(ii) Multiplicative inverse of 0 is not defined.

Question 9.

Represent the following rational numbers on the number line:

(i) \(\frac { -3 }{ 11 }\)

(ii) \(\frac { 5 }{ 17 }\)

Solution:

Question 10.

Insert five rational numbers between \(\frac { -3 }{ 7 }\) and \(\frac { 2 }{ 5 }\)

Solution:

5 rational numbers between \(\frac { -3 }{ 7 }\) and \(\frac { 2 }{ 5 }\)

LCM of 7, 5 = 35

Question 11.

If p = \(\frac { -4 }{ 9 }\) , q = \(\frac { 2 }{ 3 }\) and r = \(\frac { -8 }{ 11 }\), then verily the foflowing:

(i) p + (q + r) = (p + q) + r

(ii) p × q = q × p

(iii) p × (q + r) = p × q + p × r

(iv) (p + q) ÷ r = p ÷ r + q ÷ r.

Solution:

Question 12.

A wedding cake weighed 8 kg. If \(\frac { 2 }{ 5 }\) th of its weight was flour, \(\frac { 5 }{ 16 }\) th was sugar, \(\frac { 1 }{ 4 }\) thwas cream and the rest were nuts, find the weight of nuts.

Solution:

Weight of a wedding cake = 8 kg

Weight of Hour in it = \(\frac { 2 }{ 5 }\) th of 8 kg = \(\frac { 16 }{ 5 }\) kg