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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:

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 y² 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:

Question 8.
If \(\frac { 4 }{ 5 }\) the multiplicative inverse of -1\(\frac { 1 }{ 4 }\) ? Why or why not?
Solution:

Question 9.
Using distributivity, find

Solution:

Question 10.
Find the sum of additive inverse and multiplicative inverse of 9.
Solution:

Question 11.
Find the product of additive inverse and multiplicative inverse of \(\frac { -3 }{ 7 }\)
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 1 Rational Numbers Ex 1.2

Question 1.
Subtract:

Solution:

Question 2.
Sum of two rational numbers is \(\frac { 3 }{ 5 }\). If one of them is \(\frac { -2 }{ 7 }\), find the other.
Solution:

Question 3.
What rational number should be added to \(\frac { -5 }{ 11 }\) to get \(\frac { -7 }{ 8 }\)?
Solution:

Question 4.
What rational number should be subtracted from -4\(\frac { 3 }{ 5 }\) to get -3\(\frac { 1 }{ 2 }\) ?
Solution:

Question 5.
Subtract the sum of \(\frac { -5 }{ 7 }\) and \(\frac { -8 }{ 3 }\) from the sum of \(\frac { 5 }{ 2 }\) and \(\frac { -11 }{ 12 }\).
Solution:

Question 6.
If x = \(\frac { -4 }{ 7 }\) and y = \(\frac { 2 }{ 5 }\), then verify that x – y ≠ y – x.
Solution:

Question 7.
If x = \(\frac { 4 }{ 9 }\), y = \(\frac { -7 }{ 12 }\) and z = \(\frac { -2 }{ 3 }\), then verify that x – (y – z) ≠ (x – y) – z
Solution:

Question 8.
Which of the following statement is true/fasle?
(i) \(\frac { 2 }{ 3 } -\frac { 4 }{ 5 }\) is not a rational number.
(ii) \(\frac { -5 }{ 7 }\) is the additive inverse of \(\frac { 5 }{ 7 }\).
(iii) 0 is the additive inverse of its own.
(iv) Commutative property holds for subtraction of rational numbers.
(v) Associative property does not hold for subtraction of rational numbers.
(vi) 0 is the identity element for subtraction of rational numbers.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 1 Rational Numbers Ex 1.1

Question 1.
Add the following:

Solution:

Question 2.
Simplify:

Solution:

Question 3.
Verify commutative property of addition for the following pairs of rational numbers:

Solution:

Question 4.
Find the additive inverse of the following rational numbers:
(i) \(\frac { 2 }{ -3 }\)
(ii) \(\frac { -7 }{ -12 }\)
Solution:

Question 5.
Verify that -(-x) = x for
(i) x = \(\frac { 10 }{ 13 }\)
(ii) x = \(\frac { -15 }{ 17 }\)
Solution:

Question 6.
Using appropriate properties of addition, find the following:

Solution:

Question 7.
Fill in the following blanks:

Solution:

Question 8.
If a = \(\frac { -11 }{ 27 }\), b = \(\frac { 4 }{ 9 }\) and c = \(\frac { -5 }{ 18 }\), then verify that a + (b + c) = (a + b) + c.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths