Chapter 1: Rational Numbers Exercise – 1.6

Question: 1

Verify the property x × y = y × x by taking:

Solution:

 

Question: 2

Verify the property: x × (y × z) = (x × y) × z

Solution:

We have to verify that, x × (y × z) = (x × y) × z

 

Question: 3

Verify the property:  x × (y × z) = x × y + x × z:

Solution:

We have to verify that, x × (y × z) = x × y + x × z

 

Question: 4

Use the distributivity of multiplication of rational numbers over their addition to simplify:

Solution:

 

Question: 5

Find the multiplicative inverse (reciprocal) of each of the following rational numbers:

Solution:

 

Question: 6

Name the property of multiplication of rational numbers illustrated by the following statements:

Solution:

(i) Commutative property

(ii) Commutative Property

(iii) Distributivity of multiplication over addition

(iv) Associativity of multiplication.

(v) The existence of identity for multiplication.

(vi) Existence of multiplicative inverse

(vii) Multiplication by 0

(viii) Distributive property

 

Question: 7

Fill in the blanks:

(i) The product of two positive rational numbers is always ……………….

(ii) The product of a positive rational number and a negative rational number is always ……………

(iii) The product of two negative rational numbers is always …………………

(iv) The reciprocal of a positive rational number is ……………….

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

(vi) Zero has ………… reciprocal.

(vii) The product of a rational number and its reciprocal is ……………….

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

(ix) If a is reciprocal of b, then the reciprocal of b is …………………

(x) The number 0 is …………. The reciprocal of any number.

(xi) Reciprocal of 1a, a ≠ 0 is …………………

(xii) (17 × 12)^-1 = (17)^-1 ×………

Solution:

(i) Positive

(ii) Negative

(iii) Positive

(iv) Positive

(v) Negative

(vi) No

(vii) 1

(viii) -1 and 1

(ix) a

(x) not

(xi) a

(xii) 12⁻¹

 

Question: 8

Fill in the blanks:

Solution: