### EXERCISE 1.1

Question 1

Using appropriate properties find .

(i)

sol :

= 2

(ii)

sol :

Question 2 :

Write the additive inverse of each of the following :

(i)

sol :

Additive inverse=

(ii)

sol :

Additive inverse=

(iii)

sol :

Additive inverse=

(iv)

sol :

Additive inverse=

(v)

sol :

Additive inverse =

Question 3 :

Verify that -(-x)=x for

(i)

sol :

The additive inverse of is as

This equality represents that the additive inverse of is or it can be said that i.e., -(-x)=x

(ii)

sol :

The additive inverse of is as

This equality represents that the additive inverse of is or it can be said that i.e., -(-x)=x

Question 4 :

Find the multiplicative inverse of the following.

(i) -13

sol :

Multiplicative inverse =

(ii)

sol :

Multiplicative inverse =

(iii)

sol :

Multiplicative inverse =5

(iv)

sol :

Multiplicative inverse =

(v)

sol :

Multiplicative inverse =

(vi) -1

sol :

Multiplicative inverse =-1

Question 5 :

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

(i)

sol : 1 is a multiplicative identity.

(ii)

sol : Commutativity

(iii)

sol : Multiplicative inverse

Question 6 :

Multiply by the reciprocal of .

sol :

*** QuickLaTeX cannot compile formula: \\=\dfrac{6}{13}\times\Bigg(Reciprocal~of~-\dfrac{7}{16}\Bigg)\\=\dfrac{6}{13}\times-\dfrac{16}{7}\\=-\dfrac{96}{91} *** Error message: Missing $ inserted.

Question 7 :

Tell what property allow you to compute

as

sol : Associativity

Question 8 :

Is the multiplicative inverse of ?Why or why not ?

sol : If it is the multiplicative inverse , then the product should be 1. However, here the product is not 1 as

Question 9 :

Is 0.3 the multiplicative inverse of ? Why or Why not ?

sol :

*** QuickLaTeX cannot compile formula: \\=3\dfrac{1}{3}=\dfrac{10}{3}\\=0.3\times3\dfrac{1}{3}=0.3\times\dfrac{10}{3}\\=\dfrac{10}{3}\times\dfrac{3}{10}\\=1 *** Error message: Missing $ inserted.

Here is the product is 1 . Hence , 0.3 is the multiplicative inverse of

Question 10 :

Write :

(i) The rational number that does not have a reciprocal .

sol : 0 is a rational number but its reciprocal is not defined.

(ii) The rational numbers that are equal to their reciprocals .

sol : 1 and -1 are the rational numbers that are equal to their reciprocals .

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

sol : 0 is the rational number that is equal to its negative.

Question 11 :

Fill in the blanks.

(i) Zero has No reciprocal.

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

(iii) The reciprocal of -5 is

(iv) Reciprocal of , where

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

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