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Learn Exercise 1.1 with Free Lessons & Tips

Find the multiplicative inverse of the following.

(i)  (ii)  (iii) 

(iv)  (v)  (vi) −1

(i) −13

Multiplicative inverse = −

(ii)

Multiplicative inverse =

(iii)

Multiplicative inverse = 5

(iv)

Multiplicative inverse

(v)

Multiplicative inverse

(vi) −1

Multiplicative inverse = −1

 

Comments

Write the additive inverse of each of the following:

(i)  (ii)  (iii)  (iv)  (v) 

(i)

Additive inverse =

(ii)

Additive inverse =

(iii)

Additive inverse =

(iv)

Additive inverse

(v)

Additive inverse

 

Comments

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

(i) 

(ii) 

(iii) 

(i) 1 is the multiplicative identity for rational numbers.

If we multiply a rational number with multiplicative identity(1), then the product will be the same rational number itself.

(ii)commutativity 

For any two rational numbers a and b aXb=bXa

(iii)Multiplicative inverse

The product of a rational number and its multiplicative inverse is 1. 

Comments

Multiply by the reciprocal of

reciprocal of  is -.

 X - = - 

Comments

Tell what property allows you to compute

Associative Property

Comments

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

0.3 × = 0.3 ×

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

Comments

Write:

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

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

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

(i) 0 is a rational number but its reciprocal is not defined.

(ii) 1 and −1 are the rational numbers that are equal to their reciprocals.

(iii) 0 is the rational number that is equal to its negative.

Comments

Fill in the blanks.

(i) Zero has __________ reciprocal.

(ii) The numbers __________ and __________ are their own reciprocals

(iii) The reciprocal of − 5 is __________.

(iv) Reciprocal of, where is __________.

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

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

(i) No

(ii) 1, −1

(iii)

(iv) x

(v) Rational number

(vi) Positive rational number

Comments

Using appropriate properties find:

(i) 

(ii) 

(i)

(ii)

(By commutativity)

 

Comments

Verify that −(−x) = x for.

(i)  (ii) 

(i)x= 

 + - =0 

additive inverse of x=-

that is -x=- 

from  + - =0, we can find that additive inverse of - is 

that is -(-) = 

that is -(-x)=x

(ii)

x= -

 + - =0 

additive inverse of x= 

that is -x=

from + - =0, we can find that additive inverse of  is -

that is -() = -

that is -(-x)=x

Comments

Is the multiplicative inverse of? Why or why not?

-1 1/8=(-8+1)/8=-7/8

8/9*-7/8=-7/9 is not equal to 1. hence not the multiplicative inverse

Comments

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