Rational Numbers

Question 1.
Using appropriate properties find.

Solution:

Question 2.
Write the additive inverse of each of the following:

Solution:

Question 3.
Verify that – (-x) = x for:
(i) 
(ii) .

Solution:

Question 4.
Find the multiplicative inverse of the following:

Solution:

Question 5.
Name the property under multiplication used in each of the following:

Solution:
(i) Existence of multiplicative identity.
(ii) Commutative property of multiplication.
(iii) Existence of multiplicative inverse.

Question 6.
Multiply  by the reciprocal of .

Solution:

Question 7.
Tell what property allows you to compute.

Solution:
Associative property of multiplication over rational numbers allows us to compute :

Question 8.
Is  the multiplicative inverse of – 1 ? Why or why not?

Solution:
No,  is not the multiplicative inverse of -1 .
Because .

Question 9.
Is 0.3 the multiplicative inverse of 3? Why or why not?

Solution:
Yes, 0.3 is multiplicative inverse of 3.
Because .

Question 10.
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.

Solution:
(i) We know that there is no rational number which when multiplied with 0, gives 1. Therefore, the rational number 0 has no reciprocal.
(ii) We know that the reciprocal of 1 is 1 and the reciprocal of -1 is -1. 1 and -1 are the only rational numbers which are their own reciprocals.
(iii) The rational number 0 is equal to its negative.

Question 11.
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 ≠0 is ………
(v) The product of two rational numbers is always a ………….
(vi) The reciprocal of a positive rational number is ………..

Solution:
(i) No,
(ii) 1, -1,
(iii) 
(iv) x,
(v) rational number,
(vi) positive.