This document contains solutions to problems involving additive inverses, multiplicative inverses, and reciprocals of rational numbers. It verifies properties such as -(-x)=x and finds multiplicative inverses. It identifies the rational number with no reciprocal as 0 and those equal to their reciprocals as 1 and -1. It also fills in blanks about properties of reciprocals and inverses of rational numbers.

1. Write the additive inverse of each of the
following

3.  Verify that – (-x) = x for:
(i) x= 11/15 (ii) x =-13/17
Solution:

4.  Find the multiplicative inverse
of the following:

6.  Name the property under multiplication used
in each of the following:

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

8.  Multiply 6/13 by the reciprocal of -7/16

9.  Tell what property allows you to compute.
 Solution:
Associative property of multiplication over
rational numbers allows us to compute :

10.  Is 9/8 the multiplicative inverse of – 9/8 ?
Why or why not?
 No, is not the multiplicative inverse of
 -9/8 .
Because .

11.  Is 0.3 the multiplicative inverse of 10/3 ? Why
or why not?
Solution:Yes, 0.3 is multiplicative inverse of
10/3 .
Because .


12.  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.

13.  Fill in the blanks :
(i) Zero has ……………. reciprocal.
(ii) The numbers ……………. and ………. are their own
reciprocals.
(iii) The reciprocal of – 5 is …………….
(iv) Reciprocal of1/x , where x≠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) -1/5
(iv) x,
(v) rational number,
(vi) positive.

