**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.