# Rational Numbers

## Key Concept

Any number which can be expressed in the form of p/q, or number in the form of p/q; where q ≠ 0 is called rational number.

For example: 1/2, 2/3, -3/4, etc.

Since, q can be equal to 1, thus, all integers can be expressed in the form of p/q, hence, all integers are also rational number.

As, 0 (zero) is also an integer, hence, 0 (zero) is also rational number.

### NCERT Exercise 1.1 (Part 1)

Question 1: Using appropriate properties find;

(i) -2/3xx3/5+5/2-3/5xx1/6

Solution: Given, -2/3xx3/5+5/2-3/5xx1/6

=-2/3xx3/5-3/5xx1/6+5/2

(Using commutativity)

=3/5(-2/3-1/6)+5/2

(Using distributivity)

=3/5((-4-1)/(6))+5/2

=3/5(-5/6)+5/2

=3/5xx(-5)/(6)+5/2

=-3/6+5/2=(-3+15)/(6)

=(12)/(6)=2

(ii) 2/5xx(-3)/(7)-1/6xx3/2+(1)/(14)xx2/5

Solution: Given, 2/5xx(-3)/(7)-1/6xx3/2+(1)/(14)xx2/5

Using commutative property, we get

=2/5xx(-3)/(7)+(1)/(14)xx2/5-1/6xx3/2

Using distributive property, we get

=2/5(-3/7+(1)/(14))-1/6xx3/2

=2/5((-6+1)/(14))-1/6xx3/2

=2/5xx(-5)/(14)-1/6xx3/2

=-1/7-1/4

=(-4-7)/(28)=-(11)/(28)

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

(i) 2/8

Solution: Since, 2/8+(-2/8)

=2/8-2/8=0

So, additive inverse of 2/8 is -2/8

(ii) -5/8

Solution: Since, -5/9+5/9=0

So, additive inverse of -5/9 is 5/9

(iii) (-6)/(-5)

Solution: (-6)/(-5)=6/5

Since, 6/5+(-6/5)=0

So, additive inverse of 6/5 is -6/5

(iv) (2)/(-9)

Solution: Since, (2)/(-9)+2/9=0

So, additive inverse of (2)/(-9) is 2/9

(v) (19)/(-6)

Solution: Since, (19)/(-6)+(19)/(6)=0

So, additive inverse of (19)/(-6) is (19)/(6)