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)`