Addition of Rational numbers
Raman has two milk cans of
$1Liter$
and
$2Liters$
.
He goes to a milk shop to purchase milk.
He asks the vendor to give half liter in one milk can and half liter in another milk can.
The milkman asks him to pay at the rate of
$Rs50/ltr$
.
He asks him to pay for
$1$
liter.
Raman got confused as to why does he need to pay for
$1$
liter.
Because he was unable to calculate how much liters of milk he purchased.
Letâ€™s show him the concept of adding rational numbers.
Letâ€™s understand the addition operation on rational numbers.
Addition in rational numbers depends on the value of denominators
If the denominators are the same.
Simply add the numerators.
So, while adding the rational numbers with same denominators, we add the numerators keeping the denominators same.
When both the denominators are different.
We first find the
$LCM$
of the two denominators.
Then we find the equivalent rational numbers of the given rational numbers with this LCM as the denominator.
The denominators of both the rational numbers are same now.
We simply add the numerators by keeping the denominator same .
Additive Inverse
Additive inverse of any number is the number which when added to itself gives zero.
Both numbers are additive inverse of each other.
Additive inverse of any rational number is the rational number that when added to the given number gives zero.
In rational numbers also, additive inverse is the same rational number but of
$opposite$
sign.
Now you all know why Raman had to pay for
$1$
liter of milk.
Revision
While adding two rational numbers, we try to make the denominators same.
While adding two rational numbers, we try to make the denominators same.
Then simply add the numerators and denominator remains unchanged.
The End