Division of Rational Number
Kiran is sitting with her five friends in a restaurant.
They order a big pizza and divide it among themselves equally.
Everyone get one sixth of a pizza, means
part of one pizza.
This can be written as each of them got
Meanwhile, two more friends of Kiran came there and Kiran shared her pizza with them equally.
Which means Kiran shared her own share in three equal parts.
Now she wanted to know how much part of pizza is she having.
Let us see how can we find her share in fraction. This can be done through division, so let us learn it.
Let’s understand the division operation of Rational Number.
Suppose we are given a rational number.
And if we divide this rational number by itself, we get
When we divide a rational number by another rational number, It means we multiply a rational number by the reciprocal of the other.
Now, we perform division of rational number with its reciprocal.
Further, we may simplify it as
Thus we have seen that the division of a rational number by its reciprocal, is multiplying by itself.
Let’s take another example
The above 2 fractions can be now divided as such
Let us understand division of rational number with negative rational number
Suppose we are given two rational numbers as
Division operation of rational number and negative rational number.
Solve this by ignoring the negative sign, we get
Then, put the negative sign before the result and that will be our answer
Now let’s get back to our pizza problem.
We divided the pizza in
equal pieces to distribute among six friends.
Kiran will divide his own piece as
Thus we conclude that the division of one rational number by another is multiplication of rational number by the reciprocal of the other.
Division of one rational number by other non zero rational number is its multiplication by the reciprocal of other.