Consider the following rational numbers.
Are these rational numbers representing the same rational number?
Yes, let us see how.
Notice that4 is common in the numerator and denominator of
, we can write 
Similarly, 3 is common in the numerator and denominator of 
Therefore, we can write 
We can observe that all the three given rational numbers when simplified resulted in the same rational number i.e
. Thus, we can say that the given rational numbers are equivalent rational numbers. The number is the standard form of the given numbers.
Now, a question arises. What is the standard form of rational numbers?
Standard form can be defined as follows.
“A rational number is in standard form, if the denominator is a positive integer and the only common factor between the numerator and the denominator is 1.” |
Let us consider the rational numbers
.
Can we say whether they are in the standard form or not?
We can observe that in, the denominators are positive integers and the common factor between the numerator and denominator in each of them is 1.
Therefore, are in standard form.
Any rational number that is not in the standard form can be reduced to the standard form by following a simple rule which is as follows.
“If a rational number is not in standard form, then it can be reduced to the standard form by dividing the numerator and the denominator by their highest common factor (H.C.F.).” |
