Question

Express \[\dfrac{90}{216}\] as a rational number with numerator 5?

Answer 1

Hint: To convert \[\dfrac{90}{216}\] to a rational number with numerator 5, we need to divide the numerator of a fraction by the denominator of a fraction and then see look for the common numbers. In fraction, the numerator is the number which is written above the fraction and denominator is the number which is written below the fraction. Here, we find that 3 and 2 is common in the numerator and denominator. Cancel the common terms until we get 5 in the numerator and the numerator and denominators are prime numbers.

Complete step by step solution:
The number which is given in the above problem of which we have to express as a rational number with numerator 5 is as follows:
\[\dfrac{90}{216}\]
As per the definition of rational number, the number expressed in the form \[\dfrac{p}{q}\], where p and q do not have a common term and \[q\ne 0\].
In the given fraction, there are common terms.
Here, 3 is a common term.
\[\Rightarrow \dfrac{90}{216}=\dfrac{30\times 3}{72\times 3}\]
Let us now cancel 3 from the numerator and denominator. We get
\[\dfrac{90}{216}=\dfrac{30}{72}\]
Here, we find that 2 are divisible by both the numerator and denominator.
\[\Rightarrow \dfrac{90}{216}=\dfrac{15\times 2}{36\times 2}\]
Cancelling 2 from the numerator and denominator, we get
\[\dfrac{90}{216}=\dfrac{15}{36}\]
Now, on observing the fraction, we find that 15 and 36 are the multiples of 3.
Therefore, we can write the expression as
\[\dfrac{90}{216}=\dfrac{5\times 3}{12\times 3}\]
Let us now cancel 3 from the numerator and denominator.
\[\Rightarrow \dfrac{90}{216}=\dfrac{5}{12}\]
Here, we find that the simplified fraction does not have a common factor.
And as per the question, we have converted the fraction into a rational number with numerator 5.

Therefore, \[\dfrac{5}{12}\] is the required rational number with numerator 5.

Note: Whenever we get this type of problem, we have to look for the common terms in the numerator and denominator. Here, we can also take 9 as the common term from the numerator and denominator and cancel them out. This can reduce the number of steps in the solution. We never get 0 in the denominator of a rational number. Before writing the final answer, check for any common terms in the numerator and denominator.