Question

How do you write the fraction \[\dfrac{{18}}{{54}}\] in the simplest form?

Answer 1

Hint: The given question involves the operation of addition/ subtraction/ multiplication/ division. We need to know how to find the greatest common factor between the numerator and the denominator. Also, we can multiply or divide any number with a numerator as the same as the denominator.

Complete step-by-step answer:
The given question is shown below,
 \[\dfrac{{18}}{{54}}\] =?
To simplify the above-mentioned fraction term we have to find the greatest common factor between the numerator and the denominator. Let’s see the definition of the greatest common factor. If the denominator and numerator, divided by the same term which is called a common factor. The greatest value among the common factors is called the greatest common factor. If we see the numerator we have \[18\] , which can be divided by \[1,2,3,6,9\;and\;18\] . In the denominator we have \[24\] which is divided by \[1,2,3,4,6,9,18, 27\;and\;24\] . By comparing the numerator’s dividing factor and denominator’s dividing factor the term \[18\] is common in the numerator and denominator. Also, the greatest common factor of the given fraction term is \[18\] .
Let’s divide the numerator and denominator by \[18\] . So, we get
 \[\dfrac{{18}}{{54}} = \left( {\dfrac{{\dfrac{{18}}{18}}}{{\dfrac{{54}}{18}}}} \right) = \dfrac{1}{3}\]
So, the simplified form of the given fraction is \[\dfrac{1}{3}\] .
So, the correct answer is “ \[\dfrac{1}{3}\] ”.

Note: In this type of question we would involve the operation of addition/ subtraction/ multiplication/ division. Note that we would find the greatest common factor between the numerator and the denominator. While finding the greatest common factor we shouldn’t take \[1\] it as the greatest common factor, because due to this we didn’t get the simplified form of a given question. Note that the denominator value would not be equal to zero.