Question

How do you change $\dfrac{{27}}{{36}}$ to simplest form?

Answer 1

Hint:
This is a problem in which the student has to bring the fraction in its simplest form. This can be treated as a problem on the fraction of a problem on ratio. Students can choose to solve the sum taking into consideration either fraction or ratio, as the steps are the same. Firstly the student has to find the greatest common multiple for both the numerator and denominator or the student can also bring both the numbers in their simplest form i.e in terms of prime number multiplication. The second step would be to cancel out the common multiples. This would be the final answer.

Complete Step by Step Solution:
The first step is to bring numerator and denominator in terms of its prime factors.
$\dfrac{{27}}{{36}} = \dfrac{{3 \times 3 \times 3}}{{3 \times 3 \times 4}}..........(1)$
From the above step, we can see that the fraction has the greatest common multiple $9$. Striking off the common multiple we get the fraction in its simplest form.
$\dfrac{{27}}{{36}} = \dfrac{3}{4}.........(2)$

Thus, the simplest form of the fraction is $\dfrac{3}{4}$

Note:
The only important step in this sum is to bring the fraction in terms of its prime factors. Sometimes when the complicated sum like $\dfrac{9}{4} \times \dfrac{{16}}{3} \times \dfrac{{20}}{5}$it is advisable that the student first cancels out common terms and then with the terms remaining he/she should reduce it to the prime factors.