Question

How do you simplify the fraction \[\dfrac{{27}}{{54}}\]?

Answer 1

Hint: Fractions represent equal parts of a whole or a collection. To find a fraction of a fraction, the first step is to multiply the numerators together to find the numerator of the answer and then we need to multiply the denominators together to find the denominator of the answer, hence in this way we can simplify the fraction of given numbers.

Complete step-by-step solution:
 Given, \[\dfrac{{27}}{{54}}\]
Which we need to simplify the given fraction.
To simplify the fraction, consider the common factors of the \[\dfrac{{numerator}}{{deno\min ator}}\] and cancel them.
That is 27 and 54 have a common factor of 27 and thus can be cancelled by dividing both by 27 i.e.,
\[\dfrac{{27}}{{54}}\]
\[ \Rightarrow \]\[\dfrac{1}{2}\]
A slightly longer approach is to cancel by the lowest common factor which is 3 and repeat the process as:
\[\dfrac{{27}}{{54}}\]
\[ \Rightarrow \]\[\dfrac{9}{{18}}\]
Simplify, as there are common factors i.e.,
\[\dfrac{9}{{18}} = \dfrac{3}{6}\]
Then on further simplification we get
= \[\dfrac{1}{2}\]
Therefore, the fraction \[\dfrac{{27}}{{54}}\] is \[\dfrac{1}{2}\].

Hence, it is the simplest form of fraction. The fraction is said to be in simplest form when no other factor but 1 will divide into \[\dfrac{{numerator}}{{deno\min ator}}\].

Note: The key point to solve the fractions is that we must make sure that the bottom numbers (the denominators) are the same while evaluating the fraction sums. We have a top number, the numerator, and a bottom number, the denominator. Add the top numbers (the numerators), put that answer over the denominator. Simplifying the fraction (if needed) and fraction of a whole is when we divide a whole into equal parts, each part is a fraction of the whole.