Question

What is $ \dfrac{{27}}{{63}} $ expressed in lowest terms?

Answer 1

Hint: As we know that the above question is based on the concept of how to reduce the fraction into its lowest terms. By reducing its lowest terms means finding equivalent numbers in which the numerator and denominator should be as small as possible. We will break down the numerators and denominators into their factors and then we reduce them to their lowest terms.

Complete step by step solution:
A fraction is said to be in lowest terms, if its numerator and denominator are relatively prime numbers which means that they have no common factors left other than $ 1 $ .
Here we have $ \dfrac{{27}}{{63}} $ . We can break the numerator $ 27 $ into its factors,
$ 27 = 3 \times 3 \times 3 $ .
We will now write the denominator as a product of its prime factors i.e. $ 63 = 3 \times 3 \times 7 $ .
By putting them back in the fractions we can write
$ \dfrac{{27}}{{63}} $ $ = \dfrac{{3 \times 3 \times 3}}{{3 \times 3 \times 7}} $ .
Now we will cancel out the common factors and it gives the value $ \dfrac{3}{7} $ .
Hence $ \dfrac{3}{7} $ is the lowest form of the given fraction.
So, the correct answer is “ $ \dfrac{3}{7} $ ”.

Note: We can solve the above question with an alternative way by calculating the greatest common factor (GCF) or we can say highest common factor (HCF). The HCF of $ 27 $ and $ 63 $ is $ 9 $ , so dividing it with the numerator and denominator we get the same lowest fraction as above. We can write it as $ \dfrac{{27 \div 9}}{{63 \div 9}} = \dfrac{3}{7} $