Question

How do you reduce \[\dfrac{6}{9}\] to lowest terms?

Answer 1

Hint:The above question is based on the concept of how to reduce the fraction into its lowest terms. By reducing into lowest terms means finding equivalent numbers in which the numerator and denominator should be as small as possible.

Complete step by step solution:
A fraction is said to be in lowest form, if its numerator and denominator are relatively prime numbers which means that they have no common factors left other than 1.

Even if fractions in the original and reduced form look different, they can actually represent the same amount; in other words, one of the fractions will have reduced terms compared to the other. Reducing fractions to its lowest terms involves the operation division.

Before division, we need to break down the number into its factors. So, the numerator 6 and the denominator 9 can be written as
\[
6 = 2 \times 3 \\
9 = 3 \times 3 \\
\]
On breaking down the numbers we get the factors. Further we divide the factors we get,
\[\dfrac{6}{9} = \dfrac{{2 \times 3}}{{3 \times 3}}\]

In the next step we need to cross out the common factors. In this fraction 3 is the common number present in numerator and denominator and on cancelling this number we are left with 2 in the numerator and 3 in the denominator.
\[\dfrac{6}{9} = \dfrac{2}{3}\]

Therefore, we get the above fraction in lowest form.

Note: An alternative method to solve this is by calculating the Greatest common factor of both the numerator and denominator. The GCF of 6 and 9 is 3.So,dividing it with the numerator and denominator we get the same lowest fraction.