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How do you write \[\dfrac{{30}}{{50}}\] into simplest form?

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Last updated date: 16th Jun 2024
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Answer
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Hint: The above question is based on the concept of how to reduce the fraction into its simplest forms. By reducing into simplest form 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 or simplest 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 simplest terms involves the division operation.Before division, we need to break down the number into its factors. So, the numerator 30 and the denominator 50 can be written as
\[
30 = 3 \times 10 \\
\Rightarrow 50 = 5 \times 10 \]
On breaking down the numbers we get the factors. Further we divide the factors we get,
\[\dfrac{{30}}{{50}} = \dfrac{{3 \times 10}}{{5 \times 10}}\]
In the next step we need to cross out the common factors. In this fraction 10 is the common number present in numerator and denominator and on cancelling this number we are left with 3 in the numerator and 5 in the denominator.
\[\therefore\dfrac{{30}}{{50}} = \dfrac{3}{5}\]
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 30 and 50 is 10.So,dividing it with the numerator and denominator we get the same lowest fraction.