Question

Simplify the given fraction $\dfrac{{10}}{{20}}$?

Answer 1

For solving fraction with two numbers or variables the best optimum way is to find the highest common factors of both the number or variables of the fraction and then simplify it to the least possible term such that no more possible reduction is possible after reduction.

Formulae Used: Finding HCF of both the numbers then divide it to make the lowest possible outcome finally. Highest common factor can be obtained by getting factors.

Complete step by step solution: For the given fraction $\dfrac{{10}}{{20}}$
Let's find the highest common factors of the two numbers given that is $10\,and\,20$
Factors of $10\,$ are $2\,and\,5$
Factors of $20$ are $2\,,\,2\,and\,5$
Here highest common factor is 5
Dividing with the highest common factor we get,

$$= \dfrac{{\dfrac{{10}}{5}}}{{\dfrac{{20}}{5}}} \\\ = \dfrac{2}{4} \\\$$

Now for the obtained fraction above highest common factors is $2$
Now dividing with this highest common factor we get the simplest fraction that is:

$$= \dfrac{{\dfrac{2}{2}}}{{\dfrac{4}{2}}} \\\ = \dfrac{1}{2} \\\$$

Hence the required simplest fraction for the above fraction is $\dfrac{1}{2}$.

Additional Information: In dividing the term by the HCF of both terms you should take care that both the terms are being divided every time you use the division, and the final outcome of any fraction is the least fraction that can be obtained.

Note: The fraction terms are obtained when the last possible division without making to decimal is completed, now the lowest fraction term can be written as in fraction or you can also
write in decimal terms after reduction of the last smallest fraction, fraction can be of two type rational and irrational.