Question

Simplify \[\left( \dfrac{2}{3} \right)+\left( \dfrac{5}{6} \right)-\left( \dfrac{1}{9} \right)\] ?

Answer 1

Hint: Problems like these are pretty simple in nature and are very easy to solve. It requires some basic knowledge of fractions, rational and irrational fractions. Once we understand the underlying concepts behind the problem, solving such questions wouldn’t be difficult. Here in this problem, we simply need to find the least common multiple or commonly known as LCM of the denominator of the fractions in the given question and then add them or subtract them accordingly. In cases where a fraction is not given in its simplest form, we must cancel the common terms, write it down in its simplest form and then solve the problem accordingly.

Complete step by step answer:
Now we start off with the solution to the above given problem by first trying to find out the least common multiple of the denominator of the given fractions. We can see that both \[6,9\] are multiples of \[3\] . So, we can ignore the contribution of \[3\] . Now, \[9\] is not divisible by \[6\] . This means that we have to examine their multiples. \[9\times 2=18\] and \[6\times 3=18\] . So we can easily say that, \[18\] is the LCM of the denominator of the fractions. Now writing this on the denominator we write the numerator of the corresponding fractions as,
\[\dfrac{12+15-2}{18}\] .
Now we do the necessary additions and subtractions in the given problem to find out the answer as,
\[\dfrac{25}{18}\] .
So our desired result is \[\dfrac{25}{18}\] . This fraction cannot be further simplified, hence this is our final answer.

Note: In problems like these we need to have some basic knowledge of fractions or else we would not be able to solve the problem. We must be very careful while we find the LCM of the denominator of all the given fractions as it is prone to mistakes. We should also carefully see whether our formed answer can be simplified further or not. If it can be simplified further, we need to cancel all the like terms and then form our desired answer.