Question

How do you simplify $\dfrac{1}{2} + \dfrac{2}{3} + \dfrac{3}{4}?$

Answer 1

Hint: For solving such types of questions first we will find the least common multiple of all denominators.
After that, we will multiply all the terms by LCM.

Complete step by step answer:
For finding a solution to this question we will first find the Least common multiple of all denominators.
Here, LCM of $2,3{\text{ and 4}}$is $12$
Now, in the first term if we want $12$ in the denominator so we have to multiply and divide the first term by $6$.
So, after multiplying and dividing the first term by $6$we get,
$ \Rightarrow \dfrac{1}{2} \times \dfrac{6}{6}$
So, the first term will become $\dfrac{6}{{12}}$
Now, in the second term if we want $12$ in the denominator so we have to multiply and divide the second term by $4$.
So, after multiplying and dividing the first term by $4$we get,
$ \Rightarrow \dfrac{2}{3} \times \dfrac{4}{4}$
So, the first term will become $\dfrac{8}{{12}}$
Now, in the third term if we want $12$ in the denominator so we have to multiply and divide the third term by $3$.
So, after multiplying and dividing the first term by $3$we get,
$ \Rightarrow \dfrac{3}{4} \times \dfrac{3}{3}$
So, first term will become $\dfrac{9}{{12}}$
Now, add this all terms,
$
   \Rightarrow \dfrac{6}{{12}} + \dfrac{8}{{12}} + \dfrac{9}{{12}} \\
   \Rightarrow \dfrac{{6 + 8 + 9}}{{12}} \\
   \Rightarrow \dfrac{{23}}{{12}} \\
$

Answer of these question is $\dfrac{{23}}{{12}}$

Note:
This type of question is very basic. You should solve as many questions as you can because this will help you in the future to solve other difficult questions. Try to solve directly after that use this calculation.