Question

How do you simplify \[\dfrac{3}{4} + \dfrac{5}{6}\] ?

Answer 1

Hint: Given are the two fractions written with different denominators. In that case we take the LCM first and then add the fractions. Finding LCM is nothing but cross multiplying the terms. Then the fraction so obtained should be written in simplest form. That is if the numerator and denominator have a common factor, divide them by it and rewrite the fresh simplest fraction.

Complete step-by-step solution:
Given that,
\[\dfrac{3}{4} + \dfrac{5}{6}\]
On taking the LCM,
\[ \Rightarrow \dfrac{{3 \times 6 + 5 \times 4}}{{4 \times 6}}\]
Now on multiplying we get,
\[ \Rightarrow \dfrac{{18 + 20}}{{24}}\]
On adding we get,
\[ \Rightarrow \dfrac{{38}}{{24}}\]
This is the fraction so obtained but it is not in the simplest form. That this can be further divided by 2. So on dividing we get,
\[ \Rightarrow \dfrac{{19}}{{12}}\]
Now this fraction is in simplest form since 12 and 19 do not have any common factor. So this is our answer.

Thus the correct answer is \[\dfrac{{19}}{{12}}\].

Note: Note that we cannot directly add or subtract the terms because if the denominators of the terms or fractions are different.
\[\dfrac{a}{b} + \dfrac{c}{d} = \dfrac{{a + c}}{{b + d}} \times \] this is not correct way.
So, we need to take the LCM. Like we did in the case above.
Rather if the terms had same denominator we can proceed very simply like,
\[\dfrac{a}{b} + \dfrac{c}{b} = \dfrac{{a + c}}{b}\]