Question

Simplify $\left( {\dfrac{3}{8}} \right) + \left( {\dfrac{1}{6}} \right).$

Answer 1

Hint:In order to add two fractions the denominator of those two fractions should be the same. So to add two fractions with unlike denominators, we first have to make the denominator of those two fractions same and then simply add them.The denominator of two unlike fractions can be made same or equal by taking the LCM of the two denominators and converting the two fractions into fractions with that denominator.

Complete step by step answer:
Given $\left( {\dfrac{3}{8}} \right) + \left( {\dfrac{1}{6}} \right).............................\left( i \right)$
So our two denominators are 8 and 6. We can see that these are two fractions with unlike denominators. So to add these two fractions we have to make the both denominators similar.For that we have to take the LCM of both the denominators.Such that:
\[{\text{LCM}}\left( {8,6} \right) = 24.\]
Now we know \[{\text{LCM}}\left( {8,6} \right) = 24\] such that we have to convert the given fractions into fractions with denominator 24 without hanging its value.

So converting$\left( {\dfrac{3}{8}} \right)$:
We can see that in order to make its denominator 24 we have to multiply the numerator and denominator with 3 such that in overall the value remains the same.
$\dfrac{3}{8} = \dfrac{{3 \times 3}}{{8 \times 3}} = \dfrac{9}{{24}}................\left( {ii} \right)$
Now converting$\left( {\dfrac{1}{6}} \right)$:
In order to make its denominator 24 we have to multiply the numerator and denominator with 4 such that in overall the value remains the same.
\[ \Rightarrow \dfrac{1}{6} = \dfrac{{1 \times 4}}{{6 \times 4}} = \dfrac{4}{{24}}....................\left( {iii} \right)\]
Now using equation (iii) and (iv) we can rewrite the equation as below:
$\left( {\dfrac{3}{8}} \right) + \left( {\dfrac{1}{6}} \right) = \dfrac{9}{{24}} + \dfrac{4}{{24}}.....................\left( {iv} \right)$
We can see that in (iv) we have fractions with the same denominator and thus it can be added simply using simple addition.
\[
\dfrac{9}{{24}} + \dfrac{4}{{24}} = \dfrac{{9 + 4}}{{24}} \\
\therefore\dfrac{9}{{24}} + \dfrac{4}{{24}} = \dfrac{{13}}{{24}}...................\left( v \right) \\ \]
Therefore our final answer is \[\dfrac{{13}}{{24}}\].

Note: Least Common Multiple: LCM of two numbers is the smallest number which is a multiple of both the numbers. Also similar questions with different denominators are to be solved using the method as described above, and care must be taken while finding LCM since incorrect LCM will provide an incorrect final answer.