Question

How do you simplify $\dfrac{8}{12}+\dfrac{1}{6}$ ?

Answer 1

Hint: To get the simplified value of the given question $\dfrac{8}{12}+\dfrac{1}{6}$ , firstly we well make the value of the denominator same by taking L.C.M because every term of the question is written in fraction. After that we will solve (combine or add) the question according to the previous step. Then we will get the simplified value of the given question.

Complete step by step solution:
Here is the given question that is $\dfrac{8}{12}+\dfrac{1}{6}$ . Since, every term of the question is in the form of fraction, we will make the denominator the same by taking L.C.M. So, we will find the L.C.M. of $12$ and $6$as:
$2\left| \!{\underline {\,
  12,6 \,}} \right. $
$2\left| \!{\underline {\,
  6,3 \,}} \right. $
$3\left| \!{\underline {\,
  3,3 \,}} \right. $
   $\left| \!{\underline {\,
  1,1 \,}} \right. $
Hence, the L.C.M. of $12$ and $6$$=2\times 2\times 3=12$
The first term of the question has the denominator $12$ but second term of the question does not have the denominator 12. Since, we got the L.C.M. $12$ and $6$ that is $12$, we will divide 12 by $6$ for getting the numerator of the second term of the question as:
$\Rightarrow 12\div 6=2$
So, we will multiply this $2$with previous numerator of the second term of the question as:
$\Rightarrow 2\times 1=2$
Now, applying these values in the question, we will get as:
\[\Rightarrow \dfrac{8+2}{12}\]
Here, we will combine the numerator as:
\[\Rightarrow \dfrac{10}{12}\]
This is the simplified value of the given question that is also a fraction. Since, $2$is the common factor in both the numerator and the denominator, we can eliminate the value of $2$ as:
\[\Rightarrow \left( \dfrac{2\times 5}{2\times 6} \right)\]
$\Rightarrow \left( \dfrac{5}{6} \right)$
Since, it is a fraction, we can change it into decimal number as:
$\Rightarrow \left( \dfrac{5}{6} \right)=5\div 6=0.8\overline{3}$
Hence, the simplified value of the given question $\dfrac{8}{12}+\dfrac{1}{6}$ is $\left( \dfrac{5}{6} \right)$ or $0.8\overline{3}$ .

Note: Since, the given question is in fraction as $\dfrac{8}{12}+\dfrac{1}{6}$ . Here, we will have to make the denominator of both terms the same number or equal. So, we can change the denominator of any one of the both terms as:
For first term-
$\Rightarrow \dfrac{8}{12}=\dfrac{4}{6}$ (By eliminating $2$ from the fraction.)
Or
$\Rightarrow \dfrac{1}{6}=\dfrac{2}{12}$ (By multiplying by 2 into the fraction.)
So, the given question can be written as:
$\Rightarrow \dfrac{4}{6}+\dfrac{1}{6}$ Or $ \dfrac{8}{12}+\dfrac{2}{12}$
Now, we have the same denominator in both terms. So, we can add these terms as:
$\Rightarrow \dfrac{4+1}{6}$ Or $ \dfrac{8+2}{12}$
$\Rightarrow \dfrac{5}{6}$ Or $ \dfrac{10}{12}=\dfrac{5}{6}$
We can change it in decimal value as:
$\Rightarrow \left( \dfrac{5}{6} \right)=5\div 6=0.8\overline{3}$
Hence, the solution of the given question is correct.