Question

How do you solve \[\dfrac{5}{6}+\dfrac{4}{12}\]?

Answer 1

Hint: In this problem, we have to simply the given fraction and write the answer. We can see that the given fraction does not have a similar denominator and so we cannot subtract it directly. We can now cross multiply the given fraction and simplify the terms in the left-hand side and the right-hand, we will get a simplified form, which will be the answer.

Complete step by step solution:
We know that the given fraction to be simplified is,
\[\dfrac{5}{6}+\dfrac{4}{12}\]
We can now see that the given fraction cannot be directly subtracted as it does not have a similar denominator.
We can now use the cross-multiplication method, we get
\[\Rightarrow \dfrac{12\left( 5 \right)+4\left( 6 \right)}{6\times 12}\]
We can now multiply the terms inside the bracket in both the numerator, we get
\[\Rightarrow \dfrac{12\left( 5 \right)+4\left( 6 \right)}{6\times 12}=\dfrac{60+24}{6\times 12}\]
We can now multiply the terms in the denominator and add the terms in the numerator, we get
\[\Rightarrow \dfrac{84}{72}\]
Now we can divide the terms, by cancelling the fraction as it can be cancelled by the multiplication table 2, we can also write in decimal form.
\[\Rightarrow \dfrac{84}{72}=\dfrac{7}{6}=1.1666\]
Therefore, the simplified form of the given fraction \[\dfrac{5}{6}+\dfrac{4}{12}\] is 1.1666.

Note: Students make mistakes while cross multiplying the term, where we should cross multiply the numerators and denominators respectively and the both denominators. we should know that we cannot subtract the fraction directly as it has different denominators, so that we have to cross multiply the fraction to get the simplified form.