Question

How do you simplify \[\dfrac{2}{5}+\dfrac{1}{2}\] ?

Answer 1

Hint: For adding or subtracting the fractions we first see their denominators if they are the same then add the numerators directly or if they don’t then take the \[L.C.M.\] of all the denominators that will be the denominator the answer then divide it with the denominator then multiply the given answer with the numerator, similar to this to do with other terms and add.

Complete step by step answer:
As we see the denominators are different then we take the \[L.C.M.\]
Now taking the \[L.C.M.\] of the denominators \[5\] and \[2\] that is \[10\].
(When the numbers don’t have any common factor then the \[L.C.M.\] will be the product of these numbers.)
\[\Rightarrow \]The denominator of the answer is \[10\]
Now divide the denominator of the first term with this new denominator and then multiply the given answer with the numerator of the same term.
\[\begin{align}
  & \Rightarrow 10\div 5=2 \\
 & \Rightarrow 2\times 2=4 \\
\end{align}\]
Similarly, for the second term and the sign between them is the sign between the terms.
\[\Rightarrow \dfrac{2}{5}+\dfrac{1}{2}=\dfrac{(2\times 2)+(5\times 1)}{10}\]
\[\Rightarrow \dfrac{4+5}{10}\]
\[\Rightarrow \dfrac{9}{10}\]

Hence the addition of \[\dfrac{2}{5}+\dfrac{1}{2}=\dfrac{9}{10}\]

Note: To add or subtract the fractions directly just made the denominators of all the terms same by multiplying and dividing the numerator and denominator with the same number and when the denominators become same then directly add the numerators of all terms and denominator will be the same common denominator.