Question

How do you add the fraction $\dfrac{3}{5}+\dfrac{2}{8}$ ?

Answer 1

Hint: The given expression is the addition of two fractions. If the denominator for both the fractions is the same, we can directly add the numerator keeping the denominator as it is. But here in our question, the denominators are different, so we find the least common multiple (LCM) of the denominators to get a common denominator. Multiply the common factor with the numerators and then evaluate to get a single fraction or a constant after evaluation.

Complete step by step solution:
The given expression is, $\dfrac{3}{5}+\dfrac{2}{8}$
Here we are performing the addition operation between two fractions, $\dfrac{3}{5},\dfrac{2}{8}$
If the denominators are the same for both the fractions we can directly add or perform any operations.
But here in our case, the denominators are different.
To make the denominator common we find the least common multiple (LCM) of both the denominators.
The list of multiples for the denominator $5$ is $5,10,15,20,25,30,35,40...\;$
The list of multiples for the denominator $8$ is $8,16,24,32,40,48...\;$
Here the least common multiple is $40\;$
Hence the common denominator will be $40\;$
Now to make the denominator same we try to multiply the numerator and denominator with the same number.
$\Rightarrow \left( \dfrac{3}{5}\times \dfrac{8}{8} \right)+\left( \dfrac{2}{8}\times \dfrac{5}{5} \right)$
$\Rightarrow \dfrac{24}{40}+\dfrac{10}{40}$
Since our denominators are common now, we can directly add the numerators.
$\Rightarrow \dfrac{\left( 24+10 \right)}{40}$
After evaluation we get,
$\Rightarrow \dfrac{34}{40}$
We can further simplify and write it as,
$\Rightarrow \dfrac{2\times 17}{2\times 20}$
Upon canceling the common factors in the numerator and denominator we get,
$\Rightarrow \dfrac{17}{20}$
Hence $\dfrac{3}{5}+\dfrac{2}{8}$ is equal to $\dfrac{17}{20}$.

Note: Whenever there are different denominators in a subtraction or addition or any other operation equation, the first step must be to convert it in such a way as to get the same denominators. Then only we should proceed to the given mathematical operation.