Question

Solve the following equation:
\[\dfrac{5}{3}+\dfrac{3}{5}=?\]

Answer 1

Hint: In order to find the solution of this question, we should know that the fractional terms only show addition and subtraction when they have common denominators. So, we will first make the denominator of both the terms equal and then we will add the terms to get our answer.

Complete step-by-step answer:
In this question, we have been asked to solve \[\dfrac{5}{3}+\dfrac{3}{5}.\] To solve this question, we should know that the fractional terms only show addition or subtraction when they have an equal denominator. So, to make the denominator of \[\dfrac{5}{3}\text{ and }\dfrac{3}{5}\] equal, we will multiply the numerator and denominator of \[\dfrac{5}{3}\] by 5. And we will multiply the numerator and denominator of \[\dfrac{3}{5}\] by 3. So, we get,
\[\dfrac{5}{3}=\dfrac{5\times 5}{3\times 5}=\dfrac{25}{15}\]
\[\dfrac{3}{5}=\dfrac{3\times 3}{5\times 3}=\dfrac{9}{15}\]
And by using these values, we can write,
\[\Rightarrow \dfrac{5}{3}+\dfrac{3}{5}=\dfrac{25}{15}+\dfrac{9}{15}\]
After adding both the terms, we get,
\[\Rightarrow \dfrac{25+9}{15}\]
\[=\dfrac{34}{15}\]
Hence, we get the sum of \[\dfrac{5}{3}\text{ and }\dfrac{3}{5}\text{ as }\dfrac{34}{15}.\]
Therefore, we can say, \[\dfrac{5}{3}+\dfrac{3}{5}=\dfrac{34}{15}.\]

Note: We can also solve this question by taking the LCM of the denominators and then solving it. Both the methods are somewhat the same, but the main difference is the way of expressing the solution. Also, there are possible mistakes in calculation. So, we have to be very focused while doing the calculations.