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# How do you simplify the sum of $\dfrac{3}{5}+\dfrac{2}{7}$?

Last updated date: 13th Jun 2024
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Hint: In this problem we have to calculate the sum of $\dfrac{3}{5}+\dfrac{2}{7}$. Here we can observe that the denominators in the given fractions are not the same. So, we can’t directly find the sum of the given fractions. For this, we will calculate the LCM of the given fractions and we will multiply with appropriate values to get the denominators of the two fractions. Now we will simplify the given fractions to get the required sum.

Complete step by step solution:
Given that, $\dfrac{3}{5}+\dfrac{2}{7}$.
Consider the denominators in the given fraction. We have $5$, $7$. Now the LCM of the denominators is
$5\times 7=35$
Now we need to convert the denominators of both the fractions into $35$ to add them.
Consider the first fraction which is $\dfrac{3}{5}$.
In the above fraction we have denominator $5$. To get the denominator as $35$. We are going to multiply and divide the given fraction with $7$. Then we will get
\begin{align} & \Rightarrow \dfrac{3}{5}=\dfrac{3}{5}\times \dfrac{7}{7} \\ & \Rightarrow \dfrac{3}{5}=\dfrac{21}{35} \\ \end{align}
Consider the second fraction $\dfrac{2}{7}$.
In the above fraction we have denominator $7$. To get the denominator as $35$. We are going to multiply and divide the above fraction with $5$. Then we will get
\begin{align} & \Rightarrow \dfrac{2}{7}=\dfrac{2}{7}\times \dfrac{5}{5} \\ & \Rightarrow \dfrac{2}{7}=\dfrac{10}{35} \\ \end{align}
Now the sum of the given fractions will be
\begin{align} & \Rightarrow \dfrac{3}{5}+\dfrac{2}{7}=\dfrac{21}{35}+\dfrac{10}{35} \\ & \Rightarrow \dfrac{3}{5}+\dfrac{2}{7}=\dfrac{31}{35} \\ \end{align}

Hence the value of the given expression $\dfrac{3}{5}+\dfrac{2}{7}$ is $\dfrac{31}{35}$.

Note: We can also follow the above procedure in case subtraction also. When we have $\dfrac{3}{5}-\dfrac{2}{7}$. We can calculate this value as
\begin{align} & \Rightarrow \dfrac{3}{5}-\dfrac{2}{7}=\dfrac{21}{35}-\dfrac{10}{35} \\ & \Rightarrow \dfrac{3}{5}-\dfrac{2}{7}=\dfrac{11}{35} \\ \end{align}
We can also use the direct formula $\dfrac{a}{b}-\dfrac{c}{d}=\dfrac{ad-cb}{bd}$. Here we will calculate the values of $ad$, $cb$, $bd$ and substitute those in the above formula to get the result.