Question

What is the common denominator of $\dfrac{3}{5}$ and $\dfrac{1}{3}$?

Answer 1

Hint: For solving this question you should know about the common denominator of any number. We can calculate the common denominator of any fraction by just multiplying the denominator of the fractions and the number which is dividing by every number is known as the common denominator of that fraction.

Complete step-by-step solution:
According to our question we have to calculate the common denominator of $\dfrac{3}{5}$ and $\dfrac{1}{3}$. If we want to calculate the common denominator of fractions, then we have to take multiplication of all the denominators. And then if we want to check if our common denominator is right or wrong, then we have to divide the common denominator value by the denominator values of the fractions. And after getting the common denominator for fractions we can add to the fractions and subtract to the fractions. If we take an example, it will be clear.
Example: Add $\dfrac{3}{5}$ and $\dfrac{7}{8}$.
Our fractions are $\dfrac{3}{5}$ and $\dfrac{7}{8}$, so for adding these fractions we have to make the denominator equal for both the fractions. So, to make the denominator equal, then,
$\dfrac{3}{5}$ and $\dfrac{7}{8}$$\Rightarrow 5\times 8=40$
So, we will make both the denominators as 40. And for it we will calculate $\dfrac{3}{5}$ with $\dfrac{8}{8}$ and $\dfrac{7}{8}$ with $\dfrac{5}{5}$ so, we get,
$\dfrac{3}{5}\times \dfrac{8}{8}=\dfrac{24}{40}$ and $\dfrac{7}{8}\times \dfrac{5}{5}=\dfrac{35}{40}$
Now, if we add both of them, we get,
$\dfrac{24}{40}+\dfrac{35}{40}=\dfrac{59}{40}$
So, similarly if we see our question, the fractions are $\dfrac{3}{5}$ and $\dfrac{1}{3}$.
For the common denominator $=5\times 3=15$
We have to make the denominator as 15 for both of them, so it will be,
$\dfrac{3}{5}\times \dfrac{3}{3}$ and $\dfrac{1}{3}\times \dfrac{5}{5}$
So, $\dfrac{3}{5}$ and $\dfrac{1}{3}$ have a common denominator 15.

Note: For calculating the denominator of any fraction, always be careful of the denominator of the fractions. If these are not equal then make them equal bits if the question asks for the least common denominator, then we have to find the least or value of the denominator which is divided by all the denominators.