Question

What is the common denominator of $\dfrac{4}{5}$ and $\dfrac{1}{3}?$

Answer 1

Hint: When we need to find the common denominator, We need to multiply the denominator of the first fraction with the denominator of the second fraction and the denominator of the second fraction with the denominator of the first fraction.

Complete step-by-step solution:
Let us consider the given problem.
We are given with two fractions $\dfrac{4}{5}$ and $\dfrac{1}{3}.$
We are asked to find the common denominator of the given two fractions.
We know that the numbers below the line are called the denominators.
As we can see, the denominators of the given fractions are distinct.
Now, we need to make the denominators the same.
To make the denominators of some fractions the same, we need to multiply the denominators of the fractions.
We know that we need to multiply the numerator with the same number with which we multiply the denominator.
So, as we said earlier, to make the denominators of the given fractions the same, we need to multiply and divide $\dfrac{4}{5}$ with $3$ and multiply and divide $\dfrac{1}{3}$ with $5.$
Now, as we know, $\dfrac{4}{5}$ will become $\dfrac{12}{15}$ and $\dfrac{1}{3}$ will become $\dfrac{5}{15}.$
Hence the common denominator of the given two fractions is $15.$

Note: We should remember that we cannot find the lowest common denominator using the above procedure. But it will give us any common denominator. We know that the numbers of the form $\dfrac{p}{q}$ where $p$ and $q$ are integers are called rational numbers and $p$ is called the numerator and $q$ is called the denominator.