Question

Are $\dfrac{5}{6}$ and $\dfrac{20}{24}$ pairs of equivalent fractions?

Answer 1

Hint: We solve this problem by making the denominator of both the fractions equal and check the numerators. If both the numerators and denominators of both the fractions are equal then the two fractions are said to be equivalent fractions. We check the numerators by making the denominators equal to find whether the fractions are equivalent or not.

Complete step by step answer:
We are asked to check whether $\dfrac{5}{6}$ and $\dfrac{20}{24}$ are equivalent fractions or not.
We know that if both the numerators are equal after making the denominators equal then the fractions are said to be equivalent fractions.
Now, let us make the denominators of both fractions equal.
Here we can see that the denominators of both fractions are 6 and 24.
Now, let us multiply the numerator and denominator of first fraction with 4 then we get,
$\Rightarrow \dfrac{5\times 4}{6\times 4}=\dfrac{20}{24}$
Here, we can see that the numerator and denominator of first fraction and second fraction are equal.
Therefore we can conclude that the given two fractions are equivalent fractions.

Note: We can check the equivalent fractions in other methods also.
We know that equivalent fractions are the fractions in which a constant number is multiplied to both numerator and denominator of the first fraction to get the second fraction.
Here, we can reframe the statement that if we divide the first fraction with the second fraction then the result should be ‘1’.
Now, let us divide the fraction $\dfrac{5}{6}$ with $\dfrac{20}{24}$ then we get,
$\begin{align}
  & \Rightarrow x=\dfrac{\left( \dfrac{5}{6} \right)}{\left( \dfrac{20}{24} \right)} \\
 & \Rightarrow x=\dfrac{5}{6}\times \dfrac{24}{20} \\
 & \Rightarrow x=\dfrac{4}{4}=1 \\
\end{align}$
Here, we can see that the result after dividing first fraction with second fraction is 1
Therefore we can conclude that the given two fractions are equivalent fractions.