Question

What is $\dfrac{42}{56}$ in simplest form?

Answer 1

Hint: To convert a given fraction into simplest form, we need to first write the numerator and the denominator into a product of all its common factors individually such that all the terms in the product form are prime numbers only. Once we do that, we then cancel out the common factors from the numerator and denominator until there are no common factors. This new fraction is then in its simplest form.

Complete step-by-step solution:
We have been given the fraction as $\dfrac{42}{56}$. This fraction is already in the form of a proper fraction.
Now, we can write the numerator of the fraction which is equal to $\left( 42 \right)$ as a product of its prime factors as follows:
$\Rightarrow 42=2\times 3\times 7$
Let us name the above equation as $(1)$, so we have:
$\Rightarrow 42=2\times 3\times 7$ ……...$(1)$
And, we can write the denominator of the fraction which is equal to $\left( 56 \right)$ as a product of its prime factors as follows:
$\Rightarrow 56=2\times 2\times 2\times 7$
Let us name the above equation as $(2)$, so we have:
$\Rightarrow 56=2\times 2\times 2\times 7$ ……...$(2)$
Now, on dividing equation number $\left( 1 \right)$by$\left( 2 \right)$, we get:
$\Rightarrow \dfrac{42}{56}=\dfrac{2\times 3\times 7}{2\times 2\times 2\times 7}$
On canceling out the common factors in the Right-Hand Side of the above equation, we get:
$\begin{align}
  & \Rightarrow \dfrac{42}{56}=\dfrac{3}{2\times 2} \\
 & \therefore \dfrac{42}{56}=\dfrac{3}{4} \\
\end{align}$
Hence, $\dfrac{42}{56}$ in its simplest form can be written as $\dfrac{3}{4}$.

Note: Whenever converting any fraction into its simplest form, we should at first make sure, the fraction has been converted into a proper or an improper fraction, that is, if we have been given a mixed fraction, we would need to convert it into improper fraction first and then cancel out the common factors of the numerator and the denominator to solve our problem.