Question

What is ${\displaystyle \frac{10}{4}}$ as a mixed number?

Answer 1

Hint: The given fraction is in the form of an improper fraction, that is, the denominator is less than the numerator. So, in order to convert it into a mixed number or a mixed fraction, we will first divide the numerator by the denominator and get the required quotient and reminder. Once, we have the divisor, quotient and remainder, we can write our required mixed fraction.

Complete step-by-step solution:
We have the fraction as ${\displaystyle \frac{10}{4}}$. We can convert it into a mixed number in the following steps:
At first, we will divide the numerator by the denominator and the integer obtained in our quotient will be the integer of our mixed number.
So, on dividing $10$ by $4$ , we get the integral quotient as $2$.
Then, the denominator of the mixed fraction will be equal to the denominator of the original fraction which is equal to $4$.
And lastly, we will divide the numerator by the denominator and the integer obtained as our remainder will be the numerator of our mixed number.
Thus, on dividing $10$ by $4$, we get the integral remainder as $2$.
Therefore, our mixed number will be equal to:
$=2{\displaystyle \frac{2}{4}}$
Hence, ${\displaystyle \frac{10}{4}}$ as a mixed number is equal to $2{\displaystyle \frac{2}{4}}$ .

Note: If we proceeded by finding the simplest form of the given fraction. In that case, we would get $2{\displaystyle \frac{1}{2}}$ as the answer and not $2{\displaystyle \frac{2}{4}}$. These two terms are collectively termed as mixed equivalent fraction. This is because despite having different representations, both of them have the same quantitative value. And if not mentioned in the question, we should always calculate the original value.