Question

What is \[4\] divided by \[\dfrac{12}{25}\]?

Answer 1

Hint: We are asked to divide a fraction by a whole number. Division of fractions is nothing but multiplying it with the reciprocal. So from the given question, we will be converting the divisor i.e. \[\dfrac{12}{25}\] into its reciprocal form and then multiplying it with \[4\] gives us the required answer.

Complete step-by-step answer:
Let us learn about the division of fractions. In simple words, it can be explained as dividing a fraction by another fraction is the same as multiplying the fraction with the reciprocal of the other fraction. Any type of fractions can be divided. For instance, if the given fraction is a mixed fraction, then we can convert it into an improper fraction and perform the same process of division of fractions.
Now let us solve our given question.
It can be expressed as \[\dfrac{4}{\dfrac{12}{25}}\]
Now upon taking the reciprocal and multiplying it gives us,
\[4\times \dfrac{25}{12}\]
Upon solving this we get,
\[\dfrac{25}{3}\]
This can also be expressed in decimals as \[8.33\]. It can be expressed in mixed fraction as \[8\dfrac{1}{3}\].
\[\therefore \] \[4\] divided by \[\dfrac{12}{25}\] is \[\dfrac{25}{3}\].

Note: while dividing the fractions, we take the reciprocal and multiply because the inverse operation of division is multiplication. There is an easy way in remembering the process of division i.e. “keep, change, flip” which means that keep the first number, change the division sign to multiplication and then flip the second number.