Reorder the following steps to find the right way of writing a mixed number as an improper fraction

(1) Multiply the denominator of the fraction by the whole-number part

(2) Add the numerator of the fraction to the result from step 1

(3) Write the sum from step 2 over the original denominator

Explanation

To explain this process, let's write this mixed number \(2\frac15\) as an improper fraction

\(2\frac15 = \frac{5 \cdot 2 + 1}{5} = \frac{10 + 1}{5} = \frac{11}{5}\)

Another more slower but a structured process is to split the whole number from the fraction and sum them up as follows

Write the mixed number \(2\frac15\) as a sum

$2\frac15 = 2 + \frac15$

Write 2 as a fraction 2 = \(\frac21\)

$= \frac21 + \frac15$

To build \(\frac21\) so that its denominator is 5, multiply it by a form of 1

$= \frac21 \cdot \frac55 + \frac15$

Multiply the numerators and the denominators

$= \frac{10}{5} + \frac15$

Add the numerators and write the sum over the common denominator 5

$= \frac{11}{5}$