Converting Improper Fractions to Mixed Numbers
Related calculator: Improper Fraction to Mixed Number Calculator
Converting improper fractions to mixed numbers is inverse of converting mixed number to improper fractions.
Suppose you want to convert $$${3}\frac{{4}}{{5}}$$$ to improper fraction.
We already know that $$${3}\frac{{4}}{{5}}=\frac{{3}}{{1}}+\frac{{4}}{{5}}=\frac{{{3}\cdot{5}}}{{5}}+\frac{{4}}{{5}}=\frac{{{3}\cdot{5}+{4}}}{{5}}=\frac{{19}}{{9}}$$$.
Now, imagine that you want to convert $$$\frac{{19}}{{9}}$$$ to mixed number. We can look at above transformations from right to left to find that $$$\frac{{19}}{{9}}=\frac{{{3}\cdot{5}+{4}}}{{5}}=\frac{{{3}\cdot{5}}}{{5}}+\frac{{4}}{{5}}={3}+\frac{{4}}{{5}}={3}\frac{{4}}{{5}}$$$.
From this we notice that we need only one thing to convert improper fraction to mixed number: division with remainder of numerator by denominator.
Indeed, when we talked about division with remainder we said that when 19 is divided by 5 result is 3 and something extra: $$${19}={5}\cdot{3}+{4}$$$. Now, we know that extra is nothing else than fraction $$$\frac{{4}}{{5}}$$$.
If $$${m}={n}\cdot{q}+{r}$$$ then $$${\color{red}{{\frac{{m}}{{q}}={n}\frac{{r}}{{q}}}}}$$$.
Now, let's go through a couple of examples.
Example 1. Convert $$$\frac{{23}}{{5}}$$$ to mixed number.
We can write 23 as $$${23}={5}\cdot{4}+{3}$$$ (division with remainder is performed), so $$$\frac{{23}}{{5}}={4}\frac{{3}}{{5}}$$$.
Answer: $$${4}\frac{{3}}{{5}}$$$.
Next example.
Example 2. Convert $$$\frac{{18}}{{14}}$$$ to mixed number.
First note that fraction is not irreducible. Reduce it: $$$\frac{{18}}{{14}}=\frac{{9}}{{7}}$$$.
We can write 9 as $$${9}={7}\cdot{1}+{2}$$$ (division with remainder is performed), so $$$\frac{{9}}{{7}}={1}\frac{{2}}{{5}}$$$.
Answer: $$${1}\frac{{2}}{{7}}$$$.
Next example.
Example 3. Convert $$$-\frac{{45}}{{8}}$$$ to mixed number.
First ignore minus sign: work with $$$\frac{{45}}{{8}}$$$.
We can write 45 as $$${45}={8}\cdot{5}+{5}$$$ (division with remainder is performed), so $$$\frac{{45}}{{8}}={5}\frac{{5}}{{8}}$$$.
Finally, don't forget about ignored minus sign.
Answer: $$$-{5}\frac{{5}}{{8}}$$$.
Time to practice.
Exercise 1. Convert $$$\frac{{15}}{{7}}$$$ to mixed number.
Answer: $$${2}\frac{{1}}{{7}}$$$.
Next exercise.
Exercise 2. Convert $$$\frac{{24}}{{8}}$$$ to mixed number.
Answer: 3.
Next exercise.
Exercise 3. Convert $$$-\frac{{79}}{{10}}$$$ to mixed number.
Answer: $$$-{7}\frac{{9}}{{10}}$$$.