# Converting Improper Fractions to Mixed Numbers

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**: $$$-{7}\frac{{9}}{{10}}$$$.