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 4/5` to improper fraction.

We already know that `3 4/5=3/1+4/5=(3*5)/5+4/5=(3*5+4)/5=19/9`.

Now, imagine that you want to convert `19/9` to mixed number. We can look at above transformations from right to left to find that `19/9=(3*5+4)/5=(3*5)/5+4/5=3+4/5=3 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*3+4`. Now, we know that extra is nothing else than fraction `4/5`.

If `m=n*q+r` then `color(red)(m/q=n r/q)`.

Now, let's go through a couple of examples.

Example 1. Convert `23/5` to mixed number.

We can write 23 as `23=5*4+3` (division with remainder is performed), so `23/5=4 3/5`.

Answer: `4 3/5`.

Next example.

Example 2. Convert `18/14` to mixed number.

First note that fraction is not irreducible. Reduce it: `18/14=9/7`.

We can write 9 as `9=7*1+2` (division with remainder is performed), so `9/7=1 2/5`.

Answer: `1 2/7`.

Next example.

Example 3. Convert `-45/8` to mixed number.

First ignore minus sign: work with `45/8`.

We can write 45 as `45=8*5+5` (division with remainder is performed), so `45/8=5 5/8`.

Finally, don't forget about ignored minus sign.

Answer: `-5 5/8`.

Time to practice.

Exercise 1. Convert `15/7` to mixed number.

Answer: `2 1/7`.

Next exercise.

Exercise 2. Convert `24/8` to mixed number.

Answer: 3.

Next exercise.

Exercise 3. Convert `-79/10` to mixed number.

Answer: `-7 9/10`.