# 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.

Exercise 3. Convert -79/10 to mixed number.
Answer: -7 9/10.