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 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`.