Conversion of Improper Fractions to Mixed Numbers

Grandma's magic trick

Grandma's sad. For the family party, she baked three very tasty cakes. But unfortunately, in one cake she took salt instead of sugar! This hasn't happened to her in a long time...

Of course, not a single piece of this cake was eaten. There are two pieces left of the other two cakes.

"So what to do?" asks Grandma. She remembers the ancient magic trick she learned from her grandmother:

Just like a puzzle, she can assemble 8 pieces that have already been cut into a whole cake! This will not really save the situation, but it will certainly be fun.


There are ten pieces of cake. Eight pieces are needed for a whole cake. Since 8 fits into 10 once, it is enough for 1 cake.

The denominator indicates how many pieces the whole cake was divided into. This is the same in both notations!

The numerator states the number of pieces. In addition to the whole cakes, there are 2 pieces.


Formula: Conversion of Improper Fractions to Mixed Numbers

  1. Side calculation: Divide the numerator by the denominator
  2. The result is the whole number of the mixed number (orange)
  3. Write the remainder of the side calculation in the numerator of the fraction (brown)
  4. The denominator remains unchanged (green)
If the side calculation is working, this whole number is the result!

Umwandlung gewöhnlicher Bruch in gemischten Bruch

For example, you want to convert the improper fraction 25/6 into a mixed fraction. First, divide the numerator by the denominator → 25 : 6

The result is 4 Remainder 1.

So it is: 25/6  =  4 1/6

Be aware that only improper fractions can be converted into a mixed number. Proper fractions cannot be converted to mixed numbers, because the whole number part of the mixed number would be zero: In this case, dividing the numerator by the denominator always results in "0 Remainder numerator.

Online Exercise: Conversion of Improper Fractions to Mixed Numbers

You can practice the conversion of improper fractions to mixed numbers online:

If you have any problems with the excercise, please have a look at the hint and the sample solution first.


Video: Conversion of Improper Fractions to Mixed Numbers

Finally, a video about: Change an Improper Fraction to a Mixed Number:

Let's continue with: "Reciprocal of a Fraction"