AI Tutor
Imagine you have 5 slices of an 8-slice pizza on your plate. How many different ways could you split those 5 slices between two or three friends?
To decompose a fraction simply means to break it apart into a sum of smaller fractions that have the same denominator.
Can we break that exact same fraction apart in a completely different way?

Different Ways to Break Apart 58\frac{5}{8}

A unit fraction is any fraction with a top number (numerator) of 1, such as 18\frac{1}{8}.
You can always break a fraction down into all unit fractions: 58=18+18+18+18+18\frac{5}{8} = \frac{1}{8} + \frac{1}{8} + \frac{1}{8} + \frac{1}{8} + \frac{1}{8}.
Notice that the bottom number, the denominator, stays 8 in every single piece because the size of each slice never changes.
As long as the numerators add up to the original numerator (3+2=53 + 2 = 5 or 4+1=54 + 1 = 5), your decomposition is correct!
What if we have a larger numerator, like 610\frac{6}{10}?

Worked Example: Decomposing 610\frac{6}{10}

Let's find two different decompositions for 610\frac{6}{10} into non-unit fractions.