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Imagine snapping a brand-new candy bar into 5 equal pieces. If you take just 1 piece, you have 15\frac{1}{5} of the bar — but what if you eat 3 of those pieces?

The Building Blocks of Fractions

A unit fraction is a fraction where the top number (the numerator) is 1, like 15\frac{1}{5} or 18\frac{1}{8}. It represents exactly one equal slice of a whole.
When you put several unit fractions together, you build a non-unit fraction, which has a numerator greater than 1.
How do we write this mathematically using addition?

Counting by Unit Fractions

Just like counting whole numbers (1+1+1=31 + 1 + 1 = 3), you can count unit fractions. To make 35\frac{3}{5}, you simply add three 15\frac{1}{5} pieces together: 15+15+15=35\frac{1}{5} + \frac{1}{5} + \frac{1}{5} = \frac{3}{5}
In any fraction ab\frac{a}{b}, the bottom number tells you the size of each piece, and the top number tells you how many pieces you have joined.
Does this building-block rule also work if we count objects in a set instead of slices of a bar?

Building Fractions of a Set

Think of a pack of 4 tennis balls. Each individual ball is 14\frac{1}{4} of the set.