A complex fraction is a fraction that has another fraction in its numerator, denominator, or both. In other words, it's a fraction within a fraction. For example, if you see ½ over ¾, that's a complex fraction: you have one fraction on top of another fraction.

These appear more complicated than regular fractions, but they follow the same mathematical rules. To simplify a complex fraction, you can multiply the top fraction by the reciprocal (flip) of the bottom fraction. So ½ over ¾ becomes ½ times 4/3, which equals 2/3.

Complex fractions show up when you're working with rates or ratios that themselves involve fractions. Imagine calculating how many quarter-cup servings fit into half a cup: you'd write ½ cup divided by ¼ cup, creating a complex fraction. Once you understand the technique for simplifying them, complex fractions become much less intimidating than they first appear.