An improper fraction is a fraction where the top number (the numerator) is bigger than or equal to the bottom number (the denominator), like 7/4 or 5/5. Despite the name, there's nothing actually wrong or “improper” about these fractions. They're perfectly valid numbers that just happen to be equal to or greater than one whole.

Think of it this way: if you have 7/4 of a pizza, you have more than one complete pizza. You have one whole pizza (4/4) plus three more quarters (3/4). That's the same as 1¾ pizzas, which mathematicians call a mixed number. An improper fraction and its equivalent mixed number are just two different ways of writing the same amount.

Improper fractions are actually easier to work with when you're multiplying or dividing fractions, which is why mathematicians use them so often in calculations. If you're multiplying ¾ times 1⅔, it's much simpler to first convert 1⅔ into the improper fraction 5/3, then multiply straight across: ¾ × 5/3 = 15/12, which simplifies to 5/4 (or 1¼).

The opposite of an improper fraction is a proper fraction, where the numerator is smaller than the denominator, like 3/4 or 2/5. Proper fractions are always less than one whole.