Imagine you are throwing a pizza party. You order 3 pizzas. You eat 2 whole pizzas, and then one slice from the third pizza. You could say you ate “$2 \frac{1}{4}$” pizzas. This is a mixed number. However, if you counted every single slice you ate, you would find you ate 9 slices total. Since each slice is one-fourth of a pizza, you ate “$9/4$”. This is an improper fraction.

The M.A.D. Strategy

Converting a mixed number to improper fraction is easy if you get “MAD”! This acronym helps you remember the three steps involved:

• M – Multiply the whole number by the denominator. This tells you how many pieces are in the whole pizzas.
• A – Add the numerator. This adds the extra slices from the partial pizza.
• D – Denominator stays the same. The size of the slices hasn’t changed!

For example, to convert $2 \frac{1}{4}$:
1. Multiply: $2 \times 4 = 8$ (There are 8 slices in the 2 whole pizzas).
2. Add: $8 + 1 = 9$ (Add the 1 extra slice).
3. Denominator: The bottom number is still 4.
Result: $9/4$.

Why Convert?

While mixed numbers are great for everyday counting (“I ran 3 and a half miles”), they are terrible for math operations. It is very difficult to multiply or divide mixed numbers directly. By converting a mixed number to improper fraction, you turn the number into a simple format that follows standard math rules. This is why learning to convert a mixed number to improper fraction is a critical bridge between arithmetic and algebra.

Essentially, converting a mixed number to improper fraction allows you to stop seeing “pizzas” and start seeing “slices,” which makes calculating much easier.