Mixed numbers

Imagine you have three pizzas on the table: a cheese one, a salami one and then the best pizza in the world, a Hawaiian:

If we didn’t want to use the word “three”, we could write that there are 3 pizzas on the table. Now let’s imagine we eat three slices of the Hawaiian. How much pizza do we have left?

We can see that we have two whole pizzas left, and from the third we have five slices out of eight. How would we write that as a number? We can use mixed numbers, in which we mix together integers and fractions. So we can say that we have

$$2\frac{5}{8}$$

pizzas left. A mixed number consists of two parts: first an integer, followed by a fraction. There is no operator or sign between the integer and the fraction. Watch out: if you put a dot there, $2\cdot \frac{3}{8}$, it would not be a mixed number but the product of an integer and a fraction. So a mixed number has the form

$$a\frac{b}{c}$$

and its value is equal to

$$a+\frac{b}{c}.$$

We use mixed numbers only for numbers greater than one. If you have only half of one pizza, we don’t write $0\frac{1}{2}$. We write only $\frac{1}{2}$. Likewise, we don’t use mixed numbers for negative numbers.