Fractions

Fractions are another way of expressing division. The expression 12/3 is equal to 4 because 12 divided by 3 is 4. If you don't believe me, check that 3 · 4 = 12; that's an equivalent statement.

Now you have your proper fractions, where the numerator (top) is smaller than the denominator (bottom), like 5/12. These give numbers that are less than 1.

On the other hand, there are improper fractions like 19/8. Think of pizzas each cut into eight slices; each slice is one eighth, or 1/8 of a pizza. Then 19 slices would be the same as 16 slices and 3 more slices; making 2 pizzas and 3 extra slices.

Therefore we get 19/8 = 2 + 3/8, which is written as 2 ³/₈, called a mixed number.

To convert 19/8 you do division; 8 into 19 goes 2 times with 3 left over; so 2 ³/₈.

If you have a mixed number like 3 ¹/₇, you do the reverse: 3 · 7 + 1 = 22 ; so 22/7.

Some misguided people (not you!) think that π (pi) is equal to 3 ¹/₇ or 3.14; it's close to these values, but not exactly equal. π is an irrational number, which means it's a real number, but not equal to any fraction. (But 355/113 is closer to π.)

Fractions can be put into lowest terms, meaning you cancel out common factors of the top & bottom. For example,

6 / 8 = (2 · 3) / (2 · 4) = 3 / 4 ;

six eighths equals three fourths.

(Think of eating six slices of the aforementioned pizza! Hungry yet?)