A fraction is a number that represents a part of a whole. Fractions are commonly written as where a and b are any number and b is not equal to 0. In a fraction, the top number is referred to as the numerator, and the bottom number is referred to as the denominator:
While the term "fraction" commonly refers to "common fraction," (the form described here) fractional numbers can also be expressed as decimal fractions and percents. There are a number of different types of fractions including improper fractions, reciprocals, equivalent fractions, and more.
Slices of pizza can be a good way to picture fractions. In a pizza that has 8 slices, 1 slice is a fraction of the whole pizza, written as . Two slices would be , 3 slices , and so on. In this example, the top number, known as the numerator is the number of slices of pizza we have, while the bottom number, the denominator, is the total number of slices of pizza in the whole pizza.
In the figure below, the fractions represent how many slices of the whole pizza have pepperoni on them.
For each pizza, how many slices of the pizza only have cheese on it?
One way to solve this is to count the number of slices of pizza that only have cheese on them. Another way is to subtract the number of pepperoni slices from the total number of slices in the pizza. Since each pizza has 8 slices:
Equivalent fractions are widely used when working with fractions. For example, finding a common denominator, which involves converting a fraction into another equivalent fraction, is necessary to perform fraction addition and subtraction. Simplifying fractions also results in equivalent fractions.
We can talk about having 2, 4, 6, or even 8 slices of pizza. In these cases the fractions would be written as
respectively; the fractions can further be simplified or reduced as follows:
These are known as equivalent fractions. Having 2 slices out of 8 of a pizza is equivalent to one fourth of the pizza, and so on. Fractions can be reduced when the numerator or denominator share a factor. The fraction is equal to 1, and is an equivalent fraction to any number divided by itself (except for 0).