A fraction is a part of a whole.

The top number indicates the number of
parts being considered
.
(such as 3 pieces of pizza)

The bottom number indicates the number of
parts into which the whole is equally divided.

(such as a pizza divided into 4 equal pieces)

Visualizing Fractions: Name the fraction represented by the following shadings?

A fraction with a one in the numerator is called a unit fraction.

When dealing with fractions, the top number is called the numerator and the bottom number is called the denominator.
These are terms that you need to know.
The numerator is the number of the sections considered (it is multiplication): 3 • ¼
The denominator is the number of parts into which the whole is divided: 1 ÷ 4

 The fraction bar (called a vinculum or a division bar) may be read as "divided by" as when converting ¾ into a decimal (¾ = 3 ÷ 4 = 0.75). Did you notice the connection between a fraction, such as a/b and the division symbol, ÷. The dots above and below the bar represent 2 numbers.

Fractions on a Number Line:
Represent the fraction, illustrated by the circle diagram below, on a number line.

 One sixth of the whole is shaded.
To create a number line representation of a fraction:
1. Draw a number line.
2. Label the location of 0 and 1 (leave plenty of room)
3. The denominator (bottom) will tell you the number of equal sections to create
between 0 and 1.
4. The numerator (top) will tell you the number of the equal sections to shade to
represent the fraction.

Decomposing Fractions: (breaking fractions down into parts)

A single fraction can be represented as several fractions put together (added together).

All of these entries represent the same quantity, which is 7 "one-eighth" sections, as seen by the same total shadings in the diagrams. In the second and third listings above, notice that the numerators add up to the numerator of the original (first) fraction which is 7.

Improper Fractions and Mixed Numbers:
A proper fraction is a fraction that is less than one, with the numerator (top) less than the denominator (bottom). It is the type of fraction we most often see, such as ¼, ¾, and ½.

An improper fraction is a fraction where the numerator (top) is greater than (or equal to) the denominator (bottom).

The fraction can be thought of as 7 x , described as "7 one-eighths", and displayed as:

The fraction can be thought of as 10 x , described as "10 one-eighths", and displayed as:

Notice that in the improper fraction we have the entire "whole" plus a little more. Improper fractions may have ONE copy of the "whole" or multiple copies of the "whole".
Notice in this problem we have "ONE whole" plus "2 one-eighths".
This can be written as a mixed number as . We now know that .

A mixed number is number consisting of an integer and a proper fraction.
Improper fractions can be changed into mixed numbers, as we saw above.

A quick method to covert an improper fraction to a mixed number:
 Convert to a mixed number. Divide the numerator by the denominator. (Divide the top by the bottom.) The answer will be the number of wholes. The remainder will be the new numerator.

A quick method to covert a mixed number to an improper fraction:

Convert to an improper fraction.
Multiply the whole times the denominator,

2
x 5 + 4 = 14
This number will be the numerator
of the improper fraction.

2 x 5 + 4 = 14

 When dealing with mixed numbers, remember what you say when you read the number aloud.     4½ is read as "4 and one-half" The "and" means addition, not multiplication. 4½ = 4 + ½          4½ ≠ 4 x ½

 NOTE: In mathematics, the word fraction is also used to describe mathematical expressions that are not rational numbers (where the numerator and denominator are not integers). For example, there are expressions that contain radicals such as , and expressions such as that are referred to as fractions. There are also algebraic fractions such as where the values of a and b are not known (assuming b ≠0).