Fraction Definition

In this section, we ask what is the fraction definition? We have seen that whole numbers allow us to describe or count a number of objects. Integers allow us to expand on the whole numbers and consider negative values. A fraction is defined as being used to describe a part of a whole amount. For an easy example, most people use a pizza. Suppose the pizza is cut up into 5 equal slices. After 2 slices of the pizza are eaten, we can say that we have 3 slices of the pizza remaining out of a total of 5 slices. This can be represented with the fraction: $$\frac{3}{5}$$ The 3 represents the number of equal parts remaining, this is known as the numerator. The numerator displays the number of parts under consideration (being used or discussed). The 5 represents the total number of equal parts, this is known as the denominator. The horizontal bar that sits between the 3 and 5 is known as a fraction bar, this separates the numerator from the denominator.
Example 1: Identify the Numerator and Denominator $$\frac{2}{3}$$ The 2 is the numerator, this is the top number
The 3 is the denominator, this is the bottom number
This fraction represents 2 parts out of a total of 3.
We will also discuss the types of fractions that we will encounter. In most cases, we will deal with a proper fraction. We will also come across improper fractions, and mixed numbers.

Proper Fraction

Used to describe a fraction quantity whose value is less than one, this occurs when the numerator is less than the denominator

Improper Fraction

Used to describe a fraction quantity whose value is one or larger, this occurs when the numerator is greater than or equal to the denominator

Mixed Number

Used to describe the sum of a whole number and a proper fraction

Example 2: Determine if each is a proper fraction, improper fraction, or mixed number $$\frac{1}{7}$$ -Proper Fraction, 1 the numerator is less than 7 the denominator $$1 \frac{2}{13}$$ -Mixed Number, represents the sum of a whole number and a proper fraction $$\frac{8}{7}$$ -Improper Fraction, 8 the numerator is larger than 7 the denominator