Fractions

Let's review some basic functions as well as some basic operations with fractions.

Understanding Fractions

A fraction is part of an entire object. A fraction is always a rational number. We call the top number the numerator; it is the number of parts you have. We call the bottom number the denominator; it is the number of parts the whole is divided into. There are three different types of fractions; proper, improper, and mixed fractions. The following is a table which provides a brief explanation and example of each:

Type of Fraction	Definition	Example
Proper	The numerator is less than the denominator	⁵/8 or ¹¹/22
Improper	The numerator is greater than (or equal to) the denominator	¹²/7 or ⁸/8
Mixed	A whole number and proper fraction together	1 ¹/3 or 2 ¹/4

Converting Fractions

Since a mixed fraction is just a whole number and a fraction combined into one "mixed" number, you can use either an improper fraction or a mixed fraction to show the same amount. To convert an improper fraction to a mixed fraction, follow these steps:

Divide the numerator by the denominator.
Write down the whole number answer.
Then write down any remainder above the denominator

Example: Convert the improper fraction \(\frac{7}{4}\) to a mixed fraction.

Solution:

Divide the numerator by the denominator \(\frac{7}{4}=1\) with a remainder of 3.

So we write down the 1 as a whole number and then write down the remainder (3) above the denominator (4), like this: \(1\frac{3}{4}\)

To convert from a mixed fraction to an improper fraction, follow these steps:

Multiply the whole number part by the fraction denominator,
Add that to the numerator,
Then write the result on top of the denominator.

Example: Convert the mixed fraction 5 ⁶/7 to an improper fraction.

Solution:

Multiply the whole number by the denominator: 5 x 7= 35

Add the numerator to that: 35 + 6 = 41

Then write that down above the deonominator (7), like this: ⁴¹/₇

Equivalent Fractions

Before doing operations with fractions one must understand equivalent fractions. For example, these fractions are really all the same:

\(\frac{1}{3}=\frac{2}{6}=\frac{3}{9}\)

They are all the same because any time you multiply or divide both the numerator and denominator by the same number, the fraction keeps its value. For example, \(\frac{1}{7}\cdot\frac{2}{2}=\frac{2}{14}\) means that \(\frac{1}{7}=\frac{2}{14}\). For equivalent fractions, always remember that what you do to the numerator, you must do to the denominator. This process will help you in understanding how to obtain a common denominator for two fractions.