Dictionary for Basic and Intermediate Algebra
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Working with Fractions

A fraction (part of a whole), written one number above another, the top number is called the numerator and the bottom number is called the denominator. Example:  is read three fourth obtained by dividing an item into four equal parts and using 3 of the 4 parts.When the numerator and the denominator are the same, the fraction is 1.
1 written as a fraction is extremely useful when performing the addition or subtraction of two fraction with different denominators.

Example:

 

When the numerator is smaller than the denominator, the fraction is less  than 1, is called a proper fraction. For example, 7/8 is a proper fraction, since 7/8 < 1.
When the numerator is larger than the denominator, the fraction is greater than 1, is called an improper fraction. For example, 5/3 is an improper fraction, since 5/3 > 1. 
Calculation with fractions:
1.  Addition and subtraction of fraction
(a)  With the same denominator:

    To add or subtract fractions with the same denominator, just add or subtract their numerators and keep their denominators

Example: 

(b)  With unlike denominators:
       To add or subtract fractions with different denominators, you must first change each fraction to an equivalent fraction with least common denominator (LCD) as the common denominator  and then proceed as in part (a). 

Example 1:

Example 2:

2.  Multiplication of fractions
     When multiplying two or more fractions together, first cancel all pairs of common factors from both numerator and denominator, and then multiplying their respective remaining numerators and denominators.

Example:  Multiply: 
              

3.  Division of fractions
     To divide one fraction by another means to multiply the reciprocal of its divisor

Example:  Divide:
               

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NVCC Alexandria Campus Math Dictionary