Adding and Subtracting Fractions: Common Denominator Method

Fractions

Fractions are a mathematical concept used to represent parts of a whole. They consist of two components: a numerator, which represents the number of parts being taken out of a whole, and a denominator, which indicates how many equal parts the whole is divided into. When dealing with fractions, it's essential to understand common operations such as addition and subtraction. In this article, we will explore these concepts in detail.

Adding Similar Fractions

To understand how to add fractions, one must first recognize that all fractions have a common denominator. This means that they can be added by finding their equivalent fractions using the common denominator. For example, if you want to add (\frac{3}{8}) and (\frac{5}{8}), you would find the equivalent fraction of each with respect to the common denominator of (8):

• (\frac{3}{8} + \frac{2}{8} = \frac{5}{8})
• (\frac{5}{8} + \frac{3}{8} = \frac{8}{8} = 1)

So, when you add (\frac{3}{8}) and (\frac{5}{8}), you get (\frac{3}{8}).

Another method involves multiplying the numerators together and dividing by the greatest common factor (GCF) of the denominators:

[ \frac{a}{m} + \frac{b}{n} = \frac{an+bm}{mn}, ] where (a) and (b) are the numerators, and (m) and (n) are the denominators. Using this rule, the sum of (\frac{3}{8}) and (\frac{5}{8}) is (\frac{3(8)+5(8)}{8(8)}=\frac{24+40}{64}=\frac{64}{64}=1).

Subtracting Similar Fractions

Subtracting fractions works much like adding them. To subtract a fraction from another, you need to make sure both fractions have the same denominator. Then, you can follow the formula:

[ \frac{a}{m} - \frac{b}{n} = \frac{an-bm}{mn}. ] In this case, (a) and (b) are the numerators, and (m) and (n) are the denominators. Just as seen in the addition problem, subtracting (\frac{5}{8}) from (\frac{3}{8}) yields (\frac{-2}{8}) or equivalently, (\frac{3}{8}-\frac{5}{8}=\frac{-2}{8}).