When adding fractions, you must make sure that they have a common denominator. This means that their bottom number, the denominator, is the same.
For example, for this equation:
You need to find a common denominator for 3 and 5. Do this by multiplying the denominators by each other. For example, multiply 3 times 5 to get 15.
Remember that whatever you do to the bottom number you must also do to the top number. So now multiply both numerators by the number you multiplied their denominator by.
Now that the fractions have the same denominator, you can add them regularly. Only add the numerators; don't add the denominators. The solution's denominator will be the common denominator of the two fractions. Reduce the fraction, if necessary.
The notion of number has intrigued mathematicians since ancient times. While fractions were understood by the Greeks and used with a geometrical meaning, the nature of irrational numbers such as the square root of 2 became clearer during the Renaissance and has been formalized since the eighteenth century.http://www.geom.uiuc.edu/~demo5337/Group3/hist.html