It is important that you develop a logical, systematic approach to the arithmetic of fractions because the principles involved apply more generally to many algebraic problems. Addition and subtraction You cannot add 2 apples and 3 oranges. You need to think of them in terms of their common property fruit. Then, adding them, you have 5 pieces of fruit. The addition of fractions is analogous.
Subtraction involves the same basic steps.
Similarly, means half of , i.e. . Similarly, division by a fraction is equivalent to multiplication by the inverse of the fraction. A power may also be a rational number but, in order to avoid complications some restrictions the definition are needed. Using long division you can represent any rational number as a decimal. It can be proved that the representation of any rational number is either finite or, after a certain stage, the digits repeat themselves in groups.