While in arithmetic only numbers and operators like + , â ' , Ã -- , and Ã occur ; in algebra , variables ( like a , x , y ) are used to stand for numbers . The major difference between algebra and arithmetic is the inclusion of variables . While in arithmetic only numbers and their arithmetical operations ( such as + , â ' , Ã -- , Ã ) occur , in algebra , one also uses symbols such as x and y , or a and b to denote variables .