Some real-life situations involving numbers can directly be solved using the four fundamental operations: addition, subtraction, multiplication and division. For instance, if 1 apple cost 5 pesos, how much do 15 apples cost? To solve this problem simply multiply 15 by 5. However, there are other practical applications which can best be solved by looking for a general pattern, relationship or formula before arriving at the answers.
An example would be, study the sequence: 2, 4, 8, 16, 32 and so on, what is the sum of the first 12 numbers in this sequence? This problem entails a formula to shorten the procedure. It is on this context, that the core of Algebra lies on representing quantities, patterns or relationships by symbols other than numbers. These symbols, which can be any letter in the English alphabet, are called variables that can take on more than one value. These symbols can further be grouped using the four fundamental operations, which in turn give meaning to equations or inequalities. These groups of symbols are called mathematical expressions which are used to represent verbal expressions or phrases.