Math is a mental construct. it has no inherent "Basic Components".
Back in the mid 1900 century there was a French Mathematician who spent some 20 year tying to prove that the number '1' was a 'real' quantity. He eventually gave up (or maybe he just died of old age).
Both Sharonna and Glis above mention adding and subtracting. But why mention subtraction at all ? It just means that the number you add is negative ;-))
Likewise multiplication is just adding the same number more than once.
And so it goes, math defines itself by itself for itself. It has no real tie-in to reality.
But it does have real usefulness. It let us build bridges that dont fall down, make spacecraft that successfully arrive at the moon (or Mars), make mobile phones, etc, etc.
Because adding a negative and subtracting a positive are different values that have the same outcome. In some instances you can express it either way but not in all.
The basic operations of mathematics are those of arithmetic, so adding, subtracting, multiplying and division; but in algebra not actual numbers (the latter come into specific calculations).
Algebra because that is the language of mathematics: you cannot have maths without algebra because you'd have no tools for expressing and manipulating the concepts and in real life problems, the values and moves in the particular calculations.
JakobA the unAmerican. 