Fundamental Laws of Arithmetic

< 21.1 Properties & Relations of Operations | Topic Index | 21.3 Order of Operations >

Axioms of Arithmetic

In the previous chapters we explored the reasons why certain axioms were laid down for arithmetic operations.

These formulated rules of operation when multiple numbers were operated upon by multiple operators.

A slightly abridged version of these axioms, considered very fundamental to arithmetic operations, are called “Fundamental Laws of Arithmetic”.

Fundamental Laws of Arithmetic

These laws are listed in the table below.

These laws may look simple & intuitive and can be verified visually or with objects. But they helped mathematicians to define what a number is. They also helped them derive the rules of operation of new kinds of numbers like integers.

What is a number?

Mathematicians defined that any entity which obeys these laws can be considered as a number. In fact, this could be taken as a general definition of a number.

It also ensures that the rules of operations of different kinds of numbers yield consistent results. You will recall that we derived integer operation rules both by extending patterns and by using distributive law.

Fundamental Laws of Algebra

Even in school level algebra we operate only on numbers, except that the numbers are sometimes represented with letters of the alphabet. Hence the same laws apply in algebra also. In fact in the above table, we have represented the laws in algebraic notation.

This is different from the Fundamental Theorem of Algebra which is beyond the K-8 curriculum.

< 21.1 Properties & Relations of Operations | Topic Index | 21.3 Order of Operations >