Integer Operations - 1

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How do we know work out the results of the four operations on integers? What are the rules to be remembered for these operations? For this, mathematicians went back to the axioms of arithmetic. We can understand this in 2 ways.

Chapter 19.7 works out the rules of multiplication by applying the Fundamental Laws of Arithmetic.
 * 1) The application of the fundamental laws of arithmetic (Chapter 21.2).
 * 2) By applying the logic of patterns in the numbers being operated on

Chapters 19.8, 19.9 &amp; 19.10 show this process of pattern extension as applied to the addition, subtraction and multiplication operations. The rules followed have also been explained. The important results have been highlighted. We see that both approaches give us the same results.

The rules have been summarized below, for convenience. The rules for division have been worked out from those for multiplication as it is just the inverse operation.

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