Arithmetic - An Introduction to Mathematics by L. Clark Lay

By L. Clark Lay

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Example text

Associative Principles The diagram below shows 3 fives, or 5 threes, depending on whether we count by rows or by columns. 3 • 5 The = 5 • 3 is an example of the commutative property of multiplication. general principle, which is assumed to hold for all natural numbers, called the commutative principle for multiplication and (A)(B) = (B)(A) Since the natural numbers arose out of counting, fundamental properties may is is written as we may expect that their The diagram below be illustrated by counting.

A = -j 1, if A This follows from 9^ 0. same number 2. y= A. A B 3. -Tj 7* -j A 4. -7r If a unless A B ^ ^ number B = is A. Division is • 1 = A number A. gives a quotient of divided by Division A is I, 1, if the quotient is the number is not 0. same number. commutative. not, in general, not, in general, associative. the divided by Note that the bars being used to indicate division are of different length (or width), and 7T hence set up a different order of division. The A is left member The divided by ~- and then A -^ of the equation states that first right divided by C.

4(9 ? + + (3) (2) + 5) (6) 14. 30 ? 3)(7) • 28. 20 2. = 2 • 22. 5 • 4 = 3) (2) - 13. 50 2 = = ? first. = ? (4) (3 + 2) • • • • ? • • • • + 6) (2 + 5) = ? Multiplication of Natural 20 Whenever more than one kind it of operation [Ch. 2 to be used in a computation, is customary to name the computation by the is Numbers operation that last is to be performed. Examples: + 2 (8) (5) is a sum, since the multiplication and the addition + (2 is 8) (5) is done a product, since the addition and the multiplication 2 • 8 first, Problems Name — 5 done first, done is is done first, last.

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