By Lloyd Motz

We have designed and written this publication. now not as a textual content nor for the pro mathematician. yet for the final reader who's evidently interested in arithmetic as an exceptional intellec­ tual problem. and for the specified reader whose paintings calls for him to have a deeper knowing of arithmetic than he received at school. Readers within the first team are interested in psychological leisure actions corresponding to chess. bridge. and numerous different types of puzzles. yet they typically don't reply enthusiastically to arithmetic as a result of their unsatisfied studying stories with it in the course of their university days. The readers within the secondgrouptum to arithmetic as a need. yet with painful resignation and enormous apprehension relating to their skills to grasp the department ofmathematics they wish of their paintings. In both case. the phobia of and revulsion to arithmetic felt by way of those readers frequently stem from their prior challenging encounters with it. vii viii PREFACE This publication will express those readers that those fears, frustrations, and common antipathy are unwarranted, for, as said, it's not a textbook filled with lengthy, dull proofs and hundreds of thousands of difficulties, really it really is an highbrow event, to be learn with excitement. It was once written to be simply available and with predicament for the psychological tranquilityofthe reader who willexperience enormous achievement while he/she sees the simplicity of simple arithmetic. The emphasis all through this publication is at the transparent clarification of mathematical con­ cepts.

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Having received elaborate and precise instructions as to the problem at hand, the computer proceeds to grinding out figures at a prodigious rate . In the course of this operation it in many ways apes the process of a human calculation. The machine can organize its problem into separate steps; it can use the results obtained in one step to execute the next; sometimes partial results are laid aside, that is, 'remembered,' while an intermediate step is carried through; trial and error methods are frequently used.

We have already discussed the multiplication of fractions but it is worth repeating the rule that the product of any number of fractions is a fraction whose numerator is the product of all the individual numerators and whose denominator is the product of all the individual THE NUMBER SYSTEM 4S denominators. , 2/3 x 3/5 x 5/6 = 2/6 = 1/3. The division of one fraction by another is governed by the same rule that governs the division of integers which we can represent as a fraction by putting the dividend in the numerator and the divisor in the denominator, as in the example 6/2 when we divide by 2.

The number of factors in a large integer is, in general, larger than the number in a small integer, as illustrated by the integer 36, which has the factors 2, 3, 4, 6, 9, 12, and 18 in various product combinations such as 9 x 4, 62 , 32 X 4, 3 x 12, etc . Consider now the integer 32, which we may write as 2 x 16 = 4 x 8 = 22 X 23 = 25, which illustrates a very important arithmetic rule: to multiply two or more powers of the same integer, simply add all the exponents (the individual powers) and raise the integer to the power equal to that sum .

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