By Isaiah Leslie Miller

AN advent TO arithmetic With functions to technological know-how and Agriculture by way of ISATAII LESLIE MILLER Professor of arithmetic, South Dakota kingdom university of Agriculture and Mechanic Arts F. S. CROFTS CO. long island ----MCMXXX COPYRIGHT, 1930, by means of F. S. CROITS Co., INC. synthetic within the u . s . a . through BRAUNWORTH CO., INC., BROOKLYN, ny PREFACE AFTER a few fourteen years of training in American faculties and universities the writer unearths that the common highschool graduate has now not constructed in himself a mathematical form of reasoning. lie accordingly hopes that this therapy may well in a few degree accomplish this function. the 1st few chapters are dedicated to an intensive assessment of highschool algebra, for the writer is confident that almost all university novices want huge drill at the basic strategies of algebra ahead of making an attempt a truly huge examine of arithmetic. In getting ready this booklet the writer has saved in brain sorts of scholars first, those that won't ever take extra paintings in arithmetic, and moment, those that will proceed the paintings in technology or agriculture for complex levels and should no doubt wish to pursue extra classes in arithmetic. He has for that reason tried to write down a ebook uncomplicated within the primary rules of arithmetic and while has endeavored to make useful functions to the fields of technological know-how and agri tradition, anyplace attainable. He feels thorough wisdom of the fabric lined during this paintings will let the second one kind of scholar to effectively pursue a direction in analytical geometry through a path within the calculus. the writer gratefully recognizes his indebtedness to his colleagues, Professor Win. Asker for getting ready the bankruptcy on data, and Mr. H. B. MacDougal for checking a lot of the cloth, to Professor I. W. Smith of the North Dakota Agri cultural collage for utilizing the fabric in mimeographed shape and delivering many priceless feedback, to Dean D. A. Roth VI PREFACE rock of Indiana college for interpreting many of the manuscript and to Professor Wm. Marshall of Purdue college for encouraging him within the paintings. the writer additionally wants to thank Professor E. S. Crawley of the college of Pennsylvania for his beneficiant permission to exploit the higher a part of his Tables of Logarithms as a element of this e-book. I. L. MILLER SOUTH DAKOTA kingdom university CONTENTS bankruptcy I ALGEBRAIC OPERATIONS ARTICLE web page 1. 4 basic OPERATIONS 1 2. ADDITION AND SUBTRACTION 1 three. USE OF PARENTHESES, symptoms OF AGGREGATION 1 four. MULTIPLICATION three five. department four 6. department OF A POLYNOMIAL via A POLYNOMIAL four 7. 0 IN department four bankruptcy II FACTORING eight. vital sort items i nine. different very important items eight 10. optimum universal issue nine eleven. LOWEST universal a number of 10 bankruptcy III LINEAR EQUATIONS in a single UNKNOWN 12. EQUALITIES 12 thirteen. answer OR ROOT OF AN EQUATION 12 14. an identical EQUATIONS thirteen 15. OPERATIONS ON EQUATIONS thirteen sixteen. variety kind of THE LINEAR EQUATION in a single UNKNOWN. . . thirteen 17. VERIFICATION via SUBSTITUTION thirteen bankruptcy IV FRACTIONS 18. ALGEBRAIC FRACTION sixteen 19. OPERATIONS sixteen vii Vlll CONTENTS ARTICLE web page 20. aid OP a fragment TO ITS LOWEST phrases 17 21. ADDITION AND SUBTRACTION 18 22. MULTIPLICATION AND department 19 23. complicated FRACTIONS 20 24. FRACTIONAL EQUATIONS 21 bankruptcy V features 25. CONSTANTS AND VARIABLES 24 26. DEFINITION OF A functionality 24 27. practical NOTATION 24 28. useful family 25 29. formulation TAKEN FROM GEOMETRY . . . 26 30. GRAPHICAL illustration OF useful family members. ... 29 31. STATISTICAL info 34 bankruptcy VI structures OF LINEAR EQUATIONS 32. GRAPHS OP LINEAR EQUATIONS . 39 33. GRAPHICAL resolution forty-one 34. ALGEBRAIC answer forty three 35. answer of 3 LINEAR EQUATIONS IN 3 UNKNOWNS. forty four 36. SLOPE OF A instantly LINE forty eight 37. DISTANCE among issues 50 38. EQUATION OF A immediately LINE 50 39. challenge aspect type of THE EQUATION OF A LINE . fifty one forty. challenge SLOPE AND ONE aspect type of THE EQUATION OF A LINE fifty three 41...

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_J, + + So; 18. 7 (a - fe)(6 6 - a: 2 c) - - 55 + 8x + 12 (o 6a - 22. Multiplication and (Art. ) Example Find (a). x2 Solution. 1 c)(c - a2 6) division. - 15a (6 - + 44 a)(c - a) See principles V and VI. AN INTRODUCTION TO MATHEMATICS 20 ^x , Example (<* (b). a - + 2 2 *>) - [CHAP. IV 6 * / b b Solution. Exercises Perform the following multiplications and divisions: s 2 + *)'* (1 a m 5. + ab m + mn 6. - mn m* a &\y 2 06 - (a \ x* - y . a-b a + b + 2mn ^ m m* ! + -- a 20 n 2 - ^ + a - a - 4n 2 62 2c 2 2 n2 25 n+l r 2 - a2 b c \a 800; ' 2 / ^ b/ 2 25 n2 o / 9.

We have = x Substituting this value for x in 4 +y- Substituting 6 for y in x (1), - = 6 we (2), =- 4y -3y = - or 4 14, y 18, find we find 4, or (4) = 6. x = 10. Hence the required values for x and y are 10 and 6 respectively. This method is known as elimination by substitution. Solution. From Second Method. (1) subtract (2) and we get 3y Multiplying (1) by 4 and (4) and (5), Hence the required (2) = y 18, by 6. (3) 1, the two equations become - 4y = 16, (4) -s + 4y = 14. (5) 4x Adding = we get 3x = solution 30, is x x = = 10.

31] 35 measured on the horizontal axis. The temperature degrees is measured vertically upward and downward. m. we count 4 spaces to the right and 2 spaces down locating a point. In a similar way we locate points for hours is in all of the data. By joining these points in order the graph is obtained. From temperature curve we may obtain much informathe temperature changing most rapidly? g. When was it warmest? When coldest? When was the change a rise? When a fall? this : When was Exercises 1. The daily gain in weight of a calf in pounds for period of one is given in the following table: hundred days Draw a curve showing this information.