# Arithmetic for carpenters and builders

ARITHMETIC FOR CARPENTERS AND BUILDERS

BY R. BURDETTE DALE, M.E.

NEW YORK; JOHN WILEY & SONS, INC.
LONDON: CHAPMAN & HALL, LIMITED
1915

Arithmetic for carpenters and builders

PREFACE

This book was written for the purpose of presenting the subject of arithmetic, as used in the daily work of the carpenter and builder, in a simple form. It is intended for the practical man as well as for the beginner and the student.

The material is such that the work can be followed successfully by those who have had an eighth-grade education. Upon the completion of this study the student should be prepared to take up the problem of estimating the cost of buildings.

The author has not attempted to treat the subject exhaustively. Though the first chapters may seem elementary to some, they will furnish a much-needed review to others. Geometry is touched upon merely to serve as a foundation for the work in mensuration. Practical applications of geometric truths are emphasized, while rigid proofs and developments are omitted. Two chapters on the steel square, that most useful tool of the carpenter, are included.

Many of the problems do not admit of exact answers for the reason that the judgment of the student plays an important part in the solution. Different results will be obtained, depending upon the lengths and widths of the boards chosen and other similar details. Careful planning for the economical use of material is required, for this is an essential training for the work of the practical carpenter.

Students will do well to take advantage of this and every similar opportunity to develop their judgment. It is believed that the reader who follows this text carefully as a guide may learn much that may not strictly be classed as arithmetic. If the manner in which the subject is treated and the many applications made inspire the practical worker and the beginner to seek a better understanding of the fundamentals of carpentry, the author's most sanguine hopes will be justified.

As a text in vocational mathematics it is believed that this little volume should find a place in vocational and industrial schools, trade schools, manual training schools and night schools. It is also well adapted for use in correspondence instruction. The material has been used by the author in the Vocational Courses in Engineering at the Iowa State College and also in the extension classes of the Department of Engineering Extension in various cities in the state of Iowa.

No single book is the entire and original product of one man's mind; it consists rather of accumulated knowledge interpreted and adapted for a particular purpose. The author gratefully acknowledges assistance rendered knowingly and unknowingly by many others. Material borrowed from other sources is acknowledged in the text.

R. BURDETTE DALE.

CHAPTER I
UNITS OF LENGTH, ADDITION, SUBTRACTION, MULTIPLICATION AND DIVISION OF UNITS OF LENGTH

CHAPTER II
FRACTIONS, MIXED NUMBERS, LEAST COMMON DENOMINATOR, ADDITION AND SUBTRACTION OF FRACTIONS

CHAPTER III
MIXED NUMBERS, ADDITION, SUBTRACTION AND MULTIPLICATION OF MIXED NUMBERS, CANCELLATION.

CHAPTER IV
DIVISION OF FRACTIONS AND MIXED NUMBERS, COMPOUND FRACTIONS

CHAPTER V
MONEY, ADDITION, SUBTRACTION, MULTIPLICATION AND DIVISION OF MONEY QUANTITIES, CHECKS, STATEMENTS, RECEIPTS, ESTIMATES

CHAPTER VI
DECIMALS, ADDITION, SUBTRACTION, MULTIPLICATION AND DIVISION OF DECIMALS, CHANGING FROM COMMON FRACTIONS TO DECIMAL FRACTIONS

CHAPTER VII
THE USE OF RULES, PULLEY SIZES, WIDTH OF BELTS, FORMULAS, SHORT METHODS OF MULTIPLICATION AND DIVISION

CHAPTER VIII
PERCENTAGE, DISCOUNTS, PROFIT, INTEREST

CHAPTER IX
RATIO, PROPORTION, CEMENT AND CONCRETE MIXTURES, SLOPES, LEVERS

CHAPTER X
LINEAR MEASURE, AREA, VOLUME, LIQUID MEASURE, DRY MEASURE, WEIGHT, THE CIRCLE, WEIGHT OF BUILDING MATERIALS, BEARING POWER OF SOILS, FOOTINGS, CONCRETE MIXTURES,

CHAPTER XI
POWERS, ROOTS, RIGHT TRIANGLES, AREA OF CIRCLES, CAPACITY OF TANKS AND CISTERNS

CHAPTER XII
LUMBER TERMS AND DIMENSIONS, FLOORING, SHINGLES

CHAPTER XIII
BUILDERS GEOMETRY, GEOMETRIC CONSTRUCTIONS, ANGLES AND ANGULAR MEASURE, ELLIPSE, POLYGONS

CHAPTER XIV
AREAS OF SURFACES AND VOLUMES OF SOLIDS, AREA OF TRIANGLE, PYRAMID, CYLINDER AND CONE, VOLUME OF CYLINDER, PRISM, PYRAMID AND CONE, MEASURING SURFACES AND VOLUMES

CHAPTER XV
USE OF THE CARPENTER'S SQUARE, BRACE MEASURE, OCTAGONAL SCALE, ESSEX BOARD MEASURE, DIAGONAL SCALE, POLYGON SCALE, GEOMETRIC APPLICATIONS

CHAPTER XVI

USE OF THE CARPENTER'S SQUARE IN FRAMING, FLOOR BRIDGING, STAIR BEAMS, RAFTER FRAMING, ROOF PITCHES, RAFTER TABLE, ROOF FRAMING, HIP OR VALLEY RAFTERS, JACK RAFTERS