one on which write in red ink "Corrected on next page,' with date of correction. 10. Solution of Equations. Number equations at the left in a vertical column with Arabic numerals in parentheses. Separate equations from specified operations, by a horizontal, rippled line not shorter than half an inch. It must follow each equation except those taken from the text or formed from the conditions specified in the problem. The following model solution shows how to number, how to use the rippled line, and how to abbreviate. (1) Mul (a) by 8 (2) (3) 5x-24x=2mm —19x=2~~~~Col in (1) x= -2/19mm Div (2) by -19 As illustrated, equations from the text are numbered with the first letters of the alphabet. Equations resulting from operations, are numbered in succession in Arabic numerals. 11. Indication of Results. Indicate final results in all problems by double underlining with parallel hair-lines not over one-sixteenth of an inch apart. Do not write the word "Answer." On the same line with the result write a statement in initial capitals specifying exactly what the result represents, whether horse-power, or speed, etc. 12. Index. At the end of the school year arrange all the work-books of the year in order, make an alphabetic index for your combined book, cut the work-book cover in two through the back, and bind all together with one pair of fasteners. On the front cover, attach a label about 4×5, with a line border and lettered title, enumerating the subjects covered. CHAPTER I THE FUNDAMENTAL OPERATIONS SECTION 1, ADDITION. SECTION 2, SUBTRACTION. SECTION 3, MULTIPLICATION. SECTION 4, DIVISION. SECTION 5, APPLIED PROBLEMS 1. The Symbols of Arithmetic. All computation is carried on through the use of the following symbols: 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. These symbols are called numbers, digits, or figures, figures being the usual name. The last is called cipher, nought, or zero, as may be convenient. The name ought, by which it is sometimes known, is incorrect and should not be used. The value of these symbols depends entirely on how they are written with respect to each other. When used separately, or together with commas between them as above, they denote one, two, three, four, five, six, seven, eight, nine, nought. When written one after the other with no marks between, their value is determined by their position. For example, 75483 is read seventy-five thousand, four hundred eighty-three. 3, being in the first place, counting from the right, means three units, the same as when written alone. 8, being in the second place from the right, means ten times eight, or eighty. 4 in the third place means four hundred; 5 in the fourth place means five thousand; 7 in the fifth place means seventy thousand. Below is shown the values of figures to right and left from the decimal point. 9 This number is read, three million, nine hundred seventy-two thousand, one hundred sixty-nine, and one hundred eighty-four thousandths. It should be noted that "and" is used in place of the decimal point in the reading, and that the figures following the decimal point are read as thousandths, because the last figure is in thousandths place. .1364 is read thirteen and sixty-four ten-thousandths because the last figure is in ten-thousandths place. Another way of reading is illustrated below, and is recommended because it makes it unnecessary to think the name of the place in which the last figure of the decimal stands. may be read or. .224, 5.17, 381.03, point two twenty-four, five point seventeen, three eighty-one point nought three; two hundred twenty-four thousandths, five and seventeen hundredths, three hundred eighty-one and three hundredths. 2. Examples in Reading Numbers. Between the holes at the top of the first page of your work-book, write your last name. In the upper right corner, not less than one inch from the top of the page, enter the date on which you are doing the work required in this paragraph. Beginning not less than one and one-half inches from the top of the page, near the left margin, enter the paragraph number and title. Under the paragraph title, copy any five of the following numbers and write two different readings for each. 3. The Four Fundamental Operations. The operations of arithmetic by means of which all computations are made, are Addition, or finding the sum of numbers, § 1. ADDITION 4. How to Add. In setting down numbers having no decimal points, so that they may be added, the margin is kept straight on the right so that units shall be under units, ten under tens, hundreds under hundreds, etc. In setting down numbers having decimal points, no attention is paid to right or left margins, the only requirement being that the decimal points shall be in a vertical column, so that units shall be under units, tens under tens, etc. Thus to add 134, 17, 1763, 21783, 9 and 10005; Also 17.962, .00073, 184.005, 9.64, 1732.4, and 18, set them down as follows: Each column is then added, beginning at the right. The sum of the units column of the first group of numbers, is 31 which is one unit and three tens. 1 is therefore entered under the units column and the 3 is added (or carried as it is called) to the tens column. 5. Examples in Addition. While one may learn to add from one example, to gain accuracy and rapidity much practice is necessary. Under the paragraph number and title, copy and add the following numbers: |