ARITHMETIC. Characters used in this Book. 1s. signifies that 12 penco are equal ARITHMETIC is the art of computing and has five principal rules for its operation, tion, Addition, Subtraction, Multiplication, an dition; as, 5+7=12, signifies that er, are equal to 12. n of Şubtraction; as, 6–2=4, sigo d from 6, leaves 4. the sign of Multiplication; as, at 4 multiplied by 3, is equal to 1.2 NUMERATION. Numeration is the art of numbering. It press the value of any proposed number hy characters, or figures : 1, 2, 3, 4, 5, 6, 7, 8, 9, 0-or ci Besides the simple value of figures, eac value, which depends upon the place it stan ngure in the place of units, represents only it: ar so many ones; but in the second place, or cecomes so many tens, or ten times its simple the third place, or place of hundreds, it becom times its simple value, and so on, as in the fol *; as, 8=2=4, signifies that 8 die 4; or thus, £=4, each of which e middle of four numbers, dengte al to one another, by the rule of 16; that is, as 2 to 4, so is 8 to 16. er, supposes that the square root of Note.-Although a cipher standing alone signifies no Is placed on the right hand of figures, it increases their proportion, by throwing them into higher places. Thus, nexed to it, becomes 20, twenty, and with two ciphers, thus 2. When numbers consisting of many figures, are e will be found convenient to divide them into as many pe six figures each, reckoning from the right hand towards first the period of units, the second that of millions, the fourth trillions, &c. as in the following number : 8 07 3 6 2 5 4 6 2 7 8 9 0 1 2 5 4. Period of 3. Period of 2. . Period of Trillions. Billions. Millions. er, supposes the cube root of that root, or fourth power, &c. 8073 789012 The foregoing number is read thus-Eight thousand trillions ; six hundred and twenty-five thousand, four two billions ; seven hundred and eighty-nine thousand a five hundred and six thousand seven hundred and ninet N. B. Billions is substituted for millions of millior 'Trillions for millions of millions of millions. Quatrillions for millions of millions of millions of m TABLE. Millions, 1 -One • 2 1 -Twenty-one. • 3 2 1 -Three hundred twenty-one. 1 4 3 2 1 -Four thousand 321. • 5 4 3 2 1 -Fifty-four thousand 321. 1 6 5 4 3 2 1 -654 thousand 321. • 7 6 5 4 3 2 1 -7 million 654 thousand 321. • 8 7 6 5 4 3 2 1 -87 million 654 thousand 321. 9.8 7 6 5 4 3 2 1 -987 million 654 thousand 321. 1 2 3 4 5 6 7 8 9 -123 million 456 thousand 789. 9 8 7 6 5 4 3 4 8 -987 million 654 thousand 348. To know the value of any number of figures : RuLk.-1. Numerate from the right to the left hand, each figure in its proper place, by saying, units, tens, hundreds, &c. as in the Numa ration Table. 2. To the simple value of each figure, join the name of its place, beginning at the left hand, and reading to the right. EXAMPLES. 1234, One thousand two hundred and thirty-four. hundred and sixty-one. 4666240, Four millions, six hundred and sixty-six thou sand two hundred and forty. NOTE. For convenience in veading large numbers, they may be divided into periods of three figures each, as follows: 987, Nine hundred and eighty-seven. hundred and fifty-four thousand, three hun. BLE. To write numbers. RULE.-Begin on the right hand, write units in the Jens in the tens place, hundreds in the hundreds plac luwards the left hand, writing each figure according to it in numeration ; taking care to supply those places a order with ciphers which are omitted in the question, EXAMPLES. Write down in proper figures the following ty-one. hundred twenty-004 housand 321. four thousand 321. cousand 321. on 654 thousand 321. ion 654 thousand 391. llion 654 thousand 321. llion 456 thousand 789. Ilion 654 thousand 348 ny number of figures : hi to the left hand, each figura s, hundreds, &c. as in the form igure, join the name of its plach ng to the right ES. SIMPLE ADDITION. IS putting together several smaller numbers denomination, into one larger, equal to the v total; as 4 dollars and 6 dollars in one sum is RULE.—Having placed units under units, tens under a line underneath, and begin with the units ; after a figure in that column, consider how many tens are co sum ; set down the remainder under the units, and ca you have tens, to the next column of tens; proceed in ner through every column or row, and set down the of the last row. EXAMPLES, (1.) (2.) (3.) ng numbers. sixty-five. . ndred and thirty-four . nd twenty-six enty-three thausand four e. dred and sixty-six thor forty. 20 Units. o CG A Co er C. of Thous. 100 hoek or X. of Thous. 4 1 Eighty-seven. ding large numbers , they figures each, as follows: ighty-seven thousand. ghty-seven million. ghty-seven million, siz I thousand, three hua To prove Addition, begin at the top of the sum, and reckon the hgures downwards in the same manner as they were added up EXA wards, and if it be right, this sum total will be equal to ti cut off the upper line of figures, and find the amount of th if the amount and upper line, when added, be equal to tl work is supposed to be right. 2. There is another method of proof, as follov Reject or cast out the nines in each row or sum of figures, and set down the re 3 may mainders, each directly even with the figures 57 in its row ; find the sum of these remain- 87 ders; then if the excess of nines in the sum found as before, is equal to the excess 18 3 of nines in the suin total, the work is supposed to be right. 15. Add 8635, 2194, 7421, 5063, 2196, and gether. Ans 16. Find the sum of 3482, 783645, 318, 9678045. Ans. I 17. Find the sum total of 604, 4680, 98, 64, Ans. Fifty-five 18. What is the sum total of 24674, 16742, 34 and 13439? Ans. One hundred t 19. Add 1021, 3489, 28763, 289, and 6438, Ans. Forty t 20. What is the sum total of the following n 2340, 1066, 3700, and 4005 ? An (12.) 3 7 1 8 4 5 6 87 51 1704 2 29 1 9 4 6 6 3 7 % 834073 270155 3 6 0 23 1 950 (14.) 2 5 900 340 0 4 5 5 40 4 4 3 3 370 5 5 3 2 6 4052174 4 0 64 762 6 9 2 0 68591 Answer, 22. Required the sum of the following numbe Five hundred and sixty-eight, op of the sum, and reckor per as they were added up |