ARITHMETIC is the art of computing by numbers, and has five principal rules for its operation, viz. Numeration, Addition, Subtraction, Multiplication, and Division. NUMERATION. Numeration is the art of numbering. It teaches to express the value of any proposed number by the following characters, or figures: 1, 2, 3, 4, 5, 6, 7, 8, 9, 0-or cipher. Besides the simple value of figures, each has a local value, which depends upon the place it stands in, viz. any figure in the place of units, represents only its simple yalue, or so many ones; but in the second place, or place of tens, it becomes so many tens, or ten times its simple value; and in the third place, or place of hundreds, it becomes a hundred times its simple value, and so on, as in the following Note.-Although a cipher standing alone signifies nothing; yet when it Is placed on the right hand of figures, it increases their value in a tenfold proportion, by throwing them into higher places. Thus, 2 with a cipher annexed to it, becomes 20, twenty, and with two ciphers, thus, 200, two hundred. 2. When numbers consisting of many figures, are given to be read, it will be found convenient to divide them into as many periods as we can, of six figures each, reckoning from the right hand towards the left, calling the first the period of units, the second that of millions, the third billions, the fourth trillions, &c. as in the following number: 8 0 7 3 6 2 5 4 6 2 7 8 9 0 1 4. Period of 3. Period of 2. Period of Trillions. 8073 Billions. 625462 Millions. 789012 2.5 067 9 2 1. Period of Units. 506792 The foregoing number is read thus-Eight thousand and seventy-three trillions six hundred and twenty-five thousand, four hundred and sixtytwo billions; seven hundred and eighty-nine thousand and twelve millions; five hundred and six thousand seven hundred and ninety-two. N. B. Billions is substituted for millions of millions. 'Trillions for millions of millions of millions. Quatrillions for millions of millions of millions of millions, &c. TABLE. C. of Thousands, X. of Thousands, Millions, C. of Millions, X. of Millions, Thousands, Hundreds, • 1 -One 21 -Twenty-one. 3 2 1 -Three hundred twenty-one. 4 3 2 1 -Four thousand 321. 5 4 3 2 1 -Fifty-four thousand 321. 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: RULE.—1. Numerate from the right to the left hand, each figure in its proper place, by saying, units, tens, hundreds, &c. as in the Numeration 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. Read the following numbers. 365, Three hundred and sixty-five. 5461, Five thousand four hundred and sixty-one. 1234, One thousand two hundred and thirty-four. 54026, Fifty-four thousand and twenty-six. 123461, One hundred and twenty-three thousand four hundred and sixty-one. 4666240, Four millions, six hundred and sixty-six thousand two hundred and forty. NOTE. For convenience in reading large numbers, they may be divided into periods of three figures each, as follows: 987, Nine hundred and eighty-seven. 987 000, Nine hundred and eighty-seven thousand. 987 000 000, Nine hundred and eighty-seven million. 987 654 321, Nine hundred and eighty-seven million, six hundred and fifty-four thousand, three hun. dred and twenty-one. To write numbers. RULE.-Begin on the right hand, write units in the units place, lens in the tens place, hundreds in the hundreds place, and so on, towards the left hand, writing each figure according to its proper value in numeration; taking care to supply those places of the natural order with ciphers which are omitted in the question. EXAMPLES. Write down in proper figures the following numbers : Two hundred and seventy-nine. Thirty-seven thousand, five hundred and fourteen. SIMPLE ADDITION. IS putting together several smaller numbers, of the same denomination, into one larger, equal to the whole or sum total; as 4 dollars and 6 dollars in one sum is 10 dollars. RULE. Having placed units under units, tens under tens, &c. draw a line underneath, and begin with the units; after adding up every figure in that column, consider how many tens are contained in their sum; set down the remainder under the units, and carry so many as you have tens, to the next column of tens; proceed in the same manner through every column or row, and set down the whole amount of the last row. spuesnoчLOSID | 1756 7422 Thousands. ∞ ∞ & C. of Thous. er X. of Thous. Units. 55 26 2 34 6.97 7 To prove Addition, begin at the top of the sum, and reckon the figures downwards in the same manner as they were added up wards, and if it be right, this sum total will be equal to the first: Or cut off the upper line of figures, and find the amount of the rest; then if the amount and upper line, when added, be equal to the total, the work is supposed to be right. 2. There is another method of proof, as follows:— Reject or cast out the nines in each row or sum of figures, and set down the remainders, each directly even with the figures in its row; find the sum of these remainders; then if the excess of nines in the sum found as before, is equal to the excess of nines in the sum total, the work is supposed to be right. EXAMPLE. 3782 5 7 6 6 8755 18 3 0 3 2 6 7 15. Add 8635, 2194, 7421, 5063, 2196, and 1245, together. Ans. 26754. 16. Find the sum of 3482, 783645, 318, 7530, and 9678045. Ans. 10473020. 17. Find the sum total of 604, 4680, 98, 64, and 54. Ans. Fifty-five hundred. 18. What is the sum total of 24674, 16742, 34678, 10467, and 13439 ? Ans. One hundred thousand. 19. Add 1021, 3489, 28763, 289, and 6438, together. Ans. Forty thousand. 20. What is the sum total of the following numbers, viz. 2340, 1066, 3700, and 4005? Ans. 11111. 21. What is the sum total of the following numbers, viz. Nine hundred and forty-seven, Seven thousand six hundred and five, Forty-five thousand six hundred, Three hundred and eleven thousand, Nine millions, and twenty-five, Fifty-two millions, and nine thousand? Answer, 61374177 22. Required the sum of the following numbers, viz. Five hundred and sixty-eight, Eight thousand eight hundred and five, |