MERCANTILE ARITHMETIC. ARITHMETIC is the art of computing by numbers, and has five principal rules for this purpose, viz. Numeration, Addition, Subtraction, Multiplication, and Division. NUMERATION Teacheth to express any proposed number by these ten characters, Ọ. 1. 2. 3. 4. 5. 6. 7. 8. 9.-0 is called a cipher, and the rest, figures or digits. The relative value of which depends upon the place they stand in, when joined together, beginning at the right hand, as in the following Though the table consists of only nine places, yet it may be extended to more places at pleasure; as, after hundreds EXPLANATION OF THE CHARACTERS USED IN THIS WORK. = SIGNIFIES equality, or equal to: as 20 shillings = one pound: that is, 20 shillings are equal to 1 pound. +Signifies more, or Addition: as, 6+6=12: that is, 6 added to 6 is equal to 12. Signifies less, or Subtraction: as, 6-2-4: that is, 6 less 2 is equal to 4. × Signifies Multiplication: as, 6×2—12: that is, 6 multiplied by 2 is equal to 12. Signifies Division: as, 62-3: that is, 6 divided by 2 is equal to 3. Division is sometimes expressed by placing the numbers like a fraction, the upper figures being the dividend, and the lower the divisor: thus, 549: that is, 54 divided by 6 is equal to 9. :::: Proportion as 3:6::9:18: that is, as 3 is to 6, so is 9 to 18. ✓ Prefixed to any number, signifies that the square root of that number is required. A line or vinculum, drawn over several numbers, signifies, that the numbers under it are to be considered jointly. as 8—3+4=1 : but without the line, 8—3—4—9. of millions, read thousands of millions, ten thousands of millions, hundred thousands of millions, billions, trillions, quadrillions, quintillions, sextillions, septillions, octillions, nonillions, decillions, undecillions, &c. as in the following example: Periods. Quadrill. Trillions. Billions. Millions. Units. Half-per.| th. un. th. un. th. un. th. un. c.x.t.c.x.u. Figures. 123, 456. 789, 098. 765, 432. 101, 234. 567, 890. TO WRITE NUMBERS. RULE. Write down the figures as their values are expressed, and supply any deficiency in the order with ciphers. EXAMPLES. Write down in proper figures the following numbers. Twenty-nine. Two hundred and forty-seven. Seven thousand nine hundred and one. Eighty-four thousand three hundred and twenty-nine. Nine hundred and two thousand six hundred and fifteen. Eighty-nine millions and ninety. Four millions four hundred thousand and forty. Nine hundred and nine millions nine hundred and ninety. Seventy millions seventy thousand and seventy. To express in words any number proposed in figures. RULE. To the simple value of each figure, join the name of its place, beginning at the left hand, and reading towards the right. EXAMPLES. Write down in words the following numbers. 11911911. 46, 199, 1169990, 9919, 7114320, 3155000510, 1375684001957. SIMPLE ADDITION Teacheth to collect numbers of the same denomination into one sum. RULE. Place the numbers under each other so that units may stand under units, tens under tens, and so on, and draw a line under them. Add the first row or right hand column, and find how many tens are contained in them.-Set down the remainder, and carry as many units or ones to the next column, as there are tens. In like manner carry the tens of each column, till the whole be finished. PROOF. The mercantile method of proving addition is to reckon downwards as well as upwards, or to divide the sum to be added into several divisions or parcels, add these separately, and then add their sums together.-If the amount of these be the same as the amount obtained by adding at once, it may be presumed the true amount is obtained. Add the following sums, viz. 76389. 576. 8799. 7. 532. 6741. 86. 95310. 15. 10019. 900.45913 and 19, together. 76389 571. 26 and 7993, together. 576 8799 532 7 900 45913 19 6741 86 95310 15 10019 571 26 7993 Add the following numbers, viz. 1.2.3.4.5.6.7.8 and 9 together. Ans.45 9.8.7.6 5.4.3.2 1 5.6.7.9.8.6.3.5.4 2 6.7.9.3.4.9.6.7.4 8 8.4.7.6.9.4.3.9.7 6 7.3.8.4.7.9.5.6.8.5 4 6.9.5.4.8.6.3.9.9.8.6 9 9.6.8.9.9.3.6.8.4.5.9 6 7.8.9.4.5.6.8.9.9.7.7.3 4 4.3.7.7.9.9.8.6.5.4.9.8 7 8.7.4.9.5.2.1.7.9.8.3.6.2 9 9.2.6.3.8.9.7.1.2.5.9.4.7 5 6.5.8.9.3.7.4.9.8.7.5.6.3.7.9.9.8.7.4 7.3.9.5.8.5.6.9.4.8.6.5.7.9.3.7.7.8.9.6 8 6 4 SIMPLE SUBTRACTION Teacheth to take a less number from a greater of the same denomination, and thereby show the difference. The greater is called the minuend, and the less the subtrahend. RULE. Place the subtrahend or less number, under the minuend or greater, and subtract units from units, tens from tens, and so on. If any figure of the subtrahend be greater than the corresponding one of the minuend, borrow ten; that is, add ten to the upper figure, and then subtract the lower from the sum, set down the remainder, and carry one to the next figure of the subtrahend. PROOF. Add the remainder to the subtrahend, and if the sum is equal to the minuend, the work is right. |