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, 0. 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

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.

46, 199, 2267, 86693,

289732,

11911911.

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.

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.

Is a compendious way of adding numbers of the same name, as in the following tables of adding and multiplying. The number to be multiplied is called the multiplicand. The number which multiplies is called the multiplier. The number arising from the operation is called the product.

12 24 36 48 60 72 84 96 108 120 132 144 240