To multiply by 21, 31, 41, &c. to 91: Multiply by the ten's figure, only, of the multiplier, and fet the unit figure of the product under the place of tens; add them all together, and their fum will be the total product. £

DIVISION

Teaches to feparate any number, or quantity give into any number of parts affigned; or to find how ofte one number is contained in another; or from any tw numbers given to find a third, which fhall confift of f many units, as the one of thofe given numbers is compre hended in the other; and is a concife way of perform ing feveral fubtractions.

There are four principal parts to be noticed in Divifion, viz.

1. The Dividend, or number given to be divided. 2. The Divifor or number given to divide by.

3. The Quotient, or anfwer to the question, which hows how often the divifor is contained in the dividend.

4. The remainder (which is always lefs than the divifor, and of the fame name with the dividend) is very uncertain, as there is fometimes a remainder, and fometimes none.

Divifion is both fimple and compound.

PROOF.

Multiply the divifor and quotient together, and add the remainder, if there be any, to the product: If the work be right, that fum will be equal to the dividend.

SIMPLE DIVISION

Is the dividing of one number by another, without regard to their values: As, 56, divided by 8, produces 7 in the quotient: That is, 8 is contained 7 times in 56.

CASE

CASE I.*

RULE.

Firft, feek how many times the divifor is contained in a competent number of the first figures of the dividend; when found, place the figure in the quotient; multiply the divifor by this quotient figure; place the product under the left hand figures of the dividend; then fubtract it therefrom, and bring down the next figure of the dividend to the right hand of the remainder: If, when you have brought down a figure to the remainder, it is ftill less than the divifor, a cypher must be placed in the quotient, and another figure be brought down; after which you must feek, multiply, and fubtract, till you have brought down every figure of the dividend.

EXAMPLES.

When there is no remainder to a divifion, the quotient is the abfolute and perfect answer to the question; but where there is a remainder, it may be observed, that it goes fo much towards another time as it approaches the divifor; thus, if the remainder be half the divifor, it will go half of a time more, and fo on; in order, therefore, to complete the quotient, put the last remainder to the end of it, above a line, and the divifor below it.

It is fometimes difficult to find how often the divifor may be had in the numbers of the several steps of the operation: The best way will be to find how often the first figure of the divifor may be had in the first, or two first tigures of the dividend, and the anfwer, made lefs by one or two, is generally, the figure wanted; but if, after fubtracting the product of the divifor and quotient from the dividend, the remainder be equal to, or exceed, the divifor, the quotient figure must be increased accordingly.

C

In this example, I find that 3, the divifor, cann contained in the first figure of the dividend; theref take two figures, viz. 17, and inquire how often contained therein, which finding to be 5 times, I the 5 in the quotient, and multiply the divifor by it ting the first figure of the multiplication under the 7 i dividend, &c. I then fubtract 15 from 17, and fi remainder of 2, to the right hand of which, I bring the next figure of the dividend, viz. 5; then, I in how often the divifor 3 is contained in 25, and, findi to be 8 times, I multiply by 8, and proceed as before I bring down the 1, when finding I cannot have the vifor in 1, I place o in the quotient, and bring down the 1, and proceed as at the firft.

Obferve, that in multiplying by 3, I add in the 2.

EXAMPLES

When there is one cypher, or more at the right hand of the divifor, it or they must be cut off; alfo cut off the fame number of figures from the dividend, and then proceed as in cafe firit: But the figures which were cut off from the dividend must be placed at the right hand of the remainder.

EXAMPLES.