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 given, into any number of parts affigned; or to find how often one number is contained in another; or from any two numbers given, to find a third, which fhall confift of fo many units, as the one of thofe given numbers is comprehended in the other; and is a concife way of performing feveral Subtractions.

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 queftion, which fhews 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

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 subtract, 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 queftion; 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 feveral 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 figures 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 increafed accordingly.

C.

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

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

EXAMPLES.

7.

425

5.

6.

35)197184(

85)994466(

8.

9.

236)3798567 3479)483956795 5679)19647394

3479)483956795(5679)19647324(

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 firft: But the figures which were cut off from the dividend must be placed at the right hand of the remainder.

EXAMPLES.