Note. In dividing by 10, 100, 1000, &c. when you cut off as many figures from the dividend, as there are cyphers in the divifor, your work is done; thofe figures, cut off at the right hand, are the remainder, and those on the left, the quotient, as above.

CAS E III.

Short Divifion is, when the divifor does not exceed 12.

RULE.

Firft, feek how often the divifor can be had in the first figure, or figures, of the dividend; which, when found,

place

place in the quotient; then, mentally, multiply your divifor by the figure placed in the quotient, and fubtract the product from the like number of the left hand figures of your dividend, and the units which remain, muft be accounted fo many tens, which you must fuppofe to ftand at the left hand of the next figure in the dividend, and to be reckoned with it; then, feek how often you can have your divifor in those two figures; but, if nothing remain, you must then feek how often your divifor is contained in the next figure, or figures, and thus proceed till you have done.

When the divifor is fuch a number, that any two, or more, figures in the Table, being multiplied together, will produce it, divide the given dividend by one of those figures; the quotient, thence arifing, by the other, and fo on; and the laft quotient will be the answer.*

EXAMPLES.

* As the learner, at prefent, is fuppofed to be unacquainted with the nature of fractions, and as the quotient is incomplete without the remainder; I fhall here give a rule for finding the true remainder, without having recourfe to fractions,

RULE.

In the first operation, in dividing by 9, 3 remains, and, by 8, 6 remains; which, being the last remainder, I multiply it by the first divifor, and add in the first remainder 3, and they make 57, the true remainder. In the fecond method, dividing by 8, I remains, and by 9, 7 remains, I therefore multiply 7, the laft remainder, by 8, adding in the 1, and they make 57, as before.

Supplement to Contractions in Multiplication.

r. The shortest method of multiplication, when the multiplier is any even part of 100, 1000, &c. is by divifjon; for if the multiplicand be increased by a number of cyphers equal to the places in the multiplier, and a part

RULE.

of

Multiply the quotient by the divifor; fubtract the product from the dividend, and the refult will be the true remainder.

The Rule which is moft commonly made ufe of, when the divifor is a compofite number, is

Multiply the last remainder by the preceding divifor, or laft but one, and to the product add the preceding remainder; multiply this fum by the next preceding divifor, and to the product add the next preceding remainder; and fo on, till you have gone through all the divifors and remainders, to the fir.

of that product taken for the fame proportion, which the multiplier bears to I, and the fame number of cyphers annexed to it, the quotient will be the product.

125

1. Mult. 39756 into 125.

2. Mult. 57638 by 333.

of 1000, wherefore, 33 of 100, therefore,

8)39756000

3)5763800

*

4. APOTHECARIES'

By this weight are weighed Gold, Silver, Jewels, Ele&tuaries, and all Liquors.

NOTE. 175 Troy Ounces are precifely equal to 192 Avoirdupois Ounces, and 175 Troy pounds are equal to 144 Avoirdupois. 1lb Troy 5760 grains, and 1lb Avoirdupois 7000 grains.

By Avoirdupois are weighed all coarfe and droffy goods, grocery and chandlery wares; bread, and all metals, except Gold and Silver.