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Node. In dividing by 10, 100, 1000, &c. when you cut off as many figures from the dividend, as there are cyphers in the divisor, your work is done ; those figures, cut off at the right hand, are the remainder, and those on the left, the quotient, as above.
Short Division is, when the divisor does not exceed 12.
First, reek how often the divisor can be had in the first figure, or figures, of the dividend ; which, when found,
place in the quotient; then, mentally, multiply your divisor by the figure placed in the quotient, and subtract the product from the like number of the left hand figures of your dividend, and the units which remain, mult be accounted so many tens, which you must suppose to stand at the left hand of the next figure in the dividend, and to be reckoned with it ; then, seek how often you can have your divisor in those two figures ; but, if nothing remain, you must then seek how often your divisor is contained in the next figure, or figures, and thus proceed till you have done.
When the divisor is such 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.*
As the learner, at present, is supposed to be unacquainted with the nature of fractions, and as the quotient is incomplete without the remainder ; I shall here give a rule for finding the true remainder, without having recourse to fractions,
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 divisory, and add in the first remainder 3, and they make 57, the true remainder. In the second method, dividing by 8, I remains, and by 9, 7 remains, I therefore multiply 7, the last remainder, by 8, adding in the 1, and they make 57, as before.
5. 36179638 25)197835
25)197835 · 84)93975 54-)93738764 6. 7.
8. 121)75323939 132)38473692 144)891376429732
Supplement to Contractions in Multiplication. 1. The shortest method of niultiplication, when the multiplier is any even part of 100, 1000, &c. is by divifion ; for if the multiplicand be increased by a number of cyphers equal to the places in the multiplier, and a part
RULE. Multiply the quotient by the divisor ; fubtract the product from the dividend, and the result will be the true remainder.
The Rule which is most commonly made use of, when the divisor is a composite number, is
RULE II. Multiply the last remainder by the preceding divisor, or last but one, and to the product add the preceding remainder ; nultiply this fun by the next preceding divisor, and to the product add the next preceding reinainder; and fo
gone through all the divifors and remainders, to the first
of that product taken for the same proportion, which the multiplier bears to 1, and the same number of cyphers annexed to it, the quotient will be the product.
1. Mult. 39756 into 125. 2. Mult. 57638 by 33 125= 5 of 1000, wherefore, 3315 of 100, therefore, 8)39756000
By this weight are weighed Gold, Silver, Jewels, Electuaries, and all Liquors.
Note. 175 Troy Ounces are precisely equal to 192 Avoirdupois Ounces, and 175 Troy pounds are equal to 144 Avoirdupois. lb Troy=5760 grains, and Ilb Avoirdupois=7000 grains.
+ By Avoirdupois are weighed all coarse and drofly goods, grocery and chandlery wares ; bread, and all metals, except Gold and Silver,