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C A S E X. To multiply by 21, 31, 41, &c. to 91: Multiply by the ten’s figure, only, of the multiplier, and set the unit figure of the product under the place of tens ; add them all together, and their sum will be the total product.
4. 759846 x 51
5. 37954 x 61
6. 73958 x 71
DI V I S I O N
Teaches to separate 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 shall consist of so many units, as the one of those given numbers is comprehended in the other; and is a concise way of performing feveral Subtractions.
There are four principal parts to be noticed in Division, viz.
1. The Dividend, or number given to be divided. 2. The Divisor, or number given to divide by.
3. The Quotient, or answer to the question, which fhews how often the divisor is contained in the dividend.
4. The Remainder (which is always less than the divisor, and of the same name with the dividend) is very uncertain, as there is sometimes a remainder, and some. times none.
Division is both simple and compound.
Multiply the divisor and quotient together, and add the remainder, if there be any, to the product ; If the ork be right, that sum will be equal to the dividend.
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.
CA SE I.*
RULE.First, seek how many times the divisor is contained in a competent number of the firit 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 :lf, when you have brought down a figure to the remainder, it is till less than the divisor, a eypher must be placed in the quotient, and another figure be brought down ; after which, you must seek, multiply and subtract, till you have brought down every figure of the dividend.
* When there is no remainder to a division, the quotient is the absolute and perfect answer to the question ; but where there is a remainder, it may be observed, that it goes so much towards another time as it approaches the divisor; thus, if the remaindc' be half the divisor, it will go half of a time more, and so 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 sometimes difficult to find how often the divisor may be had in the numbers of the several steps of the operation : The best way will be to find how often the firit figure of the divisor may be had in the first, or two firit figures of the dividend, and the answer, made lefs by one or two, is, generally, the figure wanted; but if
, after fubtracting the product of the divisor and quotient from the dividend, the remainder be equal to, or exceed the divisor, the quotient figure must be increased accordingly.
In this example, I find that 3, the divisor, cannot be contained in the first 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 divisor by it, fetting the first figure of the multiplication under the 7 in the dividend, &e. I then subtract 15 from 17, and find a remainder of ze to the right hand of which, I bring down the next figure of the dividend, viz. 5 ; then, I inquire how often the divisor 3, is contained in 25, and, finding it to be 8 times, I multiply by 8, and proceed as before, till I bring down the 1, when, finding I cannot have the divisor in 1, I place o in the quotient, and bring down 7 to the 1, and proceed as at the first.
Observe, that in multiplying by 3, I add in the 2.
85)9944.65( 7. 8.
9. 236)3798567( 3479)483956795( 5679)19647394/
When there is one cypher, or more, at the right hand of the divisor, it or they must be cut off ; also, cut off the fame number of figures from the dividend, and then proceed as in case first : But the figures which were cut off from the dividend must be placed at the right hand of the remainder,