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the divisor, i. e. place its denominator for its numeratov, or uppermost, and its numerator lowermost, and then proceed as in multiplication, by multiplying the two uppermost, or those now in the place of nuinerators together, for a new numerator, then multiply the two lowermost together for a new denominator.
Nore. When mixed numbers are given to be divided, ae pounds, shillings, and pence, hundreds, and quarters, &c.
Reduce the dividend and divisor to the lowest denomination inentioned, and to a common denominator, then diy.de this reduced numerator of the dividend by the reduced numerator of the divisor, and under the quotient place the common denommator, or invert the reduced divisor, and then multiply as above directed, the result will be the quotient in a fraction of the highest denomination mentioned.
Note. Multiplication and Division of Vulgar Fractions, prove each other. *
= 9 numerator. 77 denominator.
* When fractions only are divided by fractions only, then if the dividend is greater than the divisor, the quotient, will be greater than the dividend, but if the dividend is less than the divisor, the quotient will be less than the dividend, and in the same proportion as an unit or 1, is greater or less than tha divisor
5. Multiply by
Ans. 6. Divide by s
Ans. 354 = f = ĝo 7. Multiply 4 off, by to of the.
= 156. 8. Divide 1'3o by to of 19. Ans. = 4 of 4.
This may be proved thus, 1 off reduced is us, there. fore divide the numerator 1320 by 4, the quotient will be 330; divide the denominator 11550 by 35, the quottient will also be 330, this proves to be equal to 4 off, and proves example 7th to be done right. 9. Multiply 4 by š.
Ans. 10. Multiply j of 7, by š.
Ans. 118 11. Divide by
Ans. 4. 12. Divide 1 to by š.
Ans. 34 = g of 7.
14. Multiply £3 19 11 %, by itself.
Ans. £15 19 10
T1600 ar. Divide £3 4 1 by 9s. 6d. Ans. 6s. 9d.
RULE OF THREE, OR PROPORTION
1. Prepare the first and third terms as directed in Addition of Vulgar Fractions ; if more than three terms are given, prepare all but the middle term as above. 2. If the middle term is a compound or a mixt fraction, reduce it to a single fraction, and to its lowest term.
3. In stating, use the numerators only, and proceed with them as with whole numbers, the result will be the numerator of the quotient, or answer, whose denominator is the same as that to which the middle term was reduced.
NOTE. These examples may be proved by varying their order,
EXAMPLES. 1, If of a yard of cloth cost of a dollar, low much will į a yard cost ?
6 : 7 :: 4
6)280 ** Ans. which reduced 24 by Case X, will be
for the answer. 2. If of a ton of hay cost $16, 'how much will jo of a ton cost?
Ans. $18. 3. If of a hogshead of wine cost $30, what will s cost?
Ans. $5. 4. If of a hogshead of wine cost 85, what is it a hogshead?
Ans. $40. 5. If of a yard of painting cost to of a dollar, what is it a yard? Ans. 4*4=14=130sor 45 cents.
6. If 1 yard of paint cost 45 cents, what will of a yard cost?
Ans. 40 cents, is of a dollar. Note. The 5 and 6 examples prove each other by vary., ing their order.
7. If ; of a dollar be worth 5 shillings, how much of the same currency is 3275 dollars worth?
Ans. of a shilling, which reduced to its proper quantity is £9 15.
EXTRACTION OF THE SQUARE ROOT.
The square root of any number is that number which being multiplied by itself* will produce the number of which it is called the square root, and the number so produced is called its square.
The square root of a given, number is found as follows : viz.
Begin with the unit figure, and place a point over it, then proceed towards the left, pointing every second figure, as is done with the example below, each tivo figures are called a period.
If there are decimals, proceed towards the right from the unit figure, pointing every second figure : should a place be wanting in the decimals, supply it with a cipher.
The figure under the left hand point and that to the left of it (if any) is the first resolvend.
Find such a figure as, being involved to the second power,t will come the nearest to this resolvend, and not exceed it.
Place the number thus found under the resolvend, and subtract it there from ; and place the figure, so involved, in the quotient, or root; to the remainder bring down two figures, or the next period, placing them at the right of it, for a new resolvend; draw a crooked stroke or line at the left of this new resolvend.
Double the quotient, and place it for a divisor at the left of the new resolvend, leaving room for more figures at the right of this divisor.
See how often this divisor is contained in the resolvend, excluding its right hand figure, allowing for the
By some called involving the number to the second power, &c. thus 4 X 4=16, the square of 4, or 4 involved to the second power ; also 4x4x464, the cube of 4 ; or 4 involved to. the third power. + Multiplied by itself.
This is called a subtrahend.