EXAMPLE 1. Multiply,17504, by 76. 3. Mul. 8,04704, by,2575. 5. Mul.,4 by ,2. 7. Mul. ,0476 by,02078. 9. Mul.,1076 by 1000. S. 2. Mul. 27,42, by 3,56. 2d. When the Product will contain more Decimals than are neceffary for the prefent Purpose, the Work may be contracted by the following RULE. Write down the Multiplicand as ufual, then write under it the Multiplier inverted, with the Unit Place thereof under that Place of the Multiplicand, whofe Place you intend the Product fhall extend to; then multiply as ufual, by each Figure of the Multiplier, beginning with those of the Multiplicand which stand over it, neglecting those to the Right Hand, unless fo far as to obferve what would arise from multiplying the Figures immediately foregoing, which must be taken in at the Beginning of each Line, the first Figure of each particular Product muft ftand underneath one another. Note. In multiplying the Figure left out every Time, next the Right Hand in the Multiplicand, if the Product be 5, or upwards to 15, carry 1; if 15, or upwards to 25, carry 2; and if 25, or upwards to 35, carry 3, &c. 11. Let it be required to multiply 3,17678, by 276782, and to have only three Places of Decimals in the Product. 12. Multiply 47,689464 by 26,17694, retaining five Decimals in the Product. 3d. If the Right Hand Figure of the Multiplicand be a Circulate. RULE. Multiply the Multiplicand before, by every Figure in the Multiplier; obferving to increase the Right Hand of each each refulting Line, by as many Units as there are Nines in the Product of the first Figure in that Line, and the right Hand Figure of each Line will be a Circulate; and before add them together, make them all end at the fame Place as fhewn in Addition, you EXAMPLE S. 13. Let it be required to multiply 147,64 by,7. 14. Multiply 42,642 by,276. 4th. When the right Hand Figure of the Multiplier be a Circulate. RULE. Multiply by, as by a finite Digit, fetting the Product one Place extraordinary towards the left Hand; then divide the Product by 9, continuing the Quotient if needful, till it arrives at a Circulate; then beginning at the Place under the right Hand Figure of the Multiplicand, cut off for Decimal Parts. EXAM P LE S. 15. Multiply 46,2762 by,8. 16. Let it be required to multiply 261,276 by ,47• 5th. When the Multiplicand and Multiplier are each a fingle Circulate. RULE. The firft Line (or that produced by multiplying the Circulate in the Multiplier) must be managed as in Note 2, only the right Hand Figure must be increased by as many Units as there are Nines in the Product of the First Figure of that Line; the Product of the Rest must be managed as directed in Note 1. EXAMPLES. 17. Multiply 141,14 by 8,47. 18. Let it be required to multiply 24,6072 by ,496. 6th. If the Multiplicand be a compound Repetend, and the Multiplier a finite Number. RULE. RULE. In multiplying, observe to add to the right Hand Place of the Product, fo many Units as there are Tens in the Product of the left Hand Place of the Repetend; and the Product fhall contain a Repetend, whofe Places are equal to thofe in the Multiplicand, and if there be more Places of Figures in the Multiplier than one, make all the feveral Products conterminous towards the right Hand, (3. and 6th.) EXA MPLE S. 19. Multiply 7,642 by 6. 20. Multiply 64,84% by 27,9. 7th. If the Multiplier be a compound Repetend. R U L E. Multiply each Figure of the Repetend, and add the feveral Products together, then add the Result in this Manner; fet the left Hand Figure fo many Places forward, as exceeds the Number of Places in the Repetend by one, and the Reft of the Figures in Order after it; and thus proceed, till the Refult laft added is beyond the firft; lastly, add the several Results together, beginning under the right Hand Place of the first, and from thence dafh as many Figures for a Repetend, as the Repetend of the Multiplier confifts of. 21. Mul. 46,74 by 4,207.` 22. Mul. 764,742 by 6074. 8th. If both Factors have compound Repetends. RULE. Proceed as in the two last Cases; for as the Places of the Repetend in the Product will be uncertain as to their Number, they can only be determined (in any Manner fit for Practice) by continuing and repeating the firft Product, which will contain a certain Repetend, equal to that of the Multiplicand. EXAMPLES. EXAMPLE 23. Mul. 47,642 by 3,574. S. 24. Mul. 7,628 by 8,495. 48. DIVISION of DECIMALS. In Divifion of Decimals, the Work is likewife performed as in Whole Numbers; the only Difficulty is in valuing the Quotient, which will be very easy by obferving either of the following general 1. The firft Figure in the Quotient is always of the fame Value with that Figure of the Dividend, which answers or ftands over the Place of Units in the Divisor. 2. The Quotient must always have fo many as the Dividend has more than the Divifor. EXAMPLE 1. Divide 1735,5 by 6,5. Decimal Places, S. 2. Divide,8332 by ,0084. 2d. There is also a compendious Way of contracting the Work, reverfe to that in Page 162, by which much Labour is faved, efpecially when the Divifor hath many Places of Decimal Parts in it; and is performed by the following R U L E. By the first Rule find what is the Value of the first Figure in the Quotient; then, by knowing the Denomination of the first Figure, the Decimal Places may be reduced to any Number propofed, by taking as many of the left Hand Figures of the Dividend as will answer them, and in dividing, omit, or prick off one Figure of the Divifor at each Operation, that is, for every Figure you place in the Quotient, prick off one in the Divifor; having a due Regard to the Increase which would arise from the Figure fo omitted. (See Note in Page 166.) EXAMPLES. 11. Divide 913,08 by 2137,2, and let the Quotient only contain three Decimal Places. 12. Divide 6109,2674 by 240,649, and let there be only four Places of Decimals in the Quotient. 3d. When the Dividend is a fingle or compound Repetend. R U L E. If it be a fingle Repetend, bring down the circulating Figure, until the Quotient either repeats, or is as exact as required; but if the Repetend in the Dividend be a compound one, then bring down the circulating Figures in the fame Order they stand in; and when you have got through them all, bring down the firft Figure in the Repetend over again, and fo proceed until your Quotient either repeats, or be as exact as neceffary. EXAMPLE S. 13. Divide 14,4 by 6,84. 14. Let it be required to divide 1694,647 by 46,849. 4th. If the Divifor be a fingle Repetend. Place the Dividend under itself, but removed one Place towards the right Hand, which fubtract, and the Remainder will be a new Dividend; which Divide by the Divifor in the fame Manner, as if it was a terminate Number. EXAMPLE S. 15. Divide 42,86 by 8. 16. Divide 6,426 by 6,8. 5th. If the Divifor and Dividend confift of terminate Numbers joined to the Repetend. RULE. |