79. A sheet folded into two leaves is called a folio. 66 folded into four leaves is called a quarto, or 4to. 66 folded into eight leaves is called an oc tavo, or 8vo. folded into twelve leaves is called a duo decimo, or 12mo. folded into eighteen leaves is called an 18mo. When a sheet is folded into two leaves what is it called? How called when folded into four leaves? How, when folded into eight leaves? How, when folded into twelve leaves? How, when folded into eighteen leaves? REDUCTION. 80. REDUCTION is the changing of numbers from one name or denomination to another, without altering their value. When the denominations are to be reduced from a higher denomination to a lower, it is called Reduction Descending; but when they are to be reduced from a lower to a higher denomination, it is called Reduction Ascending. REDUCTION DESCENDING. Let it be required to reduce £7 5s. 10d. 3 far. to farthings. OPERATION. 7 the number of pounds. Multiply by 20, the number of shillings in one pound. 140 product in shillings. Add 5 shillings. 145 the number of shillings. Multiply by 12, the number of pence in one shilling. 290 145 1740 product in pence. Add 10 pence. Multiply by Add 1750 the number of pence. 4, the number of farthings in one penny. 7000 product in farthings. 3 farthings. 7003 the number of farthings sought. From the above operation, we readily deduce this general RULE. Multiply the number in the highest denomination by the number indicating how many of the next lower make one in that higher; to this product add the number, if any, belonging to this lower denomination; we shall thus obtain an equiva lent value in the next lower denomination. II. Proceed in a similar way for all the successive denominations; the last result will be the number sought. What is Reduction? When is it called Descending? And when Ascending? Repeat the rule for Reduction Descending. REDUCTION ASCENDING. 81. Let it be required to reverse the last example, that is, to find the number of pounds, shillings, pence, and farthings, in 7003 farthings. We must obviously perform a reverse operation to that performed under Reduction Descending. Collecting results, we have 7003 farthings, equivalent to £7 5s. 10d. 3 far. EXPLANATION. First, we divide the number of farthings, 7003, by 4, because 4 farthings make one penny; the quotient is 1750 pence, and 3 farthings remaining. Secondly, we divide the number of pence, 1750, by 12, because 12 pence make one shilling; the work being performed by Long Division, we get for the quotient 145 shillings, and 10 pence remaining. Thirdly, we divide the number of shillings, 145, by 20, because 20 shillings make one pound; cutting off the cipher from the right of 20, and the right-hand figure from the dividend, (ART. 30,) we perform the work by Short Division, and obtain the quotient, 7 pounds, and 5 shillings remaining. We may, therefore, deduce this general RULE. I. Divide the given number by as many of its denomination as make one of the next higher; write down the quotient and remainder, if any. II. Divide the quotient by as many of its denomination as make one of the next higher; write this new quotient and the remainder as before. III. Proceed in this way through all the denominations to the highest, and the quotient last found, together with the several remainders, if any, will give the value sought. Repeat the Rule for Reduction Ascending. |