86. What is the value of 416 gal. 3qt. 1 t. of wine, at $1.359 per gallon? In this example, first reduce the quantity of wine to a decimal expression, - the gallon being the unit- and then multiply this quantity into the price of 1 gallon: the answer will be $566.533+. The following examples in this case are to be performed in like manner. 87. What is the value of 57 yd. 2 qr. 3 na. of cloth, at $6.78 per yard ? 89. What is the value of 748 yards of ribbon, at 9 cents 8 mills [.098) per yard ? 89. What is the value of 5741 yd. 3qr. of tape, at 7 mills [.007] per yard ? 90. What is the value of 4cwt. 1qr. 19 lb. of raisins, at $ 12 per hundred-weight? 91. What is the value of 32 h...) 22 gal. of molasses, at $ 19.22 per hogshead ? 92. What is the value of 3 pk. 7 qt. of corn, at 75 cents 93. What is the cost of 15 E.e. 4 qr. 3 na. of linen, at $1.15 per ell ? 94. What is the cost of 7 A. 2 R. 38r. of land, at $64.50 per acre ? 95. What is the cost of 28 square rods and 260 square feet of land, at $84.25 per rod ? 96. What is the cost of 29 lb. 6 oz. 8 dr. of indigo, at $ 3.75 per pound? 97. What is the cost of 4qr. 3 na. of thread lace, at $4.50 per French ell.? 98. What is the value of 7 lb. 10 oz. 18 dwt. of copper, at 27 cents per pound? 99. What is the value of 11 oz. 19 dwt 23 gr. of silver at $ 15.25 per pound ? per bushel? CASZ IV. To reduce the decimal of a higher denomination to its value in whole numbers of lower denomination. RULE. Multiply the decimal by that number of the necl lower denomination which makes a unit of the higher, anl the product will be of the lower denomination. Proceed in like manner with the decimal in each succeeding product. 100. Reduce .769r. to its value in yards, feet, and inches; that is, change .769 of a rod to yards, &c. .769 There are 5 times, or 5.5 times 5.5 as many yards as rods in any quantity, whether that quantity be a whole num3045 ber or a decimal: therefore, we mul3845 tiply the decimal of a rod by 5.5, and 4.2295 the product is 4.2295 yards. We 3 then multiply .2295 of a yard by 3, to .6885 find the feet; but there is not a whole foot in this decimal, and we proceed 12 to find the inches. The whole result 8.2620 is, 4 yd. Oft. 8.262 in. 101. Reduce .775 £ to its value in shillings, &c. 102. Reduce .625 s. to its value in pence and farthings. 103. Reduce .4694 lb. Troy, to oz., dwt., &c. 104. Reduce .624cwt. to its value in qr., lb., &c. 105. Reduce .0653 mile to its value in yd., &c. 106. Reduce .3875 A. to its value in R. and rods. 107. Reduce .0098 ton to its value in lb., oz., and dr. 109. Reduce .2033 hhd. to its value in gallons. 109. Reduce .467 cwt. to its value in qr. Ib. &c. ,' 110. Reduce £741.697 to its proper expression, in pounds, shillings, pence, and farthings. 111. Reduce 84.704 miles to its proper expression, in miles, furlongs, rods, yards, &c. 112. Reduce 50.742 A. to its proper expression, in the several denominations of square measure. EXCHANGE OF CURRENCIES. Before the adoption of the Federal currency, merchants in this country, kept their accounts in the denominations of English money. The value of the Pound, however, and consequently the value of its subdivisions, was various: that is, a pound, and consequently a shilling, signified a greater value of money in some of the states, than in others. Accounts are now kept, in Federal money, and its denominations are generally used in stating prices. In some sections of the country, however, prices are frequently mentioned in shillings and pence—a custom which is inconvenient, and which ought to be discontinued. In New England, Virginia, Kentucky, and Tennessee, 1 of a dollar is called a shilling. In New York and North Carolina, į of a dollar is called a shilling. In Pennsylvania, New Jersey, Delaware, and Maryland, is of a dollar is called a shilling. In South Carolina and Georgia, of a dollar is call. ed a shilling. In Canada, } of a dollar is called a shilling. 113. How many cents and mills, that is, what decimal of a dollar, in a New-England shilling ? in 2 shillings ? in 3 shillings? in 4 shillings? in 5 shillings? 114. How many cents and mills in a New-York shilling? in 2 s.? in 3 s.? in 4 s.? in 5ş.? in 6 s.? in 7s.? 115. How many cents and mills in a Pennsylvania shilling? in 2 s.? in 3s.? in 4s.? in 5 s.? in 6 s.? 116. How many cents and mills in a Georgia shilling ? in 2s.. in 3s.? in 4 s.? 117. How many cents are there in a Canada shilling? in 2 s. ? in 35. in 4s.? in 5 s.? RULE. To change the old currencies to Federal money. Reduce the pounds, if there be any, to shillings. Denote the shillings as units, reduce the pence and farthings to the decimal of a shilling, and multiply the whole sum by that fraction of a dollar which is equal to one shilling 118. Change 13s. 6 d., of the old currency of New England, to Federal money. 119. Change £42 19 s. 4 d. of the old currency of New England, to Federal money. 120. Change 13s. 6 d., of the old currency of New York, to Federal money. 121. Change £25 175. 8 d., of the old currency of New York, to Federal money. 122. Change 18s 11 d., of the old currency of Pennsylvania, to Federal money. 123. Change £14 7s. 6 d. of the old currency of Pennsylvania, to Federal money. 124. Change 16 s. 10d., of the old currency of Georgia, to Federal money. 125. Change £54 12 s. 11 d., of the old currency of Georgia, to Federal money. 126. Change 17 s. 5 d., of the currency of Canada, to 127. Change £21 9s. 3 d., of the currency of Canada, to Federal money. 128. What is the value, in Federal money, of 9 New England shillings? 9 New York shillings ? 9 Pennsylvania shillings ? 9 Georgia shillings? 9 Canada shillings? Federal money. MISCELLANEOUS EXAMPLES. Any vulgar fraction, which shall appear in the following examples, must be reduced to a decimal; and the lower denominations of compound numbers must also be reduced to decimals, before they are brought into operation. No decimal need be continued lower than six places. An swers to be given in decimals. 129. What is the sum of 6 tons 18cwt. 1 qr., 5cwt. 3qr. 2lb., 4.093325 tons, 2 qr. 27 lb., 8cwt. 2 qr. 4lb., and 17 tons 5cwt. Oqr. 19 lb.? 130. What is the difference between 2.90843 hhd. and 4 hhd. 47 gal. 3qt. 1 pt. of wine ? 131. What is the cost of 15.179 yards of broadcloth, at $6 per yard? 132. If 57 yards of cloth cost $ 197, what costs 1 yd.? 133. What is the cost of 28 yd. 3qr. of cloth, at $ 7.55 per yard? 134. If 18yd. 1 qr. of cloth cost $91.16, what is the cost of 1 yard? 135. What is the cost of 25cwt. 2qr. 20lb. o hops, at $4.96 per hundred weight? 136. What is the cost of 24 hhd. 15gal. of molasses, at $25.36 per hogshead ? 137. What is the cost of 256 yd. 3qr. of ribbon, at 8 cents 5 mills [ 085] per yard ? 138. What is the cost of 24 } yards of ribbon, at 7 cents per yard? 139. What is the cost of 3qr. 2 na. of broadcloth, at $10.35 per yard ? 140. What is the cost of 1 fir. 7 gal. 3qt. of beer, at $3.50 per firkin? 141. What is the value of 23 grains of silver, at $11' per pound, Troy? 142. What is the value of 25 square rods of land, at $75 per acre ? 143. If $238.86 be divided equally among 18 men, what will each man receive ? 144. If $775 be divided equally among 8 men, what will each man receive ? 145. If a man travel 73.487 miles in 15 hours, what distance does he travel in 1 hour ? 146. What is of 1142.26 ? The result will be the same, whether we divide 1142. 26 by the denominator 8, (which is multiplying by b), or, reduce to a decimal and multiply this decimal into 1142.26. The former method is to be preferred; and the learner is here reminded, that the product of any decimal will be such a fractional part of the multiplicand as the decimal indicates. 147. What is .125 of 1142.26 ?. 6 of 37241 dollars ? 155. What is .06 of 37241 dollars ? 156. Suppose I have $ 5872, and pay away .06 of it; how much shall I have left ? 157. A owes B $ 430.40 to be paid in 10 months; but B relinquishes .05 of the debt for having it paid immediately. How much does B relinquish ? |