EXERCISES. Find the value at the next higher integer, and subtract the value of the difference.* When the price is only an even number of shillings. Rule. Double the unit figure of the given quantity for shillings, and take the other figures as pounds, and the result will be the value at 2 s. each; then multiply this amount by half the number of the shillings in the rate of the price.† * That is, for the first, multiply 673 s. or £ 33 13 by 2 for 2 s. and from the product subtract 1-6 th of 673 s. for the value at 2 d.; so for 2 s. 11 d. multiply by 3 and take off 1-12th. + When the rate of the value is an odd number of shillings, it is generally the best When the given quantity is in a higher denomination than the integer of the price, it must be reduced into the denomination of that integer. EXAMPLE 3. To find the value of 21 cwt. 3 qrs. 17 lb. at 8 s. 6 d. per lb. For the mode of reduction of cwt. into lb. see page 25, and for the valuation at 2 s. see the last page. EXERCISES. Find the amount of Ex. 1. 17 lb. 11 oz. at 1 s. 1 d. per oz. Product £15 6 7 31 18 9 2. 31 lb. 15 oz. at 1 s. 3 d. per oz. 92 4 6 per lb. 5. 11 cwt. 2 qrs. 0 lb. at 1s. 74 d. per method to set down the value at 1 s., expressed in pounds, and multiply it by the number of shillings, as, for 456 yards at 7 s. multiply £ 22 16 s. by 7. Case 2. When the given quantity contains fractional parts. Rule 1. Find the separate values of the whole quantity, and of the fractional parts, and add the products together. Rule 2. To the assumed value for the integral part, add the value at the same integer for the fractional part, and find the required value from this amount. * When the value is found in this manner, that is, by subtracting the difference, if there is any remainder in the farthings or half farthings, it should be reckoned as producing i more; thus this 4 th of 3 d. gives 7-8 ths and a half, which are reckoned as 8-8 ths, or I penny. When the rate is low the variations in the price are made by 8ths or half farthings, and some times by 16 ths or quarter farthings, which are to be worked for similarly to farthings. When the quantity is not very large, and the value is assumed at 1 d. or 1 s., the amount at that rate may be estimated as in the following example. It may be added as a general remark upon the calculations of Practice that when the parts are numerous, it will sometimes save much trouble if the fractions EXAMPLE 5. To find the amount of 497 yards at 71⁄2 d. per yard. The value of 497 yards is here assumed, first, at 1 d. making 497 pence or £ 2 1 5, and, next, at 497 s. or £ 24 17 0, the value of 3-8 ths of a yard then produces 3-8 ths of a penny in the former, and 3-8 ths of a shilling, or 44 d. in the latter. of the remainders are valued alternately at 1 farthing more, and 1 farthing less, than the exact results; and, indeed, the same can be frequently done in pence, when the amount is required, according to the practice of business, to be found only to the nearest penny. Case 3. When the given quantity is a compound quantity, having denominations lower than the integer of the rate. Rule. Separately find the value of the lower denominations, and add it to the value of the other part. * EXAMPLE 6. To find the amount of 73 cwt. 1 qr. 17 lb. at 47 s. 6 d. per cwt. In the practice of business it is very common to unite the two parts in the following form; but it requires much caution to avoid confusion and inaccuracy. We here first multiply 73 s. by 47 for 47 s., and take the half for 6 d.; then reckoning the multiplier as 47 s. 6 d., we take parts out of this value for the 1 qr. 17 lb. * For various particular rules for Practice calculations, see the Appendix. |