EXAMPLE II. Reduse I cwt. 2qrs. 7 Ib. to the fraction of a ton. 1cwt. 2qr. 7lb. = 175lb. 5 1 ton = 2240lb. = Answer. 3. Reduce 5d. to the fraction of a shilling. 4. Reduce 9s. 7d. to the fraction of a £. 5. Reduce 6oz. 2dwt. 104 grains, to the fraction of a lb. troy. 6. Reduce 5 hours, 48 minutes, 48 sec. to the fraction of a day. 7. Reduce Ir. 10p. 12yds. to the fraction of an acre. 8. Reduce lb. 3p. to the fraction of a quarter. CASE X. To find the value of a fraction in the known parts of the integer. RULE. Multiply the numerator by the number of parts contained in the next lower denomination; then divide the product by the denominator, and, if there be any remainder, multiply it by the parts in the next inferior denomination, and again divide by the denominator, and continue this mode of operation to the lowest denomination possible. EXAMPLE I. What is the value of of a L.? 7 20 8)140(17s. 6d. Answer. 60 56 4 12 48 48 1 Although the value of the fraction should not amount to a unit of the lowest denomination, yet it may be reduced to a fraction of that or any other denomination, by multiplying the numerator according to the value of the denominations, as directed in the rule. ADDITION OF VULGAR RULE. 1. If the fractions to be added have a common denominator, add the numerators together and place the common denominator under the sum. 2. If the fractions have not a common denominator, reduce them to one, and then add the numerators. 3. When mixed numbers are to be added, find the sum of the integers and fractions separately, and add them together; or reduce them to improper fractions, and then add them. 4. If the given fractions are of different denominations, find the value of each, and add them, or reduce them to one denomination, and then add them. The reason for reducing fractions to a common denominator, before adding them, is obvious; for, when the denominators are the same, the numerators signify like parts of unity, or the integer of which they are parts; and, therefore, the rule for adding them is similar, in effect, to that for adding pence, shillings, or any other inferior denominator of an integer. 11. Add of a guinea, of a moidore, and of a shilling. 12. Add of a lb. troy, of an oz., 7 of a dwt., and of a grain. |