Note 4.- When a fraction or a mixed number is to be subtracted from a whole number, subtract the numerator of the fraction from its denominator, and under the remainder set the denominator; then carry it to be subtracted from the integers. Note 5.- When the given fractions are of different d nominations, reduce them to their proper values, or quantities, and subtract as in the following example. 19. From of a L. take of a shilling. 1 Result 14 s. 3 d. take of an ounce. Result 8 oz. 16 dwt. 16 grs. of an inch. 20. From & of a lb. troy, 21. From of a yard take 22. From of a L. take Result 5 in. §. of of a shilling. Result 10 s. 7 d. 1 qr. }. MULTIPLICATION OF VULGAR FRACTIONS. GENERAL RULE. Reduce compound fractions to single ones, and mixed numbers to improper fractions; then multiply the numerators together for a new numerator, and the denominators for a new denominator. VULGAR FRACTIONS. 130 4. Multiply 123 by 73. Result 963. 123=63 and 73=23; then 3× 23 — 1449—963. 5 Multiply 74 by 81. Result 614. 6. Multiply 41 by . Result 16 7. Multiply by 13%. Result 1213 8. Multiply of by 1 of 11. 10. Multiply of 7 by 3. 9. Multiply 42 by 3 of 2. 11. Multiply 21 by 11, and multiply the product by 8 Result 450 Result 13. of & of 3. Result. DIVISION OF VULGAR FRACTIONS. GENERAL RULE. Prepare the given fractions, if necessary, then invert the divisor, and proceed as in Multiplication. THE SINGLE RULE OF THREE, IN VULGAR FRACTIONS. RULE. Prepare the given terms, if necessary, and state them as in whole numbers; multiply the second and third terms together, and divide the product by the first. Or, Invert the dividing term, and multiply the three terms together, as in Multiplication. EXAMPLES. of e Ans. 2 s. 4 d. 1. If of a yard cost of a shilling, what will yard come to? 15 24 2. If of a yard cost of a pound, what will of 38 a yard come to? 15 14 Ans. 3 s. 4 d. 3. If of a lb. of sugar cost of a shilling, what cost of a lb. ? 32 1657 Ans. 4 d. 3 qrs. 2365 cost 7 s 3 d. what will 10 Ans. 4L. 19 s. 10 d. 2 qrs. §. is the value of 161 4. If of a yard of lawn yards cost? 5. If 1 yard cust 9 s., what yards? 6. What is the value of 100 shillings per yard? 7. If 1 ounce of silver cost 5 of 161 oz.? Ans. 5 L. 17 s. yards of cloth, at 11 Ans. 6 L. s., what is the value Ans. 4 L. 12 s. 13 qrs. come to, at 123 Ans. 5528 cents. 8. How much will 45 lb. of cheese cents per lb. ? 9. What will of a pound come to, if of a lb. cost of a shilling? Ans. 425 d. 10. If one yard of cloth cost 155 s., what will 4 pieces, each containing 273 yards, cost? Ans. 85 L. 10 s. 114 d. 11. A person having of a sloop, sells of his share for 319 L., what is the value of the whole vessel at that rate ? Ans. 598 L. 2 s. 6 d. VULGAR FRACTIONS. 141 12. A merchant had 58 cwt. of sugar, at 6 d. per lb., which he bartered for tea, at 85 s. per lb. How much tea did he receive for the sugar ? Ans. 43 lb. INVERSE PROPORTION. 4 1. How much shalloon, of a yard 4 yards of cloth, 1 yard wide? #1 wide, will line Ans. 9 yards. Or thus: yd. yd. yd. yd. As9 2. What quantity of shalloon, & yard wide, will line 74 yards of cloth, 1 yards wide? Ans. 15 yards. 3. If 18 men finish a piece of work in 28 days, how long will 12 men require to do the same work? Ans. 373 days. 4. If 3 men can do a piece of work in 41⁄2 hours, in how many hours will 10 men do the same? Ans. 1. 5. How many pieces of cloth, at 20 dollars per piece, are equal in value to 240 pieces, at 124 dollars per piece? Ans. 14917 pieces. 1127 6. A merchant bartered 58 cwt. of sugar, at 6 d. per lb., for tea, at 85 s. per lb. How much tea did he receive? Ans. 43 lb. 69 THE DOUBLE RULE OF THREE, IN VULGAR FRACTIONS. RULE. Prepare the given terms, when necessary, by reduction, then proceed as directed in whole numbers. Or, Invert the dividing terms, and multiply the upper figures continually for the numerator, and those below for the denominator of the fractional answer. EXAMPLES. 1. If yard of cloth, yard wide, cost L., what is the value of ğ yard, 12 yards wide, of the same quality ? 8 2. If 24 yards of cloth, 18 yd. wide, cost 33 L., what is the value of 38 yds. 2 yds. wide? Ans. 76 L. 10 s. 3. If 3 men receive 8 L. for 19 days' labor, how much must 20 men have for 100 days? Ισ 3 Ans. 305 L. Os. 88 d. 4. If 50 L. in 5 months gain 24 L. interest, in what time will 13 L. gain 1L.? Ans. in 9 months. 5. If the carriage of 60 cwt. 20 miles cost 141⁄2 dollars, what weight can I have carried 30 miles for 51% dollars? Ans. 15 cwt. DECIMAL FRACTIONS. A Decimal Fraction is a fraction whose denominator is 1, with as many cyphers annexed as there are places in the numerator, and is usually expressed by writing the numerator only with a point prefixed to it: thus 10, 100, 1000, are decimal fractions, and are expressed by .5, .75, .625. 5 75 625 A mixed number, consisting of a whole number and a decimal, as 25, is written thus, 25.5. As in numeration of whole numbers the values of the figures increase in a tenfold proportion, froin the right hand to the left; so in decimals, their values decrease in the same proportion, from the left hand to the right, which is exemplified in the following |