Note 2-When mixed numbers are given, reduce them to improper fractions, and reduce these to fractions which have a common denominator; then subtract as before. 9. From 8 take 6. 10. From 9 take 43. 11. From 77 take 33. Result 19 Result 4. Result 4 Note 3.-When compound fractions are given, reduce them to single ones, and these again to a common denominator; then subtract as before. 12. From of take 1 of 4. 13. From of 11 take 14. From take of §. of 2. Result. Result 133 Note 4-When a fraction or a mixed number is given to be subtracted from a whole number, sübtract the numerator of the fraction from its denominator, and under the remainder set the aenominator; then carry 1 to be subtracted from the integers. 15. From 6 take 1. 16. From 3 take 17. From 100 take 9900 Result 5. Result 218. Result To Note 5. When the given fractions are of different denominations, reduce them to their proper values, or quantities, and subtract as in the following example. 18. From of a pound, take of a shilling. 19. From 2 of a L. take of a shilling. Result 14s. 3d. 20. From of a lb. troy, take of an ounce. Result 8 oz. 16dwt. 16grs. 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. 123=3 and 7-23; then 63 X 231449963. 11. Multiply 21 by 14, and multiply the product by of 3 of 3. Result 23. · Result 13. Result. DIVISION OF VULGAR FRACTIONS. GENERAL RULE. Prepare the given fractions, if necessary, then invert the divisor, and proceed as in Multipliation. 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 term's together, as in Multiplication. EXAMPLES. 1. If of a yard cost of a shilling, what will of a yard come to? Ans. 2s. 4d. 3. If of a lb. of sugar, cost of a shilling, what cost of a lb. Ans. 4d. 3qrs. 1657 4. If of a yard of lawn cost 7s. 3d. what will 100 yards cost? Ans. 4L. 19s. 10d. 2qrs. . 5. If 14 yard cost 9s. what is the value of 164 yards? Ans. 5 L. 17s. 6. What is the value of 100 yards of cloth, at 1 shillings per yard? Ans. 6L. 7. If 1 ounce of silver cost 54s. what is the value of 1611oz.? Ans. 4L. 12s. 13qrs. 8. How much will 44 lb. of cheese come to, at 12 cents per lb. Ans. 55 cents. 9. If 11 bushels of apples cost 39 cents, what is the value of 3 bushels? Ans. $1.01. 10. What will of a lb. come to, if of a lb. cost of a shilling? Ans. 49d. 11. If ewt. cost 14 L. what will 7 cwt. amount to? Ans. 118 L. 6s. 8d. 12. If 8 lb. of sugar cost 45. 9d how much is it per lb.? Ans. 73d. 13. If 1 yard of cloth cost 154s. what will 4 pieces, each containing 273 yards cost? Ans. 85 L. 10s 111d. 14. What will 1 cwt. of pepper come to, if 151 lb. cost 123s.? Ans. 6L. 16s. 387d. 15. A person having of a sloop, sells of his share for 391 L. what is the value of the whole vessel, at that rate? Ans. 598 L. 2s. 6d. 16. A merchant had 58 cwt. of sugar, which he bartered for tea, at 8ğs. per lb. did he receive for the sugar ? at 63d. per lb. How much tea Ans. 43 lb. INVERSE PROPORTION. RULE. Prepare the terms as in Direct Proportion, then multiply the first and second terms together, and divide the product by the third. Or, Invert the third term, and multiply the three terms together as in Multiplication. EXAMPLES. How much shalloon, of a yard wide, will line 4 yards of cloth, 11 yard wide? yd. yd. yd. yd. As: 9 2. What quantity of shalloon, yards of cloth, 1 yards wide? Ans. 9 yards. Or thus: 2×2×10 = = 9. yard wide, will line 7 Ans. 15 yards. 3. If 16 men finish a piece of work in 28 days, how long will 12 men require to do the same work? Ans. 37 days. 4. If 3 men can do a piece of work in 44 hours, in how many hours will 10 men do the same in? Ans. 13. 5. If 25 dollars will pay for the carriage of 1 cwt. 1451 miles, how far may 63 cwt. be carried for the same money? Ans. 22 miles. 6. How many pieces of cloth, at 20 dollars per piece, are equal in value to 2404 pieces, at 121 dollars per piece? Ans., 149, 17 pieces. 7. A merchant bartered 58 cwt. of sugar at 62d. per lb. för tea at 8gs. per lb. How much tea did he receive? Ans. 4316. 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 yard, 13 yard wide, of the same quality? yd. yd. IL. Styd. = |