18. Add of a yard, 1⁄2 of a foot, and of a mile together. Ans. 1540 yds. 2 ft. 10 in. 19. Add of a French ell, of an English ell, 3 of a yard, and of a Flemish ell together. Ans. 3 yds. 1 qr. 33 n. 20. Add of of £350 16s. 3d., 4 of 7 guineas, 3 of 7 of 24 quarter guineas, and 4 of 36 moidores together. Ans. £167 11s. Id. 21. Add 33£. 41⁄2 moidores, & of a shilling, and of a penny together. 22. What is the value of of £36 28 quarter guineas? 23. What is the value of £33, 4 of a penny? Ans. £9. 19s. 8. d. 17s. 6d., and 3 of 3 of Ans. £10 5s. 103d. of a shilling, and of Ans. £3 18s. 1μd. of of half a crown, 24. Add of of £72 12s 73d., of 320 quarter guineas, of a shilling, & of 74d. and of a penny together. £94 6s. 11d. ΤΣ 25. A flax mill worth £12350, a coal mine £3241, and a ship £6500; what is the worth of 3 of 3 of the mill, 3 of 1⁄2 of the mine, and of of the ship? Ans. £7632 16s. 8d. 44 SUBTRACTION OF VULGAR FRACTIONS. RULE.-Reduce the given fractions to a common denominator, and subtract the less numerator from the greater; under this remainder place the common denominator, and the result will be the difference required. 2. What is the difference between 3 of 3 and 4 of 4 of 4? Here of and of of=}. 3. Required the difference between 1⁄2 and . 4. From take 3. 5. What is the difference between + ond ? 6. What is the difference between 43 and 3}? 7. Required the difference between of and. 9. What is the difference between 3 of 9 and 3 of 31? Ans. Ans. 1 Ans. 1 53 10. What is the difference between of a £. and 7 of a shilling? Ans. 12s. 5d. 11. What is the difference between of £3. 12s. and 3 of 3 of a guinea? 12. What is the difference of 3 of a cwt. and 3 of a qr. ? 49 Ans. £1. 11s. 7d. Ans. 2 qrs. 1 lb. 1313 oz. 13. What is the difference between § of a cwt. and 7 of a cwt? Ans. 1 qr. 7 lb. 12 oz. 14. What is the difference between of a £. and of 13 of a guinea? Ans. 10 d. 15. Bought 25 cwt. 2 qr. 14 lb. of sugar, and parted with g of the same; how much had I left? Ans, 16 cwt. 12 lb. 16. Bought a waggon load of hay, which weighed, including the waggon, 2 tons, 17 cwt. 3 qrs. Now the waggon weighed of the whole. Required the weight of the hay and waggon separately. T. 4 cwt. 3 qrs. wt. of waggon. T. 13 cwt. wt. of hay. between § of 7 yards and of an Ans. 3 yds. 1 qr, Ans. 17. What is the difference English ell? G 18. What is the difference between 3 of an English ell and of a Flemish ell? 19. Required the sum and difference of and §. 56 Ans. 3 yds. Ans. 1 sum, difference. 20. What is the sum and difference of of 3 and 7 of 8. ? Ans. 1 sum, difference. 45 21. What number added to 3 will make 13? 22. A, B, and C, had a ship, what part of it belonged to C.? Ans. 1 belonged to A, and to B; Ans. C's. 23. What number added to 3 of 3 of will make 2? Ans. 19 24. A person had g of a mill and sold of his share; how 323 much had he left? Ans. 25. Required the difference between 7 + and 7 × §. Ans. 25 26. Which is the greatest of the three fractions }, {, or ? Ans. 27. It is required to simplify the following expression. 100 } of 100% +1} Ans. 26,2 MULTIPLICATION OF VULGAR FRACTIONS. RULE. Reduce the fractions, if required, to simple ones; then multiply the numerators together for a numerator, and the denominators for a denominator, and this new fraction will be the product required. This rule is only the application of Case 4th. To multiply a vulgar fraction by a whole number, multiply the numerator only, and retain the given denominator. 2. What is the product of 4, 7, 44, and ? Ans. NOTE. The solution to this question is the same as question 2, Case 4. 3. Multiply by 3 5 5 8 Ans. 4. What is the continued product of 4, 5, and ? Ans. 5. Find the product of 3, 24, aud Ans. 6. Multiply, 78, and 2 together. Ans. 7. 7. Multiply, 43, 2%, and 5 together. 8. Multiply of 3, 4 of 14, and of together. Ans. 9. Multiply 2s. 6d. by 3s. 6d. a shilling being the integer. Ans. 8s. 9d. 10. Multiply 17s. 6d. by 13s. 4d., a pound being the integer. Ans. £. 11. Multiply £99 19s. 11 d. by itself, a pound being the integer, or having the product in £. Ans. £9999 15s. 10d. 12. Multiply 2 cwt. 3 qr. by 2 qr. 14 lb., a cwt. being the integer. Ans. 1 cwt. 2 qr. 24 lb. 8 oz. 13. What is the sum, difference, and product of and ? Ans. 1 sum, difference, product. of which 3 parts out How much per cent. 14. A shilling weighs 3 dwts. 15 grs., of 40 are alloy, and the rest pure silver. is there of alloy, and what weight of pure silver? Ans. 7 per cent., 3 dwts. 81% grs. pure silver DIVISION OF VULGAR FRACTIONS. RULE (a) Invert the diviser, and proceed as in multipli cation. To divide a fraction by a whole number. Multiply the denominator of the fraction by the whole number, and retain the same numerator. (a) DEMONSTRATION.-To divide one fraction by another, is to determine what multiple, part, or parts, the former is of the latter :-Thus, m m -, proposes to determine what multiple, part, or parts, m that is, what multiple part or parts we must take of to produce Now, n In words, to divide one fraction by another, we must invert the dividing m fraction, and proceed as in multiplication. From (1), n whence, Definition, this signifies only that the T ms ms th 14. Divide 3s. 6d. by 2s. 6d., a shilling being the integer, or having the quotient in shillings. Ans. 1s. 4 d. of a farth. 15. How many yards of cloth can I buy for £3 7s. 6d., at 83 shillings per yard? Ans. 7 yds. 33 qr. 16. In 7 cwt. 3 qrs. 14 lbs., how many parcels, each weighing 1 quarters? Ans. 22 17. Bought 25 cwt. 3 qr. 14 lb. of hay, which I made up into quantities, each containing 33 stones. How many had I? Ans. 61 18. What is the sum, difference, product, and quotient of ? and ?? Ans. sum, diff. prod. 13 quot. 19. What is the sum, difference, product, and quotient of of and ? Ans. sum, & diff. prod. 1 quot. 20 Required the sum, difference, product, and quotient of 21 and 3 5 Ans. 1 sum, differ., prod. 2 quot. 31 5 of 8 21. Required the sum, difference, product, and quotient of |