20. Add together of 3 A. 1 R. 20 P., of an acre, and of 3 R. 15 P. 3 21. What is the sum of of a ton, of a cwt., and of an ounce? 22. What is the sum of of of a mile, of a furlong, of a rod, and of a foot? SUBTRACTION. 165. SUBTRACTION OF FRACTIONS is the operation of finding the difference between two fractional numbers. 166. THE DIFFERENCE between two fractions is such a number as added to the less will give the greater. CASE I. 167. When the unit of the fractions is the same. 1. What is the difference between and ? ANALYSIS.-The unit of both fractions is the OPERATION. the difference of the fractions is equal to the difference of the fractional units, which is . 2. What is the difference between lb. and of a pound? ANALYSIS.-The unit in both fractions is 1lb. The fractional OPERATION. 4 2 12 10 2 5 = - = Ib. 3 15 15 15 unit of the first is lb., and of the second lb. Reducing to the same fractional unit, we have 1lb. and 1lb., the difference of which islb.; hence, 165. What is subtraction of fractions ?-166. What is the difference between two fractions ?-167. How do you subtract when the unit of the fractions is the same? Rule. I. If the fractional unit is the same in both, subtract the less numerator from the greater, and place the difference over the common denominator. II. When the fractional units are different, reduce to a common denominator; then subtract the less numerator from the greater, and place the difference over the common denominator. 18. What number added to 17, will make 5? 19. What number is that to which if 7 be added the sum will be 173? 20. From the sum of 3 and 10 take the difference of 251 and 17. 21. What number is that from which if you subtract of of a unit, and to the remainder add of of a unit, the sum will be 9? 22. If I buy of of a vessel, and sell of of my share, how much of the whole vessel will I have left? 23. A man bought a horse for of of of $500, and sold him again for of of of $1680: what did he gain by the bargain? 24. Bought wheat at 17 dollars a bushel, and sold it for 21 dollars a bushel: what did I gain on a bushel? 25. From a barrel of cider containing 31 gallons, 125 gallons were drawn: how much was there left? 26. Bought 103 cords of wood at one time, and 24 cords t another; after using 167 cords, how much remained? 27. A merchant bought two firkins of butter, one contain ing 54 pounds, and the other 561 pounds; he sold 4313 pounds at one time, and 34 pounds at another: how much had he left? 28. A man having $50, expended $15 for dry-goods, and 12 for groceries: how much had he left? 29. A boy having of a dollar, gave of a dollar for an inkstand, and of it for a slate how much had he left? 30. Bought two pieces of cloth, one containing 274 yards, the other 32 yards, from which I sold 4017 yards: how much had I left? 168. When each fraction has the numerator 1. 1. What is the difference between 1 and ? ANALYSIS.-Reducing both frac tions to a common denominator and subtracting, we find the difference to be; that is, OPERATION. -=矗矗=六 The difference between two fractions, each of whose numer ators is 1, is equal to the difference of the denominators divided by their product. 2. From take 3. From take 4. From take 2. 5. From take 168. What is the difference when the numerator of each fraction is 1? 3 139 169. When there are mixed numbers. 1. What is the difference between 16 and 3? ANALYSIS. Since we cannot take from = OPERATION. 16 = 16. 33 31 = 31. 1213. we borrow 11 from the whole number of the minuend, which, added to, gives 18: then from 1 leaves 13. We must now carry 1 to the next figure of the subtrahend, and say 4 from 16 leaves 12. Hence, to subtract one mixed number from another, Subtract the fractional part from the fractional part, and the integral part from the integral part. 2. What is the difference between 144 and 12? CASE II. and 4118? 37 and 104,3% ? 170. When fractions have different units. 1. What is the difference between of £ and of a shil Rule. I. Reduce the fractions to the same unit, and then subtrat as in Case I.: Or, II. Find the value of each fraction in units of lower denominations, and then subtract as in denominate numbers. Examples. 1. From of a pound troy, take of an ounce. of a pound. quart. of of a hogshead of wine, take of ✈ of a 4. From of a league, take of a mile. 5. What is the difference between 13s. and of 7d? 6. What is the difference between 2 of a degree and of of a degree. 7. From 18 of a square mile, take 367 acres. 8. From of a ton, take 9. From 12 lb. troy, take 10. From 2 cords, take 11. From of a yard, take of 12 cwt. of an ounce. of a cord foot. of an inch. 12. From of of a pound, take of of a dram, apothecaries' weight. 13. From a piece of ground containing 25 acres take 1A. 1 P. and 9 square yards. 14. A pound avoirdupois is equal to 14 oz. 11 pwt. 16gr. troy what is the difference, in troy weight, between the ounce avoirdupois and the ounce troy? 169. How do you subtract when there are mixed numbers? 170. What is the rule when the fractions have different units. |