TO REDUCE A COMPOUND FRACTION TO A SIMPLE FRACTION,—Multiply all the numerators together for a new numerator, and all the denominators for a new denominator: then reduce the new fraction to its lowest terms. 1. Reduce of to a simple fraction. 2. of a water melon was divided equally among 6 boys. What fraction of the melon did 1 boy receive? 3. Reduce of to a simple fraction. 4. of an acre of land was divided into 4 equal lots. What fraction of an acre did 2 lots contain? 5. Reduce of to a simple fraction. 6 6. of is equal to what part of 1? 7. Reduce of to a simple fraction. 8. 1 penny is what part of 1s.? what part of £1? 9. 7 pence is what simple fraction of £1? Suggestion. 7 pence is of 1 shilling, and I shilling is of £1. Therefore, 7 pence is of of £1. 10. Reduce 10 grains to the fraction of an ounce; that is, reduce of to a simple fraction. 11. Reduce 3 nails to the fraction of a yard. 12. Reduce 4 inches to the fraction of a yard. 13. Reduce 25 seconds to the fraction of an hour. 14. Reduce of of to a simple fraction. 15. of of is equal to what part of 1? 16. Reduce of 3 of to a simple fraction. When the lower denominations of a compound number are to be reduced to the fraction of a higher denomination,— First, reduce the given quantity to the lowest denomination mentioned, and this number will be the numerator: then reduce a unit of the higher denomination, to the same denomination with the numerator, and this number will be the denominator. 17. Reduce 14s. 10d. 2qr. to the fraction of £1. The denominator and numerator here found, Denom. 960 qr. duced, is 8. 18. Reduce 2s. 7d. 1qr. to the fraction of £1. 19. Reduce 11d. 3qr. to the fraction of a pound. 20. Reduce 15s. Od. 3qr. to the fraction of a pound. 21. Reduce 10d. 1qr. to the fraction of a shilling. 22. Reduce 2s. 9d. 34qr. to the fraction of a pound. Direction. Find the number of fifths of a farthing in 2s. 9d. 3 qr., for a numerator; then find the number of fifths of a farthing in £1, for a denominator. 23. Reduce 8 pence to the fraction of a pound. 24. Reduce 5qt. 1pt. to the fraction of a bushel. 25. Reduce 9gal. 3qt. 1pt. to the fraction of 1hhd. 26. Reduce 6 rods 3yd. 2ft. to the fraction of a mile 27. Reduce 351 seconds to the fraction of a day. When the fraction of a higher denomination is to be reduced to its value in whole numbers of lower denomination, Multiply the numerator by that number of the next lower denomination which is required to make a unit of the higher, and divide the product by the denominator; the quotient will be a whole number of the lower denomination, and the remainder will be the numerator of a fraction. Proceed with this fraction as before, and so on. 28. Reduce of £1 to its value in shillings &c. 2 20 7)40 5 5 760 8 4 4 7)16 22 Since of £1 is the same as of 20 shillings, we find of 20 shillings, in shillings and the fraction of a shilling; it is 5 shillings. Then, since of 1 shilling is the same as of 12 pence, we find of 12 pence;- it is 8 pence. Then, since of 1 penny is the same as of 4 farthings, we find of 4 farthings;-it is 24 farthings. Thus by finding one denomination at a time, we finally ob tain, 5s. 8d. 22 qr. 29. Reduce of £1 to its value in shillings &c. 30. of £1 is how many shillings, pence, &c.? 31. Ín of a shilling, how many pence, &c.? 32. Change £15 to pounds, shillings, pence, &c. 33. Reduce of 1 cwt. to quarters, pounds, &c. 34. Change 9 pounds, to pounds, ounces, and drams 35. Reduce of a mile to furlongs, rods, feet, &c. 36. In 10 acres, how many acres, roods, rods, &c. 37. How many dimes, cents, and mills, in 7 of $1? 38. In of a dollar, how many cents and mills? 39. Suppose sugar to be $12 per hundredweight; what quantity can be purchased for $113? SECTION 28. COMMON DENOMINATORS. When two or more fractions have the same number for a denominator, this number is called their Common Denominator. Fractions having different denominators, must be reduced to a common denominator, before addition or subtraction can be performed on them. RULE FOR REDUCING FRACTIONS TO A COMMON DENOMINATOR. Multiply each numerator into all the denominators except its own, for a new numerator. Then multiply all the denominators together for a common denominator, and place it under each new numerator. 1. Reduce,, and, to a common denominator. 2. Reduce,, and to a common denominator. P* or SECTION 29. 1. A farmer raised 1427 bushels of corn in one field, and 237 bushels in another. How many bushels did he raise in both fields? The learner may reduce the fraction in his answer, to its lowest terms, in this, and all future examples. 2. A farm is divided into three lots; the first lot containing 46 acres, the second 50 acres, and the third 62 acres. How many acres are there in the farm? 3. Add together 441 and 65 and 2556. 4. If 6 be taken from 8% how much will remain? 5. Subtract 4372 from 1659. 6. If 6 gallons of wine should leak from a cask containing 53 gallons, how many gallons would remain ? 7. Add together 623 and 113; and then subtract from the sum 4502. 8. Three soldiers shared a loaf of bread as follows:the first took of it, the second took of it, and the third took the remainder. What fractional part of the loaf did the third soldier receive? 9. A trader having 25 barrels of flour, sold 8 barrels to one man, and 911 barrels to another. What quantity of flour had he then remaining? SECTION 30. 1. Suppose I have 16 dollars; to how many men can I give of a dollar apiece? 2. How many times is contained in 16? 3. How many pairs of gloves can I buy for 18 dollars, the price being of a dollar a pair? 4. Divide 18 by ; that is, reduce 18 to fourths, and find how many times 3-fourths is contained therein. 5. Divide 46 by ; that is, find how many times the fraction is contained in 46. 6. If a man walk 1 mile in of an hour, what dıstance will he walk in 4 hours? 7. How many times is 8. How many times is contained in 4? contained in? Direction. Reduce and to a common denominator, and then divide one numerator by the other. 9. How many times is contained in ? 10. How many barrels of flour can be bought for 38 dollars, at 4 dollars per barrel ? 11. How many times is 25 contained in 912? 12. How many times is 6 contained in 42? Direction. Reduce the two fractions to a common denominator; then reduce the mixed numbers to improper fractions, and divide one numerator by the other. 13. If a barrel of cider will last a man 3 how many barrels will he drink in 10 months? SECTION 31. REVIEW. months, 1. (§ 13.) Suppose a man to earn 95 cents per day; how many days would it take him to earn $43.16? 2. (§ 14.) How many pounds of sugar can be bought for $143, when the price is of a dollar a pound? 3. (§ 15.) If 1 yard of silk cord cost of a dollar, what is the price of 75 yards, at the same rate? 4. (§ 16.) If 147 yards of cloth be cut from a piece containing 52 yards, how much will be left? 3 5. (§ 17.) If a pound of shot cost of a dollar, what will be the cost of 17 pounds, at the same rate? 6. (§ 18.) How much corn will grow on 140 acres of land; allowing each acre to produce 34 bushels ? 7. (§ 19.) If a man's expenses be $46.247 for of a year, what will be his expenses for 1 year! ? 8. (§ 20.) of 71 is equal to what improper fraction? Then of 71 is equal to what mixed number? 9. (§ 21.) Suppose 42 men to share equally in a prize of $1000; what is the share of one man? 10. (§ 22.) If a man can cut 46 cords of wood in 14 days, how many cords can he cut in 60 days? 11. (§ 23.) Suppose a man can build a mile of wall in 310 days; in what time can he build of a mile? 12. (§ 24.) A man bought a quantity of flour, for domestic use, and in 36 days he found that of it was consumed. How long would the whole last? |