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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 i 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. of 4 is equal to what part of 1 ? 7. Reduce , of 1 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. ?pence is iz of 1 shilling, and 1 shilling is zo of £1. Therefore, 7 pence is 12 of z% of £1.
ið. Reduce 10 grains to the fraction of an ounce; that is, reduce & of zo 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 1 of } to a simple fraction. 15. šof of to is equal to what part of 1 ? 16. Reduce is of 1% 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. 14s. 100. 2qr. £1 is 20s.
ator and numer
ator here found, 17 8d.
make 366: this 4
fraction, when reNum. 7 14 qr.
Denom. 960 qr. duced, is 18.
18. Reduce 2s. 7d. lqr. 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 pouad. 21. Reduce 10d. Iqr. to the fraction of a shilling. 22. Reduce 2s. 9d. 3 qr. to the fraction of a pound.
Direction. Find the number of fifths of a farthing in 2s. 9d. 31 qr., for a numerator; then find the number of fifths of a farthing in £1, for a denominator.
23. Reduce 84 pence to the fraction of a pound. 24. Reduce 5qt. 1 pt. 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 35 76 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
Since 4 of £1 is the same as of
20 shillings, we find of 20 shillings, 7)40
in shillings and the fraction of a shil
ling; it is 5 shillings. Then, since 5 5
of 1 shilling is the same as of 12 12
pence, we find of 12 pence;- it is 7)60 84 pence. Then, since 4 of 1 pen8 4
ny is the same as 4 of 4 farthings, we find 4 of 4 farthings;- it is 24
farthings. Thus by finding one de7)16
nomination at a time, we finally ob
2 tain, 5s. 8d. 2 qr. 29. Reduce of £1 to its value in shillings &c. 30. of £1 is how many shillings, pence, &c.? 31. În of a shilling, how many pence, &c. ? 32. Change £15 to pounds, shillings, pence, &c. 33. Reduce 7 of 1cwt. to quarters, pounds, &c.
34. Change 96 pounds, to pounds, ounces, and drams 35. Reduce of a mile to furlongs, rods, feet, &c. 36. In 104 acrés, how many acres, roods, rods, &c. 37. How many dimes, cents, and mills, in 1 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?
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. Reducé , , and 4, to a common denominator. 5 4 6
72 7 7
504 2. Reduce , to, and } to a common denominator. 3. Reduce 14 and to a common denominator. 4. Reduce , ., and ti to a common denominator. 5. Reduce , }, }, and to a common denominator 6. How much is and added together? 7. How much is 14 and added together? 8. How much is 4 and and to added together? 9. If 15 be taken from , how much will remain ? 10. If į be taken from 1, how much will remain ? 11. Which is greater, Tor M?- how much greater
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 467 acres, the second 50% acres, and the third 62 Yo acres. How many acres are there in the farm ?
3. Add together 441 and 65 and 2556 1. 4. If 6 be taken from 8% how much will remain ? 5. Subtract 4373 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 11372 ; and then subtract from the sum 450 4.
8. Three soldiers shared a loaf of bread as follows:the first took ą of it, the second took is 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 84 barrels to one man, and 9 12 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 scontained 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 distance will he walk in 4 hours ?
7. How many times is to contained in 4? 8. How many times is contained in /?
Direction. Reduce and to a common denominator, and then divide one numerator by the other.
9. How many times is a contained in 1?
10. How many barrels of flour can be bought for 38 dollars, at 41 dollars per barrel ?
11. How many times is 25 contained in 91% ? 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 months, how many barrels will he drink in 10 months ?
REVIEW. 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 $14, when the price is of a dollar a pound?
3. ($ 15.) If 1 yard of silk cord cost 15 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 ?
5. (§ 17.) If a pound of shot cost o of a dollar, what will be the cost of 17 pounds, at the same rate ?
6. (§ 18.) How much corn will grow on 140 of land; allowing each acre to produce 34 ă bushels ?
7. (§ 19.) If a man's expenses be $46.24 Lo for i of a year, what will be his
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 m 310 days; in what time can he build 4 of a mile ?
12. (§ 24.) A man bought a quantity of four, for domestic use, and in 36 days he found that 15 of it was consumed. How long would the whole last?