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19. Divide 482 bushels, 2 pecks, 4 quarts, among 3 persons.
Ans. 160 bushels, 3 pecks, 4 quarts, each. 20. A gentleman bequeathed to his 5 sons a tract of land containing 842 acres, 2 roods, 20 poles, to be divided equally among chem; required the share of each. Ans. 168A. 2R. 4po.
21. Divide 17L. 1M. 4fur. 21po. by 21. Ans. 2M. 4sur. 1po. 22. Divide 4.5 gallons of wine equally among 144 persons.
Ans. 1 gill each. 23. From a piece of cloth containing 64 yards, 2 nails, a tailor wishes to make 9 coats, which will take one third of the whole piece ; how many yards did each coat contain ?
Ans. 2 yards, 1 quarter, 2 nails. 24. If 90 hogsheads weigh 56 tons, 13 cwt. 3 quarters, 10 lb., what is the weight of one hogshead ? Ans. 12 cwt. 2 qr. 11 lbs.
25. If the earth revolve on its axis 15 degrees in one hour, how far does it revolve in one minute ?
Ans. 15'. 26. If 59 casks contain 44 hhds. 53 gallons, 2 quarts, 1 pint, what are the contents of each cask ?
27. When 175 galls. 2 quarts of beer are drunk in 52 weeks, how much is consumed in 1 week? Ans. 3 galls. 1 qt. 1 pt.
28. Divide 168 bushels, 1 peck, 6 quarts of wheat among 35 men.
29. What will be the share of one man, if 810 tons, 11 cwt 20 lb. 10 oz. 11 dr. be divided equally among 346 men ?
Ans. 2 tons, 6 cwt. 3 qrs. 11 lb. 8 oz. 13 dr 30. Suppose a man has 246 miles, 6 furlongs, 36 poles, to travel in 12 days, how far will that be in a day?
Ans. 20 miles, 4 fur. 23 po. 31. If a steamboat should go 224 miles a day, how long would it take her to go to China, it being 12000 miles ?
Ans. 53 days, 13 hours, 42 min, 51 sec. 32. If one man can lift 201 pounds, 12 ounces, how much can a boy lift, if a man can list 8 times as much as a boy?
Ans. 25 lbs. 3 oz. 8 dms. 33. If 15 loads of hay contain 35 tons, 4 cwt., what is the eight of each load ? 34. Divide 371 bushels, 1 peck of wheat equally among 270
Åns. 1 bushel, 1 peck, 4 quarts. 35 Divide 19 cwt. 3 qrs. 27 lb. 12 oz. of sugar among 48 families.
Ans. 1 qr. 18 lb. 10 oz.+28. 36. Divide 4 cwt. 2 qrs. 7 lbs. 12 oz. of rice among 14 per
Ans. 1 qr. 8 lbs. 8 oz +12
37. Divide 19 bushels, 2 pecks, 7 quarts, 1 pint, 2 gills, among 62 persons.
38. Divide 1749 acres, 2 roods, 30 poles, equally among 9 men and 7 women.
When is Division of Different Denominations used? Where will you place the divisor? If, when you divide the highest denomination by the divisor, a remainder occurs, how do you proceed? When the divisor exceeds twelve, but is a composite numbers, how can the operation be performed ? Ans. First divide the given sum by one of the numbers, and that quotient by the other, and the last quotient will be the answer.
When the divisor exceeds twelve, and is not a composite number, how will you proceed? Repeat the rule. How can you prove questions in this rule ?
APPLICATION OF THE COMPOUND RULES.
1. A man travelled in one day 27 miles, 3 furlongs; another day, 30 miles, 2 furlongs, 25 poles; required the distance.
Ans. 57 miles, 5 furlongs, 25 poles. 2. A man has three farms, the first contains 150 acres, 2 roods, 25 poles; the second, 200 acres, 1 rood, 15 poles; the third, 100 acres, 1 rood, 10 poles ; how many acres in all.?
Ans. 451 acres, 1 rood, 10 poles. 3. Add 2 cwt. 3 quarters, 27 pounds; 1 cwt. 2 quarters, 16 pounds; 3 cwt. 1 quarter, 25 pounds ; 5 cwt. 2 quarters, 12 pounds; 2 cwt. 2 quarters, 14 pounds; 5 cwt. 1 quarter, 15 pounds.
Ans. 21 cwt. 2 qrs. 25 lbs, 4. Bought 3 gallons, 2 quarts of wine; 5 gallons, 3 quarts of vinegar; 4 gallons, 1 qt. of molasses; how many gallons in all ?
5. A tailor purchased a piece of broadcloth containing 40 yards, of which he sold 36 yards, 1 quarter, 2 nails; how much will he have remaining? Ans. 3 yards, 2 quarters, 2 nails.
6. If a cask of wine contains 54 gallons, 2 quarts, 1 pint, 2 gills, and there should be 10 gallons, 3 quarts, 1 pint, 1 gill sold, how much would remain ? Ans. 43 galls. 3 qts. O pts. 1 gill
7. From 40 bush. take 23 bush. 2 pks. Ans. 16 bush. 2 pks. 8. From 1 square yard take 3.5 square feet. 9. From 1 lb. troy take 15 grains. Ans. 11oz. 19dwt. 9gr. 10. From 1 gall. take 1 gill. Ans. 3 qts. 1 pt. 3 gills.
11 A merchant bought 5 chests of tea, each weighing cwt. 2 qrs. 9 lbs.; what was the weight of the whole ?
Ans. 17 cwt. 3 qrs. 17 lbs. 12. From 1 acre take 51 poles.
Ans. 3 R. 34} po. 13. A person purchased 6 hhds. of sugar, each weighing 8 cwt. I qr. 18 lbs.; required the weight of the whole.
Ans. 50 cwt. 1 qr. 24 lbs. 14. A merchant purchased 8 casks of oil, each containing 41 galls. 3 qts. 1 pt.; required the number of gallons. Ans. 335
15. In 28 pieces of calico, each containing 35 yards, 2 quarters, 1 nail, how many yards in all ? Ans. 995 yds. 3 qrs.
16. A farmer has 6 bins of wheat, containing 53 bushels, 3 pecks, 5 quarts, 1 pint each; how much in all ?
Ans. 323 bushels, 2 pecks, 1 quart. 17. Add 3 quarts, 3 pints, 1 gill; 5 quarts, 4 pints, 3 gills, 6 quarts, 1 gallon, 1 pint, together.
18. From 1 ton of round timber take 50 cubic inches. 19. From 1 year take 12 hours. Ans. Ilmo. 3w. 6da. 12h. 20. From 12 miles, 15 rods, take 3 furlongs.
Ans. 11 m. 5 fur. 15 rods.
Resulting from a comparison of the compound rules, by the operation of which many questions may be solved in a short and elegant manner.
1. Having the sum of two numbers, and one of them given to find the other.
Rule.-Subtract the given number from the given sum, and the remainder will be the number required.
Let 154 be the sum of two numbers, one of which is 84, the other is required. 154 sum-84 given number=70 the other.
2. Having the greater of two numbers, and the difference between that and the less given, to find the less.
RULE. Subtract one from the other.
If the greater number be 672, and the difference between that and the less 389, required the other number. 672 given389 difference=283 less.
3. Having the least of two numbers given, and the difference between that and the greater, to find the greater.
Rule.- Add them together.
The less number is 142, and the difference 167; required he greater number. 309 greater number.
4. Having the product of two numbers, and one of them given, to find the other.
Rule. Divide the product by the given number, and the quo. tient will be the number required.
If the product of two numbers be 196, and one of them 4, quired the other. Thus : 196-4=49. Ans.
5. Having the dividend and quotient, to find the divisor.
Rule. Divide the dividend by the quotient. This will prove division.
Let the dividend be 144, and the quotient 16, required the divisor ? 144:16=9. Ans.
6. Having the divisor and quotient given, to find the dividend. RULE. Multiply them together.
Let the divisor be 6, and the quotient 72, required the dividend. 72 X6=432. Ans.
1. Suppose a man born in the year 1743, when will he be 77 years of age ?
Ans. 1820. 2. What number is that, which if it be added to 19418 will make 21802 ?
Ans. 2384. 3. What number must you multiply by 9, that the product may be 675 ?
Ans. 75. 4. What is the difference between thrice five and thirty, and thrice thirty-five ?
Ans. 60. 5. If a man spend 192D. in a year, how much is that
cal. endar month?
6. A. borrowed at different times the following sums, namely: of B. D625 ; of C. D721.50 ; of D. D842; and he is indebted to others as much as he has borrowed, abating D125.50 ; he is now prepared to retire from business ; required the amount of his debts.
Ans. D4251.50 7. General Burgoyne and his army were captured at Saratoga, N. Y., by General Gates, October 17, 1777, and Earl Cornwallis and his army surrendered to General Washington at York, Va., October 19, 1781 ; required the space of time between.
Ans. 4 years, 2 days 8. Bought 5 loads of wood : the first containing 1 cord, 32 feet; the second, 1 cord, 64 feet; the third, 112 feet; the fourth, I cord, 28 feet; the fifth, 1 cord, 20 feet; how much in all ?
Ans. 6 cords
9. How many bottles holding 1 pint, 2 gills each, are required for bottling 4 barrels of cider ?
10. 9 A. 7 R. 50 po.+17 A. 11 R. 70 po.; then-12 A. 5 R. 45 po.; then x by 62 ; then -- by 49.
REDUCTION OF DECIMALS.
The two following cases of Reduction of Decimals are the very reverse of each other, and by reversing the rule, one will prove the other.
The use of the rule is to change a denomination, or several denominations, from their given expression into a decimal quantity having the same value, for the purposes of multiplication, division, &c., which will then become the same as whole numbers. Thus, if you wish to find the decimal expression of 2 quarters, 14 pounds, avoirdupois, first reduce it to pounds, 2 x 28=56+14=70 pounds; now annex ciphers to the 70 pounds, and divide by 112 lbs.=1 cwt, of which you wish to make it a decimal, and you have .625; 9266==; for 14)11 3. Again, you wish to reverse the rule, and give the .625 the expression in the terms of the integer, or to reduce it to its proper value. Thus .625 cwt. multiply by the next less denomination, which is 4 qrs., and count off the three places for decimals, according to the rule in multiplication of decimals, and the quantity at the left of the decimal point is of the same name with the multiplier, that is, 2 qrs. ; then multiply the remaining decimal, .500, by the next less denomination, namely, 28 lbs., and count off as before, and you have 2 quarters, 14 pounds= 1000=112=cwt., &c.
The correctness of the operation of the rule is evident from the nature of decimals, and the explanations already given in the preceding pages.
In the third case : to reduce a vulgar fraction to its equivalent decimal, by annexing one, two, three, or more ciphers to the numerator, the value of the fraction is increased ten, a hundred, or more times. After dividing, the quotient will, of course, be ten, a hundred, or more times, too much ; the quotient must, therefore, be divided by ten, a hundred, &c., to give the true quotient or fraction. In the first example, is 1900="15, which divided by 1000 is 128=.125, and this is the rule.