37. What costs a box of sugar, weighing 106 pounds, a

151 c. per pound?

38. At D9.10 per day, how much a year?

REVIEW.

Ans. D16.164.
D3321.50.

When

What is Multiplication of Different Denominations? is it used? Under what part of the number to be multiplied do you place the multiplier? How will you then proceed? By what do you divide the product? If there is a remainder, what is to be done? How do you carry? If there be no remainder after the division, what will you then do? What will you do with the quotient? Proof? Repeat the rule. Repeat the rule when the multiplier is the exact product of any two figures in the multiplication table. When the multiplier is not a composite number, and more than twelve, how will you perform the operation? Repeat this rule.

DIVISION OF DIFFERENT DENOMINATIONS.

By this rule we can divide a number containing different denominations.

RULE.

If the divisor does not exceed twelve, proceed as in short division of whole numbers; only observe this difference, that in this rule there are several denominations; therefore divide the left hand denomination, and place the quotient under it; reduce the remainder, if any, to the next less denomination, and add in the given number of that denomination; then proceed as before.

2. When the divisor exceeds twelve, it will be more convenient to work by long division, observing the above rule. Proof: by multiplication.

EXAMPLES.

Divide 10 yards, 3 quarters, 2 nails, among 5 persons.

4. 4.

yds.qrs.na. 5)10 3 2

2 0 2+4

Explanation. First say, 5 in 10 twice and 0 over; then 5 in 3 qrs. O times, 3×4=12+2=14; then 5 in 14, 2 times and 4 remainder; and the sum is done.

4. 28. 16. 16.

40)50 2 14 9 40

10

4X

40)42(1 qr. 40

which

cwt. qr. lb. oz. dr. cwt. qr. lb. oz. drams. 11(11 1 12 3 35 Ans. Explanation. The first denomination into divide is cwt.; here you have you 1 cwt. and 10 cwt. over, or remainder, multiply this remainder by 4 qr. and add in the 2 qr. in the dividend, and you have 42 qr.; divide as before, and you have 1 qr. and 2 qr. over, multiply this remainder by 28 lb. and add in the 14 lb., and you have 70 lb. ; divide as before, and you have 1 lb. and 30. lb. remaining, multiply the 30 lb. by 16 oz. and add in 9 oz., and you have 489 oz.; divide by 40 and you have 12 oz. and 9 remaining, multiply the 9 oz. by 16 dr. and add in the 11 dr., and you have 155 dr.; divide, and you have 3 dr. and 35 remainder: these collectively are the answer.

2

28 X

40)70(1 lb.

40

30

16 X

QUESTIONS.

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 them; required the share of each. Ans. 168A. 2R. 4po.

Ans. 2M. 4fur. 1po.

21. Divide 17L. 1M. 4fur. 21po. by 21. 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 lift 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 Ans. 1 bushel, 1 peck, 4 quarts.

men.

35 Divide 19 cwt. 3 qrs. 27 lb. 12 oz. of sugar among 48 families. Ans. 1 qr. 18 lb. 10 oz.+28. 12 oz. of rice among 14 perAns. 1 qr. 8 lbs. 8 oz +12

36. Divide 4 cwt. 2 qrs. 7 lbs.

sons.

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.

REVIEW.

Where

When is Division of Different Denominations used? 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. 0 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. 10. From 1 gall. take 1 gill.

Ans. 11oz. 19dwt. 9gr. 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 ?

12. From 1 acre take 5 poles.

Ans. 17 cwt. 3 qrs. 17 lbs.
Ans. 3 R. 34 po.

13. A person purchased 6 hhds. of sugar, each weighing 8 cwt. 1 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. 11mo. 3w. 6da. 12h. 20. From 12 miles, 15 rods, take 3 furlongs.

PROBLEM:

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 the greater number. 309 greater number.