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multiply the price of 1. yard by 2 and add the product to the price of 45 yards, and the sum is equal to the price of 47 yards.
2. What will 23 yards of linen come to at 3s. 61d. per yard?
Ans. £4 1s. 5 d. 3. What quantity of hay is there in 17 loads, containing each 19cwt. 3qrs. 25lb.?
Ans. 339cwt. 2qrs. 5lb. 4. How many yards of cloth are there in 29 pieces, each containing 41 yards 2qrs. ?
Ans. 1203}yds. 5. How far will a vessel sail in 34 days, at the rate of 35le. 1m. 6fur. a day?
Ans. 1209le. 2m. 4fur.
EXAMPLES FOR EXERCISE.
1.. What is the weight of 7hhds. of sugar, each weighing 7cwt. 3qrs. 191b.?
Ans. 55cwt. lqr. 21lb. 2. What is the weight of 6 chests of tea, each weighing 3cwt. 2qrs. 9lb. ?
Ans. 21cwt. lqr. 26lb. 3. In 35 pieces of cloth, each measuring 273 yards, how many yards?
Ans. 971yds. 1qr. 4. How much brandy in 9 casks, containing each 45 gallons 3qts. Ipt.?
Ans. 412gals. 3qts. 1 pt. 5. How many bushels of corn in 15 barrels, each containing 3bu. 1 peck 4qts.?
Ans. 50bu. 2pk. 4qts. 6. How far will a man travel in 18 days, at the rate of 35m. 6fur. 25 rods a day? Ans. 644m. 7fur. 10rds.
7. How much land is contained in 9 fields, each measuring 12 acres 2 roods 25 po. ? Ans. 113A. 3r. 25po.
8. In 8 parcels of wood, containing each 5 cords 76 feet, how many cords?
Ans. 44 cord 96 feet. 9. The earth performs one revolution round the sun in 365 days 5 hours 48m. 56sec. How long will it take to make 8 revolucions ? Ans. 2921d. 22hrs. 31m. 28sec.
COMPOUND DIVISION Teaches to find how often one given number is contained in another, of different denominations.
I. When the divisor does not exceed 12.
Begin with the highest denomination, and divide as in Simple Division; and if there be a remainder, find how
many of the next lower denomination it is equal to, which add to the next denomination; then divide again, and carry the remainder, if any, as before : thus proceed till the whole is finished.
Proof—the same as Simple Division.
1. If £2047 13s. 9d. be divided equally among 6 men, how much will each man receive ?
Illustration.--We divide the pounds Operation. as a whole number, by 6, and the 6)2047 13 9 0 remainder, 1 pound, is equal to 20s.
which we add to the next denomina341 5 7 2
tion, 13s. makes 33s. which divided
by 6, the quotient is 5s. and the remainder 3s. We then multiply the 3s. by 12, the number of pence in one shilling, and add in the 9d. makes 45d.; this divided by 6, the quotient is 7d., and the remainder 3d., which we multiply by 4, makes 12qrs.; which being divided by 6, the quotient is 2qrs. 2. If 9 tons of hay cost £41 3s. 6d., what will 1 ton cost?
Ans. £4 lls. 6d. 3. If 11 bushels of corn cost £2 9s. 6d. what is that a bushel ?
Ans. 4s. 6d, 4. Divide £144 10s. equally among 12 men.
Ans. £12 Os. 10d. 5. If 26 bushels of corn be put into 8 barrels, how much will there be in each barrel ? Ans. 3 bushels 1 peck.
6. If 9 pieces of broadcloth contain 272 yards 1 quarter, what does 1 piece contain ?
Ans. 30 yds. 7. A tract of land, containing 96 acres 2 roods 16 rods, is to be divided into 7 equal lots; how much land will each lot contain ?
Ans. 13 acres 3 roods 8 rods. II. If the divisor exceed 12, and be a composite number, divide first by one of the component parts, or factors, and that quotient by another, &c., and the last quotient will be the answer.
8. Divide £39 13s. 4d. by 28.
28 being a composite number, and 7)39 13 4 its component parts, or factors, 7 and 4, 4)5 13 4
we first divide the 39 pounds, 13 shil
lings 4 pence by one of the factors, and Ans. 1 8 4
that quotient by the other factor, which gives the true quotient.
9. If £269 12s. 4d. be divided equally among 56 men, how much will each man have ? Ans. £4 16s. 30.
10. If 27 days' labour cost £10 2s.6d, what will one day's labour come to ?
7s. 6d. 11. Divide 59cwt. 2qrs. 141b. by 18. Ans. 3cwt. Iqr. 71b. 12. Divide 145yds. 2qrs. by 32. Ans. 4yds. 2qrs.t13. Divide 94 bushels 2 pks. by 56. Ans. lbu. 2 pks. 6qt. 14. Divide 232 gallons, by 64. Ans. 3gals. 2qt. Ipt. 15. Divide 149A. 1 rood 24rds. by 96.
Ans. 1A, 2roods 9rd. 16. Divide 356yrs. 9mo. 1 week 5 days, by 108.
Ans. 3yrs. 3mo. 2 weeks 4da. III. When the divisor exceeds 12, and is not a composite number, divide by the whole divisor at once, after the manner of Long Division. 17. Divide £176 9 shillings 6 pence, by 26. 26)176 9 616
ist. We divide the pounds, § 66
and the quotient is £6, and 156
the remainder £20. This 20
remainder we now multiply 20
by 20, the number of shil.
lings in 1 pound, and to the 26)409(15
product add the 9 shillings 26
in the dividend, which makes 149
409 shillings; this sum we 130
divide by 26, as before, and
the quotient is 15 shillings, 12
and the remainder is 19 shild.
lings. We then multiply the 26)23419
19 shillings by 12, the num234
pence in one shilling,
and to the product add the 0
6 pence in the dividend, making 234 pence: this sum, divided by 26, as before, the quotient is 9d. We now have for the quotient £6 15s. 9d
18. If 31 yards of cloth cost £113 138. 4d. how much is that a yard ?
Ans. £3 13s. 4d. 19. Divide 201cwt. 3qrs. 21lb. by 41.
Ans. 4cwt. 3qr. 191b 10oz. 20. Divide 861 yards lqr. by 52. Ans. 16yds. 2qr. Ina. 21. Divide 7248 gallons, by 128. Ans. 56gals. 2t. lpt. 22. Divide 6307 miles 4fur. by 96. Ans. 65m. 5fur. 25rd. 23. Divide 310a. 3 roods 5rd. by 85. Ans. 3a. 2r. 25rd. 24. Divide 754 years 3 months 1 week, by 91.
Ans. 8yrs 3mo. lw. 6d
EXAMPLES FOR EXERCISD.
1. If 9 tons of hay cost £40 14s. 6d., what will 1 ton cost?
Ans. £4 10s. 6d. 2. Divide 98lb. 2oz. 19pwt. 5grs. of silver into 7 equal parts.
Ans, 14lb. Ooz. spot. 11gr. 3. Divide 6 Ton 11cwt. 3qrs. 16lb. by 8.
Ans. 16cwt. 1qr. 261b. 8oz. 4. If 97cwt. 2qrs. 14lbs. of sugar be contained equally in 11 hogsheads, how much sugar in 1 hogshead ?
Ans, 8cwt. 3qrs. 141b. 5. If 1113 gallons 3 quarts of brandy be put equally into 18 casks, how much will each contain ?
Ans. 61 gals. 3qts. 1 pint. 6. Divide 95 gallons 3 quarts 1 pint by 25.
Ans. 3 gals. 3qts. Opt. 2gi. + 7. Divide 94 bushels 4 quarts of corn equally among 15 men, and how much will each man have ?
Ans. 6bu. 1 peck Oqt. 1 pt. + 8. If a man's yearly income be £38 145., what is that a calendar month?
Ans. £3 4s. 6d. 9. If 88 acres 1 rood 10 rods of land be divided into 18 equal lots, how much land will each lot contain ?
Ans. 4 acres 3 roods 25rd. 10. Divide 95 E.E. 4 quarters 2 nails by 7.
Ans. 13 E.E. 3qrs. 2 nails. 11. Divide 144 yards 1 quarter 2 nails by 11.
Ans. 13 yards Oqr. 2 nails. 12. Divide 36 leagues 2 miles 6 furlongs 20 poles, by 15.
Ans. 2le. I mile 3fur. 4rd.
13. Divide 18 gallons of Ale equally among 144 men
Ans. 1 pint each. 14. Bought 2 dozen silver spoons, which together weighed 4 pounds 3 ounces 13 pwt. What was the weight of
Ans. 2oz. 3pwt. 1 grain. Questions.
What is Compound Multiplication ? What does Compound Division teach?
1. When the multiplier does not ex. 1. When the divisor does not exceed ceed 12, how do you proceed ?
12, how do you proceed? 2. When the multiplier is a compo 2. If the divisor exceed 12, and be a site number, and greater than 12, how composite number, how do you prodo you proceed?
ceed? 3. When the multiplier is not a com 3. When the divisor exceeds 12, and posite number, how do you proceed ? is not a composite number, how do you
REDUCTION. Reduction teaches to bring numbers from one name, or denomination, to another, without altering their value.
Reduction is of two kinds, Descending and Ascending.
Descending is when higher denominations are brought into lower, as days into hours, &c., and is performed by multiplication.
Ascending is when lower denominations are brought into higher, as hours into days, &c., and is performed by division.
1. To reduce high denominations to lower.--Multiply the highest denomination given by so many of the next less as make one of that greater, and to the product add the next lower denomination, (if any ;) thus proceed with each succeeding denomination, until you have brought it to the denomination required.
II. To reduce low denominations to higher.—Divide the lowest denomination given by that number of the same denomination which it takes to make one of the next higher; thus proceed with each succeeding denomination, until you have brought it to the denomination required.
Proof.-Reduction Ascending and Descending alternate ly prove each other.