. Quantity of beef, for which £20 will pay, = 51⁄2 cwt. = 5·cwt. 2.qr. 24 lb. EXERCISE LXXXIV.

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EXERCISE LXXXIX.

EXAMPLES IN DIVISION OF ONE CONCRETE QUANTITY BY ANOTHER OF THE SAME KIND, QUOTIENT BEING EXPRESSED AS INTEGER, VULGAR FRACTION, OR DECIMAL.

A. EASY EXAMPLES, TO BE WORKED MENTALLY.

Answers, when Improper Fractions, to be given also as Mixed Numbers; and all Fractions to be given in their lowest terms. 1 Express as Fractions of 34d., įd.; i̟d.; ąd.; l·d.; l‡d.; l1⁄2d.; iąd.; 2.d.; 24d.; 24d.; 2ąd.; 31d.; 41d.; 74d.; 111⁄2d.

2. How many pounds, or what part of 1 lb., at 34d., can be bought for each of the above amounts; also for 1's. 3'd.; 14d.; 18 d.; 20'd.; 2's.; half-a-crown; a florin; half a sov.; half a guinea; £1'; a guinea?

3. At 1d. per pint, how much milk for 2.d.; 3·d.; 4'd.; 6·d.; d.; d.; d.; l'd.; 14d.; 14d.; 1ąd.; 24d.; 24d.; 2ąd.; 5·d.; 7d.; 8ąd.; 10'd.; 11'd.; 1's.; 13'd.?

How many yards, or what part of lyd. can be bought

4. For 6 d., at 1d. per yd.? 11. For 2's. 6 d., at

31d. per yd.?

1's. 6.d.; 3's.; 4's. 4'd.; 10's. 6'd.; 2's. 6'd.; 7's. 6'd.; 12 s. 6.d.; 15's.; 17's. 6'd.; 2's. 8.d.; 1's. 10'd.; 3's. 5 d.

B. MORE DIFFICULT EXAMPLES.

1. How many articles worth £2∙ 10′s. 7 d. each will cost £35. 8's' 9'd.? 2. Expended £78. 19's. 44d. in the purchase of sheep, which cost,

on an average, £1. 7.s. 8d. each. How many were there? 3. How many persons can be paid £4 3's. 74d. each, out of a fund amounting to £413 18's. 10d.?

4. Into how many farms, each 47 ac. 2 r. 13. po. 29 yds., can an estate of 428 ac. 1.r. 5' po. 19 yds. be divided?

5. Supposing a man to travel uniformly at the rate of 37 mi. 5 fur. 18 po. per day, how long will he be completing a distance of 1620 mi. 2. fur. 14' po. ?

NOTE TO TEACHER. It may be well here to caution the pupil against the egregious blunder inculcated by many books as to the result of Dividing one Compound Quantity by another. I have before me, at this moment, a manual, published by government authority, containing the astounding statement that £9368 14 s. 33d. ÷ £42 7's. 04d. = 4's. 74d. and a fraction of a farthing"! This error betrays an utter forgetfulness of what Division really is. It has been corrected in recent editions of the work in question. A twin absurdity is the venerable crambo, "Multiply £19 19's. 11ąd. by £19′ 19's. 11fd."

6. How many bins each containing 7 qrs. 3. bu. 2 pks. 1 gal., can be filled with flour, from a store containing 104 qrs. 2. bu. 3. pks.?

7. How many scholars are there in a school of which the gross expenses amount to £143 10's. 1 d., and the average cost per scholar £1 12's. 7gd.?

8. How many fleeces of wool, each 103 lb., will weigh 3 cwt. 2. qrs.? 9. From a tun of wine, how many dozen bottles can be filled, each bottle containing 1 pint?

10. If a cwt of sugar cost £2 6's. 4.d., how much can be bought for 5's. 9 d.?

Find what fraction 5's. 94d. is of £2⋅ 6's. 4'd.

Then, the same Fraction of 1 cwt. may be bought for 5's. 94d. 11. Express £226 11's. 0дd. as a Vulgar Fraction of £317 3′s. 5 d. 12. What is the ratio of £407 16's 54d. to £317 3's. 10ąd.?

13. Reduce 13's. 6d. to a Fraction of £1 8's. 10d.

14 Reduce 41 qrs. 5 gals. to a Fraction of 56 qrs. 1 gal.

15 What Decimal Fraction of £105 19's. 6 d. is equal to £66 4's. 81d.?

16. By what Decimal Fraction must 8 lb. be multiplied to produce 4 lb. 7 oz. 7. drs.?

17 What part of a ton is 13 cwt. 3 qrs. 21 lb.?

18. What part of 11 guineas is £1. 13's.?

19. How many times can 11 lb. 6 oz. be taken out of 1' cwt. 2. qrs.

8. lb. 5 oz.?

20. If a coat require 35 yds. of cloth, how many such may be made from a piece measuring 60 yards, and how much cloth will there be in the remnant?

Find, and accurately describe, the Quotients

21. Of £2171 5's. 73d. £56. 10's. 10 d.

22. Of 28. Tons. 8 cwt, 1' qr. 16 lb.

1. Ton. 17. cwt. 3 qrs. 16 lb.

23. Of 1500 mi. 6. po.27 mi. 6. fur. 9. po.

24 Of 61 qrs. 4. bu. 2. pe. 13 pt. 8. qr. 4. bu. 1. pe. 1· gal. 1' qt. 25 Of £312. 18's. 5 d. £40 7's. 6d.

26. Of 84 ac. 2. r. 34 per. 5 ac. 3. r. 12 per.

27. Of 1621 lb. 4 oz. 15 dwts. 13. grs.

21 lb. 13. dwts. 17' grs.

28. Of 240 yds. 2 qrs. 3 na. 14 yds. 2 qrs. 3. na. 29 Reduce £68. 3's. 34d. to the Decimal of £104′ 3′s. 4.d. 30 Reduce 3 lb. 64 oz. to the Decimal of 3 qrs. 13 lb. 10 oz. 8. drs. 31. Reduce 68 yds. 2 ft. 4 in. 6 li. to the Dec. of 183 yds. 1.ft. 4 in. 32. Reduce £1. 5's. 24d. to an Interminate Dec. of £2 18's. 10d. 33. What Interminate Decimal of £536' 4's. 34d. & q. is equivalent to £417 1's. 1 d. q.?

34. By what Decimal Fraction must 9's. 5ąd. be divided to yield a Quotient equal to 10's. 10.d.?

35 Express 46. lb. 7.3 2.3 1.9 15 grs. as a Vulgar Fraction of 111 lb. 10.3 3.3.

THE COMPOUND RULES.

Addition, Subtraction, Multiplication, and Division of Compound Quantities are usually termed "Compound Addition," "Compound Subtraction," &c., and, collec

tively, "The Compound Rules." Each of them is, however, nothing more than a combination of the simple process with Reduction.

Thus, Compound Addition consists of several Simple Additions and Reductions.

COMPOUND ADDITION.

To find the Sum of any number of Compound Quantities, of the same kind. (PRINCIPLE v.)

First. Arrange the given Quantities so that like units, or fractions of like units, shall stand in the same vertical column; placing the columns in the order of value of their units, ascending from right to left.

Second. Add the units or fractions in right-hand column. Reduce the Sum to next higher name. Carry units found of that name, and set down Remainder under its own column.

Third. Find the Sum of next column and units carried. Reduce this Sum to next higher name. Set down and carry as before. Proceed similarly with all the other

columns.

Method of Proof. The same as in Simple Addition. (Page 30)

EXAMPLES WORKED OUT AND PROVED. I. Find the Sum of £295 11 s. 83d., 18's. 11d., £31045 16's. 5 d., £41∙ 10 ́s. 4 d., £9642∙ 1∙s. d., and £70000 91d.

110730 7 73

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[omitted.

Sum of lower five amounts, top one

111025. 19. 41 Sum of the six amounts. Proof.

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II. Add together £614 17 s. 9 d., £22. 13's. 63d., £134 14 s. 51d., £84 6's. 114d., £5946. 12's. 87d., £521 19 s. 103d. and £34168 711d.

40878. 8. 18

41493 5 117

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[omitted.

Sum of lower six amounts; top one 5. 117 Sum of the seven amounts. Proof.

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EXERCISE XC.

EXAMPLES IN ADDITION OF COMPOUND QUANTITIES. Find the Sum of each of the following sets of like Compound Quantities.