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Ex. (1.) From £238 188. 1030. take £98 ls. 3 d.

Ans. £140 17s. 70. Ex. (2.) From £7 198. 20. take £2 Os. 6d.

Ans. £5 18s. sid. Ex. (3.) From £64 2s. 6 d. take £51 8s. 83d.

Ans. £12 13s. 9 d.

Troy Weight. Ex. (4.) From 13 lb. O oz. 11 dwt. 15 gr, take llb. 7 oz. 1 dwt. 2 gr. Ans. 11 lb. 5 oz. 10 dwt. 13 gr.

Ex. (5.) From 5 lb. 10 oz. 6 dwt. 12 gr. take 3 lb. 7 oz. 3 dwt. 14 gr. Ans. 2 lb. 2 oz. 17 dwt. 22 gr.

Apothecaries' Weight. Ex. (6.) From 2 lb. 8 3. 63. 2 3. take 1 lb. 11 3. 6 3. 29. 15 gr.

Ans. 3 3.7 3. 29. 5 gr.

Avoirdupois Weight. Ex. (7.) From 11 t. 9 cwt. 2 qr. 20 lb. take 9 cwt. 3 qr. 22 lb.

Ans, 10 t. 19 cwt. 2 qr. 26 lb. Ex. (8.) From 4t. 3 cwt. I qr. 10 lb. take t. 2 cwt. 3 qr. 27 lb.

Ans. 2 t. O cwt. 1 qr. 11 lb.

Long Measure. Ex. (9.) From 88 lea. 2 ml. 6 fur. 36 pol. take 70 lea. 1 ml. 7 fur. 20 pol. Ans. 18 lea. O ml. 7 fur. 16 pol

Cloth Measure. Ex. (10.) From 67 yds. 3 qrs. I nl. take 20 yds. 1q. 3 nls,

Ans. 47 yds. I qr. 2 nls.

Land Measure. Ex. (11.) From 116 a. Or. 30 p. take 45 a. 2 r. 36 p.

Ans. 70a. Ir. 34p.

Imperial Measure-Wine. Ex. (12.) From 24 tuns, 2 hhd. 50 gal. 3 qt. take 4 tuns, 1 hhd. 60 gal. 2 qt.

Ans. 20 tuns, 0 hhd. 53 gal. 1 qt.

Ale and Beer. (13.) From 14 bar. 3 fir. 2 gal. take 13 bar. 2 fir. 7 gal. 3 qt.

Ans, 1 bar. O fir. 3 gal. 1 qt.

Dry Measure. (14.) From 962 qr. 3 bush. 3 pk. take 64 qr. 2 bush. 1 pk. 1 gal.

Ans. 898 qr. 1 bush. 1 pk. 1 gal.

Time.

(15.) From 373 wk. 5 da. 5 hr, take 300 wk. 6 da. 21 hr. 18 min. 5 s. Ans. 72 wk. 5 da. ✓ hr. 41 min. 55 s.

Miscellaneous, (16.) Having received £1783 16s. 1 d., and paid £87 198. 11 d. I desire to know what is the remainder?

Ans. £1695. 16s. 1 d. (17.) I have sold goods to the amount of £76 ls. 7 d., and received on account thereof in cash, £26 14s. 7 d., and goods amounting to £15 14s. 6 d.; how much have I to receive ?

Ans. £33. 12s. 5 d. Stated thus

£

d.
£ s.

d. 76 1 anys
26 14 7 1
15 14 61 42 9 13

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The proof of Subtraction is to add the second and third lines ; that is to say, the lesser and remainder together; if they produce the top line, or greater, the work is correct.

77

COMPOUND MULTIPLICATION.

AFTER what the pupil has already learned of this branch of our subject, it ought to be comparatively easy ; with the practice that he has had in addition and subtraction, the tables ought to be familiar to him ; and I need not remind him, that to multiply is merely to repeat a certain sum or quantity a given number of times.

Let it be that the pupil has to multiply £1 4s. 3d. by 3; we place the multiplier, as in Simple Multiplication, under the right hand figure, which is the threepence.

We begin by saying, three times 3 are 9, which we write under the pence ;

three times 4 are 12, which we write under the shillings; and three times 1 are 3, which we write under the pounds. Thus we find that £3 12s. 9d. is £1 4s. 3d. thrice told.

But if we multiply the same sum by 6, we must bear in mind the different notations used in our money table.

Multiplying the pence, 3d. by six, make £ 18d. ; now as twelve of those

1
make
pence

4 3

6 one shilling, I write the remainder, 6, under

7 5 6 the pence, and carry 1 to the shillings, the next denomination, saying, six times 4 are twentyfour, and 1 makes twenty-five, twenty shillings are one pound, I therefore write down 5 under the shillings, carrying or adding one to the pounds, saying, six times 1 are 6, and one makes 7, which I write under the pounds, and we see that £7 58. 6d. is £1 4s. 3d. six times told. These examples, I feel convinced, will be sufficient to enable the student to work this rule. Where he finds a difficulty, he has only to refer to the table, as the sums will be set down in order, as in Addition and Subtraction; and where his memory does not enable him

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78

COMPOUND MULTIPLICATION.

S.

8

at once to say how many shillings there are in a certain number of pence, or how many pounds in a certain number of ounces, or how many dwts. in a certain number of grains, he has only to write on his slate the number of pence, grains, or ounces, and divide these by as many pence, grains, or ounces, as are contained in one of the next highest denomination of either, writing the re. mainder down under its proper head, and carrying the quotient to the next highest denomination ; thus,

Multiply £57 14s. 9 d. by 8. Beginning, as we always must do, at £ d. the lowest place, in this case that of

57 14 98 farthings, we find 8 times 3 make 24; now if I did not know, or if it

461 18 6 did not rise in my mind without exertion, that 24 farthings make 6 pence, I should write the twentyfour, and divide it by four, that being the number of farthings in a penny, and there being no remainder, there is nothing to write under the farthings. The quotient 6 I carry to the pence, which, when multiplied, is 72, and 6 to carry make 78; this seventy-eight, when divided by twelve, the number of pence in a shilling, gives a quotient of six, and a remainder of 6; the remainder I write under the pence, the quotient I carry to the shillings, which, when multiplied, are 112, and six carried make 118, which we divide by twenty, the number of shillings contained in a pound; this gives a quotient of five, with a remainder of 18; this eighteen, being shillings, I write under the shillings, and carry 5 to the pounds, which I multiply as in Simple Multiplication; the amount of the whole when multiplied being £161 188. 6d.

In this manner any sum in Multiplication may be worked ; but the learner may save himself a great deal of trouble by occasionally looking over the tables. It is

not necessary that he should desist from working sums until he can say the tables by rote; the knowledge of them will come by degrees, and when attained in that way will be borne in mind without encumbrance, and will never be forgotten.

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(11.) What is the value of 120 pounds of tea at 4s. 6d.

per lb.?

In this and all other sums in

4s. 6d. Compound Multiplication, when the

10 X 12 multiplier exceeds twelve, we take

2 5 0 two or three numbers that, when

12 multiplied by one another, will £27 0 0 amount to the multiplier we want ; and then, as in this case, multiply by them in succession.

(12.) Bought 127 untanned hides, at 13s. 4d. each, what did they cost?

13s. 4d.

10 X 12 = 120; and 6 13

120 + 7 = 127 4

12

80 0 0 Multiplicand x 7 = 4 13 4

£84 13 4

In this example we find that £80. would be the price

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