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III. WHEN THE MULTIPLIER DOES NOT EXCEED 144, BUT CANNOT

BE RESOLVED INTO TWO FACTORS.

RULE.-Multiply by the nearest factors, as in Rule II., then the original sum by the remainder of the multiplier, and add the two last products together for the answer.

Example.-Multiply £17, 13s. 6d. by 23.

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IV. WHEN THE MULTIPLIER EXCEEDS 144.

RULE.-Multiply as in Rule I.; only, instead of performing the process mentally, the figures, from their quantity, require to be written down separately, in order to be calculated.

Example.-Multiply £23, 14s. 74d. by 374.

£ S. d. 23 14 7 374

£8875 9 9 Ans.

Here we first multiply the 2 farthings by 374, and convert them to pence, making 187d. and no farthings over. Carry the 187d. to the pence, then multiply the 7d. by 374, and include the 187d. from the farthings: the 7d. X 374, and adding 187, are 2805d., which, converted to shillings, make 233s., and 9d. over. Place the 9d. below the pence, carry 233s. to the shillings, then multiply the 14s. by 374, and include the 233s. from the pence, making 5469s., which, converted to pounds, are £273, and 9s. over. Place the 9s. below the shillings, carry £273 to the pounds, then multiply the £23 as in Simple Multiplication, and include the £273, making £8875.

NOTE. As it is generally more convenient to multiply the greater number by the less, than to multiply the less by the greater, in the above example instead of multiplying 2 farthings, &c., by 374, we multiply 374 by 2; and so on.

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V. WHEN THE MULTIPLIER CONTAINS A FRACTION-AS 83.

RULE.-Multiply first by the integer or whole number of the multiplier, and then by the fraction (see Simple Multiplication, Rule IV., page 19), and add the products together for the answer. Examples.-Multiply £3, 15s. 44d. by 83.

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354 15 7" 12,

16 cwts. 3 qrs. 12 lbs. by 27%, Ans. 461 cwts. 3 qrs. 153 lbs.

Miscellaneous Exercises.

1. What do 8 yards of cloth cost, at 15s. 8d. per yard?

2. What do 27 yards of linen cost, at 2s. 44d.

Ans. £6, 5s. 4d. per yard? Ans. £3, 4s. 1d. " £2, 12s. 5d.

3. Find the value of 37 yards calico, at 1s. 5d. 4. What is the value of a dozen silver spoons, weighing 1 lb.

7 oz., at 7s. 6d. per ounce?

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5. What do a workman's wages amount to in 13 weeks, at 15s. 6d. per week? Ans. £10, 1s. 6d.

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6. What is the yearly income of a workman who has a wage of £1, 3s. 6d. per week?

Ans. £61, 2s.

7. A charitable institution gives relief to 170 individuals, to the amount of 3s. 3d. per week each. What is its yearly expenditure? Ans. £1436, 10s. 8. If a boy spend 4d. a week on sweetmeats, how much does he squander in a year?

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Ans. 17s. 4d. 9. If a family consume 6 loaves of bread in a week, when the price is 8d., what is the yearly expenditure? Ans. £11, 1s.

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10. Find the amount of 27 cwts. of sugar, at £3, 13s. 6d. per Ans. £99, 4s. 6d. 11. A butcher bought 3 scores of ewes, for which he paid 25s. 9d. each. How much did the whole amount to? Ans. £77, 5s. 12. What is the cost of 71 cwts. of butter, at £4, 13s. 44d. per cwt.? Ans. £331, 8s. 13d. 13. What is the cost of 549 bags of cotton, at £12, 1s. 2 d. per bag? Ans. £6621, 14s. 93d. 14. What is the cost of 936 quarters of wheat, at £2, 9s. 6d. per quarter? Ans. £2318, 11s. 15. What is the weight of 47 pieces of lead, each 25 lbs. 6 oz. 12 drs.?

16. What is the weight of 28 ounces?

17. What is the weight of 35

17 lbs. ?

Ans. 1194 lbs. 13 oz. 4 drs. loaves of sugar, each 13 lbs. 6 Ans. 374 lbs. 8 oz. blocks of tin, each 2 cwts. 1 qr. Ans. 84 cwts. O qrs. 7 lbs.

18. What is the weight of 12 dozen silver table-spoons, each 2 oz. 5 dwts. and 15 grs.? Ans. 41 oz. 1 dwt. 6 grs.

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19. How much linen will it require to make 2 dozen shirts, each shirt requiring 3 yards 1 quarter 2 nails? Ans. 81 yards. 20. What distance will a coach travel in 29 hours, at the rate of 9 miles 6 fur. 20 per. an hour? Ans. 284 miles 4 fur. 20 per. 21. What is the value of 276 tons of iron, at £4, 16s. 8d. per ton? . Ans. £1334.

22. A baker uses 4 qrs. 5 bush. 3 pecks of wheat in a week. How much does he require for a year? Ans. 245 qrs. 3 bush. 23. A field was divided into 65 lots, each lot containing 1 rood 27 per. 15 yds. What was the size of the field?

Ans. 109 roods 27 per. 7 yds. 24. The rent of my house for a week is £2, 5s. 73d., what is the rent of it for a year at the same rate? Ans. £118, 13s. 7d.

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25. There is an institution which contains 180 boys, and the yearly maintenance, clothing, and education of each comes to £18, 15s. 63d.; what sum of money is required to defray the expenses of the institution for a year? Ans. £3380, 1s. 3d. 26. A farmer has a field containing 15 acres, which is sown with wheat; how much money will he receive for the crop, if each acre produces 9 qrs., and the wheat is sold at £2, 16s. 54d. per quarter? Ans. £380, 19s. Od. 27. What is the cost of 213 sacks of oatmeal, at £1, 19s. 11d. per sack?

Ans. £425, 6s. 84d.

COMPOUND DIVISION.

COMPOUND DIVISION is the method of dividing a compound by a simple number.

RULES.

I. WHEN THE DIVISOR DOES NOT EXCEED 12.

RULE.-Divide the highest denomination of the dividend as in Simple Division, placing the quotient below the figures divided. If there is any remainder, reduce it to the next lower denomination, add to it any of that denomination in the given quantity, and divide the amount as before: if there be again a remainder, reduce it to the next lower denomination, &c.; and so on, proceeding in this way till all the denominations have been divided. The various quotients will be of the same denomination as the dividends from which they arise.

Example.-Divide £87, 14s. 93d. by 7.

£ s. d. 7)87 14 93 £12 10 8

The 87 pounds are divided by 7; the answer is £12, and £3 over: the £3, reduced to shillings, make 60s., and adding the 14s. in the dividend, amount to 74s., which, being divided by 7, give 10s., and 4s. over: the 4 shillings are 48 pence, to which adding the 9d. in the dividend, the sum is 57d., and these divided by 7, give 8d., and 1 penny over: a penny is 4 farthings; add to these the 3 in the dividend, making 7, which, divided by 7, give 1; that is, d.

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II. WHEN THE DIVISOR EXCEEDS 12.

RULE.-Divide as in Rule I., only employ long instead of short

division,

Example.-Divide £484, 19s. 7 d. by 73.

£ S. d. £ s. d.

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The pounds are first divided by 73; the answer is £6, and £46 over: the £46 are reduced to shillings, by multiplying by 20, and the 19s. in the dividend being added, make together 939 shillings, which, divided by 73, give 12s., and 63s. over: the 63 shillings are reduced to pence, and the 7d. being added, make 763d., which, divided by 73, give 10d., and 33 pence over : the 33d. being reduced to farthings, make, with the addition of the 3 farthings in the sum, 135, and these, divided by 73, give d., and 62 over. The whole answer is thus £6, 12s. 104d..

62

Ans. £2 14 1021 4 4 82

Exercises.

6 by 17,

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4383 yds. 3 qrs.

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40

59

61 6 42 34 467 14 18

59

2493

36

85

8 14 14842 14 15 24373 45 8 7125

88

137

77 2 12 21 120 11 1161

72 17 21 344

376 314

4 52 537

48

643

367 tons 15 cwts.3 qrs. by 87, Ans. 4 tons 4 cwts. 237 qrs.

15376 ac. 2 ro. 15 per.

3769 qrs. 7 bush. 3 pks.

7610 gals. 3 qts. 1 pt.

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53 ac. 3 ro. 321

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