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8. 8f of 4 ac. 3 po. - io of 1 sq. mile +1f of 3 r. 20 sq. yds.

9. (5% of zo = 11%) of 35° 36' 25"; (2751of 13) of 30°. 10. of 1 lb. Troy + 8 of 1 lb. Troy - to of 1 lb. Avoirdupois ( = 7000 grains). u -54 of 3 guineas

of £1.3s. 10d.: 8 of 1 ton + of 3 qrs. - I' of 7 cwt. 12. 27's of 15 h. 10' 13?" - al of 1 day, 12 h. 11' 12?".

To Reduce a given Quantity to the Fraction of any

other given Quantity of the same kind. 29. RULE.—Reduce both the given quantities to the same denomination, and the fraction required will have the number of units in the first quantity as numerator, and that of the second quantity as denominator. Ex. 1.-Reduce 3s. 8d. to the fraction of £1.

3s. 8d. = 44d,

and £1 = 240d. Hence, the fraction required = 4 = 37. Or, better, thus :

3s. 8d. = 11 fourpences,

and £1 = 60 fourpences. .: Fraction required = it. NOTE. It is always best to keep the denominations to which the given quantities are reduced as high as possible.

Ex. 2.-- Reduce 4 of a moidore to the fraction of 24 guineas. + of a moidore = (4 27)s., and 21 guineas = (24 21)s. Hence, the fraction required = *

2421* *x 21 5x31x;

= ****= 1 Ex. 3.—Reduce 3 cwt. 24 qrs. to the fraction of 4 cwt. 2 qrs. 4 lbs.

3 cwt. 21 qrs. = 14% qrs., and 4 cwt. 2 qrs. 4 lbs. = 4 cwt. 24 qrs. = 184 qrs.

... Fraction required = 1

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1 X9 X 2 5 X7 X7

18

2 4 5

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127

1 2 7

9 X 127

Ex. IX. Reduce

1. ls. 8d. to the fraction of £1; 74d. to the fraction of 10s.

2. 2s. 4d. to the fraction of 10s. 8d.; ls. 7}d. to the fraction of 3s. 4}d.

3. 3 qrs. 15 lbs. to the fraction of 1 ton; 2 stones 10 oz. to the fraction of 3 cwt.

4. 3 lbs. avoirdupois to troy weight; 10 lbs. 3 oz. 4 dwt. troy to avoirdupois.

5. 3 quires, 10 sheets to the fraction of 2 reams, 3 quires ; 3 ft. 8} in. to the fraction of 3 yards.

6. 30° 3' 12" to the fraction of a right angle ( = 90°); 57° 16' 21141" to the fraction of two right angles. What fraction is7. fac. of 3} ac.; 2 days of 17 weeks?

•125 + 1.875

• •0140625 - acres of 194 poles: 3:16 * 1.4.

poles ; 2.375 .j yds. of 34 m?

9. (rood + poles + 14 x 14 yd.) of 3 acres ? 10. o sal. of a pipes ?

11. What fraction of his original income has a person left after paying a tax of 4d. in the £?

12. A garden roller is 2 ft. 6 in. wide, and it is rolled at the rate of 1 mile in 20 minutes : find in what fraction of a day a man will roll of an acre.

To Find the Value of a Decimal of a Concrete Quantity. Ex. 1.–Find the value of .325 of £3, 10s. £3. 10s. = 70s.; proceeding then according to rule, we have :

30. RULE.—Multiply the given decimal by the number of units in the concrete quantity when expressed in terms of one denomination, and the integral part of the result will be the number of units of this denomination. Then multiply the decimal part of this denomination by the number of units connecting it with the next lower and the integral part will be units of this latter denomination, and so on,

•325

70 22:750s.

12

9.00d. Ans.: 228. 9d. or £1. 28. 9d. Ex. 2.-Find the value of •546875 of 3 tons.

•546875

1:640625 tons.

20

12.812500 cwt.

3.2500 qrs.

28 200 50

7.00 lbs. Ans.: 1 ton, 12 cwt. 3 qrs. 7 lbs. Ex. 3. Find the value of 6.66875 acres.

6.66875 acres.

2.675,00 roods.

40

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27.000 poles. Ans. : 6 acres, 2 roods, 27 poles. Ex. 4. Find the value of -316 of £1. First Method.

Second Method. 316 = 316_- 31.= 28.5

900 = 900 •3166667 nearly.

20 6.3333340s.

Then by rule for reduction 12

of fractions, 4.000008d. Ans.: 6s. 4d. £18 = 6s. 4d. Ans.

The latter method is preferable when perfect accuracy is required.

15* 19
15 X 60

Ex. X. Find the value of — 1. £.375; £•98125 ; £•815625. 2. .416 of £3; -428571 of 6s. 5d. ; 8.571428 of 3s. 0 d. 3. •625 of 1 ton; •046875 of 3 tons; 4.39 of 1 cwt. 53 lbs. 4. 1.6671875 acres; •3475 rood; •076923 of 5 acres, 6 poles. 5. •2083 of 1 ream; ·4583 quire; -383 of 3 reams, 12 sheets. 6. •3078125 pipe; .490625 tun; •37125 bushel.

7. Express in grains .142857 of 4 lbs. avoirdupois, and express the result in troy weight.

8. Express 10 oz. 3 dwt. 14 grs. as the decimal of 1 lb. avoirdupois.

9. What is the sum of 6 of 1 guinea, .083 of 1 crown, and •037 of £1. Os. 3d. 10. Find the value of

•20416 * 7.5 .2014. com
(4 ; --21875°°) cwt. + (-95 ton – 769230 qrs.) x 26.
11. What is the value of

1 cwt. 35 lbs. ?
i
1 + -

(3 +

+

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71 + 16 12. Simplify (

11 - .16

1 - .16)
1 + .16)

of 1 oz. 15 dwts.

.

To Reduce from one Denomination to the Decimal of

another Denomination of the same kind.

31. RULE.—Bring the given quantity to the fraction of the proposed denomination, and reduce this fraction to a decimal,

5 X 13

11.

Ex. 1.-— Reduce 3s. 3d, to the decimal of 8s. 11d.

38. 3d. = 26 three-halfpence,

88. 1}d. = 65 three-halfpence, and the fraction on = { 13 = = '4. Hence •4 is the decimal required. Ex, 2.-Reduce 3 qrs. 21 lbs. to the decimal of 2 cwt. 3 qrs.

3 qrs. 21 lbs. = 105 lbs.

2 cwt. 3 qrs. = 308 lbs.
and the fraction 3!1 = 15 x = 1 = 3:17,5 = .3409.

Hence •3409 is the decimal required.
Ex. 3.-Reduce 18s. 87d. to the decimal of £1.

The rule may be applied most concisely as follows :-
4 / 1

8.25 20 | 18.6875

•934375 .. •934375 is the decimal required. The farthing is first reduced to the decimal of a penny, and the 8d. prefixed; then 8.25d. are reduced to the decimal of a shilling, and the 18s. prefixed; lastly, 18.6875s. are reduced to the decimal of £1.

Ex. 4.-Reduce 3 qrs. 21 lbs. to the decimal of 1 ton.

28 S 7 | 21

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3.
3.75
.9375
046875

Hence •046875 is the decimal required.

Ex. XI. Reduce—

1. 12s. 6d., 10s. 77d., 11s. 1{d., 18s. 6şd., each to the decimal of £1.

2. 13s. 02d., 10s. 84d., Is. 6d., each to the decimal of 15s. 54d.

3. 78. 84d. to the decimal of a guinea ; and 3s, 24d. to the decimal of a moiềore,

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