3. of a guinea to the decimal of £1; and 3 pk. to the decimal of 2 qrs.

4. of a guinea to the decimal of £2; and of a year to the

decimal of a day.

150

5. of of 40 yds. to the decimal of of 2 miles; and of 31 sq. yds. to the decimal of 2 acres,

1 ro.

6. of 44 hrs. to the decimal of 3651 days; and 9 of 1 pecks to the decimal of 33 qrs.

7. 3 lbs., 6 oz. Troy to the decimal of 10 lbs. Avoird.; and oz. Avoird. to the decimal of oz. Troy.

(3) Express & of a crown + of a shilling as a decimal of 7s. (4) Express of half-a- crown+4 of a shilling as a decimal of £2. (5) Add together § of a day, & of an hour, and 4 of 6 hours; and express the result as the decimal of a week.

(6) Express the difference of of a guinea and 2 of 7s. 6d. as the decimal of a moidore.

(7) Express the value of '83 of 8s. + '05 of 2 guineas + 1·8 of 5s. as the decimal of half-a-guinea.

(8) Find the difference between 61 half-guineas and £3.525; and reduce the result to the decimal of a crown.

(9) Add 53 cwt. to 3·125 qrs.; and reduce the sum to the decimal of

a ton.

(10) Convert the following sums of money into the decimal coinage of pounds, florins, &c., and verify each result:

136. DEF. AN ALIQUOT PART of a number is such a part as, when taken a certain number of times, will exactly make up that number. Thus, 4 is an aliquot part of 12, 6 of 18, &c.

PRACTICE is a compendious mode of finding the value of any number of articles by means of ALIQUOT PARTS, when the value of an unit of any denomination is given.

Practice may be separated into two cases, SIMPLE and Compound.
I. Simple Practice.

In this case the given number is expressed in the same denomination

as the unit whose value is given: as, for instance, 26 lbs. at £2. 58.

or 330 articles at 5s. 6d. each.

per lb.;

The Rule for Simple Practice will be easily shewn by the following examples.

Ex. 1. Find the value of 1296 things at 16s. 10d. each.
The method of working such an example is the following:
Supposing the cost of the things to be £1. each;

71d.=1 of 1s. 3d.

81 0.0

==

cost at 1s. 3d. each.

40. 10. 0 cost at 74d. each.

£1093. 10.0=cost at 16s. 101d. each.

Note. The student must use his own judgment in selecting the most convenient'aliquot' parts; taking care that the sum of those taken make up the given price of the unit.

Ex. 2. Find the value of 3825 things at £2. 17s. 41d. each.

Ex. 3. Find the cost of 1657 cwt. at £2. 5s. 6d. per cwt.

The cost clearly=165 times £2. 5s. 6d. +§ of £2. 5s. 6d.

£377

6 cost at 6d. each.

6 cost of 165 cwt. at £2. 5s. 6d. per cwt.

=

19 93=cost of cwt. at £2. 5s. 6d. per cwt.

7.32=cost of 1653 cwt. at £2. 5s. 6d. per cwt.

Ex. 4. Find the value of 6413 things at 4s. 10d. each.

In this case the given number is not wholly expressed in the same denomination as the unit whose value is given; as for instance, 1 cwt., 2 qrs., 14 lbs, at £2. 2s. per cwt.

The Rule for Compound Practice will be easily shewn by the following examples.

Ex. 1. Find the value of 84 cwt., 3 qrs., 14 lbs. of sugar at £12. 11s. 8d. per cwt.

The method of working such an example is the following:

The value of 1 cwt. of sugar being £12. 11s. 8d.,

therefore, by adding the vertical columns,

the value of 84 cwt., 3 qrs., 14 lbs. = £1068. 0.

212

21= value of 84 cwt., 3 qrs., 14 lbs.

1

£1068.

Ex. 2. Find the value of 319 cwt., 3 qrs., 16 lbs. at £2. 12s. 6d. per cwt.

£. S.

d.

subtracting

837

7

0. 6.

6

=

= value of 320 cwt.

= value of 1 cwt.

6 = value of 319 cwt.

3 = value of 2 qrs.
11=value of 1 qr.

63 value of 14 lbs.

=

=

0 0.111 value of 2 lbs.

£839. 14. 4= value of 319 cwt., 3 qrs., 16 lbs.`

Ex. 3. Find the value of 37 yds., 2 ft., 7 in. of silk, at 5s. 34d. a yard.

Note. It will be found most convenient, in all examples of Practice, to work with fractions of a penny, and finally to find the value of the sum of these fractions in farthings, as in the above example.

Find the value of

Ex. LIII.

1. 645 things at 2s. 6d. each ; and 69 things at 10s. 6d. each.

2.

3.

454 things at 2s. 9d. each ; and 72 things at 1s. 7d. each.

52 things at 3s. 9d. each; and 1257 things at 62d. each.

4. 626 things at 8s. 8d. each ; and 286 things at 12s. 1d. each.
5. 80 things at 4s. 41d. each; and 37 things at 5s. 51d. each.
6. 138 things at £1. 14s. each; and 589 things at £1. 11s. 6d.

each.

7. 95 things at £1. 2s. 6d. each; and 107 things at £24. 6s. 2d.

each.

8. 457 things at £1. 8s. 6d. each ; and 88 things at 11⁄2d. each.

9. 111 things at £2. 5s. 10d. each; and 9251 things at 14s. 11d.

each.

10. 4681 things at 83d. each; and 1209 things at 13s. 1d. each.
11. 1450 things at £1. 7s. 8d. each; and 249 things at £2. 13s. 9d.

each.

12. 898 things at 18s. 74d. each; and 405 things at 19s. 81d.

each.

13. 744 things at £19. 19s. each; and 421 things at £4. 2s. 6d.

each.

14. 1593 things at 9s. 01d. each: and 6602 things at 7s. 1 d. each. 15. 7382 things at £3. 15s. 43d. each ; and 5614 things at £14. 14s. 51d. each.

16. 6573 things at £5. 18s. 101d. each; and 37271 things at £6. 13s. 02d. each.

17. 51143 things at £4. 17s. 91d. each; and 6293 things at £7. Os. 11 d. each.

18. 3027 things at £5. 12s. 21d. each; and 4945 things at £1. Os. lid. each.

19. 7331 things at £1. 9s. 4d. each; and 7514 things at £2. 178.

10d. each.

20. 1418 things at 7s. 91d. each; and 11783 things at 16s. 8d.

each.

21. 1762% things at £1. 18. 10d. each; and 55555 things at 6s. 101d.

each.