10. What is the value of .085 of a £? 11. What is the value of .86 of a cwt.? 12. What is the value of of .86 cwt.? 13. What is the value of .82 of a day? 14. What is the value of 1.089 miles?

15. What is the value of .09375 of a pound Avoirdupois ? 16. What is the value of .28493 of a year of 365 days? 17. What is the value of £1.046 ?

18. What is the value of £1.88 ?

CASE V.

212. To reduce a compound number to a common fraction of a given denomination.

1. Reduce 9 oz. 12 pwt. to the fraction of a pound Troy.

Reduce the compound number to the lowest denomination named in it, and divide the result by the number of units of that denomination which make 1 of the given denomination.

Examples.

1. What part of a tun of wine is 3 hhd. 31 gal. 2 qt. ? 2. Reduce 3 gal. 2 qt. to the fraction of a hogshead. 3. Reduce 2 fur. 36 rd. 2 yd. to the fraction of a mile. 4. What part of a £ is 5 s. 7} d.?

5. What part of a pound Troy is 10 oz. 13 pwt. 8 gr.? 6. 11 cwt. 0 qr. 12 lb. 7 oz. 13 dr., is what part of a ton?

212. What is Case V.? Give the rule.

7. Reduce 2 R. 32 P. 8 yd. to the fraction of an acre. 8. Reduce 12s. 9d. 1 far. to the fraction of a guinea. 9. What part of a cwt. is 9 tenths of a pound? 10. What part of an Ell English is 3 qr. 3 na. 14 in. ? 11. Reduce 3° 15′ 183" to the fraction of a sign. 12. Reduce 37 inches to the fraction of a hand.

13. Reduce 5 yd. 2 ft. 9 inches to the fraction of a mile.

CASE VI.

213. To reduce a compound number to a decimal of a given denomination.

1. Reduce £1 4s. 9 d. to the decimal of a £.

ANALYSIS.-Reduce the d. to a decimal, and annex the result to the 9d., and we have 9.75d. Dividing 9.75d. by 12 (since 12 pence =1s.), and annexing the quotient to the 4s., we have 4.8125s. Then dividing by 20 (since 20s. = £1), and annexing the quotient to the £1, we have £1.240625:

OPERATION.

d.

=

.75 d. 9åd. = .9.75 d.

12) 9.75 d.

20) 4.8125s.

Ans. £1 4s. 9 d. 1.240625 £.

Rule.

=

I. If the lowest denomination contains a fraction, reduce it to a decimal, and annex the integral part:

II. Then divide by the scale, and annex the quotient as a decimal, to the next higher denomination, and so on until the decimal is reduced to the required denomination.

Examples.

1. Reduce 4 wk. 6 da. 5 hr. 30 m. 45 s. to the decimal of a week.

2. Reduce 2 lb. 5 oz. 12 pwt. 16 gr. to the decimal of a pound.

3. Reduce 3 feet 9 inches to the decimal of yards.

213. What is Case VI.? What is the rule?

4. Reduce 1 lb. 12 dr., avoirdupois, to the decimal of pounds.

5. Reduce 5 leagues 2 furlongs to the decimal of leagues. 6. Reduce 4 bu. 3 pk. 1 pt. to the decimal of bushels. 7. Reduce 5 oz. 13 pwt. 12 gr. to the decimal of a pound. 8. Reduce 15 cwt. 3 qr. 21⁄2 lb. to the decimal of a ton. 9. Reduce 5 A. 3 R. 21 sq. rd. to the decimal of acres. 10. Reduce 11 pounds to the decimal of a ton.

11. Reduce 3 da. 123 sec. to the decimal of a week. 12. Reduce 14 bu. 33 qt. to the decimal of a chaldron. 13. Reduce 7 m. 7 fur. 1 r. to the decimal of miles. 14. Reduce 15s. 6d. 3.375 far. to the decimal of a pound. 15. Reduce 4° 36′.8125 to the decimal of a sign.

ADDITION.

214. ADDITION OF COMPOUND NUMBERS is the operation of finding a number equal to two or more given numbers.

1. How many pounds, shillings, and pence are there in £4 8s. 9d., £27 14s. 11d., and £156 17s. 10d.?

ANALYSIS. Having written the numbers, add the column of pence; then 30 pence are equal to 2 shillings and 6 pence: write down the 6, carrying the 2 to the shillings. Find the sum of the shillings, which is 41; that is, 2 pounds and 1 shilling over. down 1s.; then, carrying the 2 to the column of pounds, we find their sum to be £189 1s. 6d.

Write

OPERATION.

£

8.

d.

4

8

9

27

14 11

156

17 10

£189

1s. 6d.

NOTE.-In simple numbers, the number of units of the scale, at any place, is 10. Hence, we carry 1 for every 10. In denominate numbers, the scales vary. The number of units, in passing from pence to shillings, is 12; hence, we carry one for every 12. In passing from shillings to pounds, it is 20; hence, we carry one for every 20. In passing from one denomination to another, we divide the sum of each column by the scale, and add the quotient to the next column: Hence,

Rule.

I. Write the numbers to be added, so that units of the same name shall stand in the same column:

II. Beginning with the lowest denomination, add as in simple numbers; divide the sum of each column by the scale, and add the quotient to the next column.

PROOF.-The same as in simple numbers.

214. What is Addition of Compound Numbers? down the numbers for addition? How do you add? rule for addition? How do you prove addition?

How do you set

What is the

1. Add 46 lb. 9 oz. 15 pwt. 16 gr., 87 lb. 10 oz. 6 pwt. 14 gr., 100 lb. 10 oz. 10 pwt. 10 gr., and 56 lb. 3 pwt. 6 gr. together.

6. What is the weight of forty-six pounds, eight ounces, thirteen pennyweights, fourteen grains; ninety-seven pounds, three ounces; and one hundred pounds, five ounces, ten pennyweights, and thirteen grains?

7. Add the following together: 29 T. 16 cwt. 1 qr. 14 lb. 12 oz. 9 dr., 18 cwt. 3 qr. 1 lb., 50 T. 3 qr. 4 oz., and 2 T. 1 qr. 14 dr.

8. What is the weight of 39 T. 10 cwt. 2 qr. 2 lb. 15 oz 12 dr., 17 cwt. 6 lb., 12 cwt. 3 qr., and 2 qr. 8 lb. 9 dr.?