Oral Exercise

221. Illustrative Example. Change 30 mo. to years and months.

SOLUTION. 12 mo. = 1 yr.; 30 mo. equal 2 times 12 mo., and 6 mo. remain. Hence, 30 mo. = 2 yr. 6 mo. Ans. 2 yr. 6 mo.

222. A number, as 2 yr. 6 mo., consisting of two or more denominate numbers of different names, is called a compound denominate number.

The process of changing the form or denomination of a number without changing its value is called reduction.

Change to compound denominate numbers:

223. Illustrative Example. Reduce 4 yd. 2 ft. 6 in. to inches.

WORK

4 yd. 2 ft. 6 in.

3

14 ft.

12

174 in.

times 3 ft. = 12 ft. Adding the 2 ft., we have 14
ft. Since 1 ft. 12 in., 14 ft.
= 14 times 12 in. =
168 in. Adding the 6 in., we have 174 in.

Ans. 174 in.

In the above example the 4 yd. 2 ft. are changed to numbers of a lower denomination. The process is called reduction descending.

To change a compound number to a compound number of a lower denomination, we multiply the number of the highest denomination by the number which is required of the next lower denomination to make one of the higher, and to the product add the given number of the lower denomination. We multiply this sum in like manner, and so continue till the required denomination is reached.

#

23. 1 lb. 7 oz. oil of spearmint, Apoth. weight, at 25¢ an ounce.

24. 8 cd. 4 cd. ft. of wood at 663¢ a cord foot.

25. 27 days' work, 10 hours each, at 33 an hour.

26. T. of ice at a pound.

27. 5 bu. 3 pk. 7 qt. cranberries at 13 a quart.

Written Exercise

225. Illustrative Example. lb. of oil of cloves in 60 prescriptions gives how many grains to each?

WORK

1 × 12 × 8 × 3 × 20 - 12

=

EXPLANATION. lb. is changed to Apoth. grains which are divided by 60. Ans. 12 gr.

8 × 60
20

1. A balloon going 8 mi. an hour goes how many feet a minute?

226. Illustrative Example. Change 424 ft. to yards, etc.

WORK

3)424 —1 ft.

52)141, number of yd. 2

11)282-yd. = 31 yd. 25, number of rd.

EXPLANATION. There are 3 ft. in 1 yd.; 424 ft. divided by 3 ft. gives 141 with 1 ft. remaining. There are 5 yards in 1 rd.; 141 divided by 51 gives 25 with 31 yd. remaining. yd. with 1 ft. remaining = 2 ft. 6 in. Ans. 25 rd. 3 yd. 2 ft. 6 in.

The process of changing a number to a number of higher denominations is called reduction ascending.

To change a given number to a number of higher denomination, we divide the given number by the number it takes of its denomination to make one of the next higher. We divide the quotient in the same way, and so proceed till the required denomination is reached. The last quotient with the remainders, if there are any, will be the result required.

Reduce to higher denominations:

Written Exercise

227. Illustrative Example. 10 gal. 2 qt. is what part of

228. Illustrative Example. Change .575 mi. to rods. WORK AND EXPLANATION: .575 mi. = .575 of 320 rd. = : 184 rd. Change to compound numbers of lower denominations:

229. Illustrative

mal of a year.

WORK

30)7.00, no. of da.

Written Exercise

Example. Change 5 mo. 7 da. to the deci

12)5.2333 no. of mo. .4361.

no. of yr.

EXPLANATION. 7 da. ÷ 30 (da.) = .2333, number of months; .2333 mo. with 5 mo. = 5.2333 mo. 5.2333 mo. ÷ 12 (mo.) = .4361, number of years. Ans. .4361+ yr.

Reduce to decimals of higher denominations:

Written Exercise

230. Illustrative Examples. (1) Add 2 mi. 172 rd. 6 ft.; 1 mi. 310 rd. 14 ft.; and 95 rd. 11 ft. (2) From 7 rd. 3 yd. 1 ft., take 1 rd. 4 yd. 2 ft.

EXPLANATION. We write the numbers, with units of the same denomination in the same column, and begin to add or subtract with the numbers of the lowest denomination.

(1) 11+14 +6 (ft.) = 31 (ft.) = 1 rd. 141 ft. We write the 14 ft. and add the 1 rd. with the rods. The sum is 578 rd. = 1 mi. 258 rd. We write the 258 rd., and add the 1 mi. Iwith the miles.

=

Ans. 4 mi. 258 rd. 14 ft. 6 in. (2) To subtract, as there is but 1 ft. in the minuend, we think of 1 yd. as changed to 3 ft., making, with the 1 ft., 4 ft. 4 ft. 2 ft. 2 ft. We write the 2 ft. We think next of 1 of the 7 rd. as changed to 5 yd., making, with the remaining 2 yd., 7 yd. 7 yd. 4 yd. = 3 yd. We write 31 yd. The remaining 6 rd. —

1 rd. = 5 rd.

which added to 2 ft. equals 1 yd. 6 in.

Ans. 5 rd. 4 yd. 0 ft. 6 in.

1. Find the sum of 3 mi. 1 rd. 1 yd. 1 ft.; 5 mi. 1 rd. 2 yd.

1 ft.; 14 mi. 4 rd. 6 yd. 2 ft. ; 4 mi. 5 rd. 2 yd. 2 ft.

2. Add 3 bu. 3 pk. 7 qt. 1 pt. ; 99 bu. 6 qt.; 60 bu. 5 qt. 1 pt.; 2 pk. 5 qt. 1 pt.

3. Find the sum of 7 T. 15 cwt. 50 lb. 4 oz.; 5 T. 8 cwt. 45 lb. 12 oz.; 3 T. 4 cwt. 20 lb. 4 oz. ; 9 T. 10 cwt. 10 lb. 10 oz.; and 18 T. 19 cwt. 90 lb. 15 oz.