Multiply 3 5 17 12 10 10 Multiply 5 7

(10.)

lb. 3

35

3D gr.

3 2

9

11

wk. da. hr. min. sec.

253. Division of Compound Numbers.

In the division of compound numbers we must observe how many

units one unit of the denomination

divided makes of the next lower denomination.

In this respect alone division in compound numbers differs from division in simple numbers.

(1.)

Divide 7 cwt., 1 qr., 23 lbs., 7 oz. by 4.

the 1 qr., the new dividend is 13 qrs.

One-fourth of 13 qrs. is 3 qrs., with a remainder of 1 qr. Reducng the 1 qr. to pounds and adding the 23 pounds, the new dividend is 48 pounds.

One-fourth of 48 lbs. is 12 lbs.

One-fourth of 7 oz. is 1 oz., with a remainder of 3 oz. Reducing the 3 oz. to drams the new dividend is 48 drs.

One-fourth of 48 drs. is 12 drs.

Hence, one-fourth of 7 cwt., 1 qr., 23 lbs., 7 oz., is 1 cwt., 3 qrs., 12 lbs., 1 oz. 12 drs.

In a similar manner perform the operations indicated in the following examples:

NOTE. -a. The pupils should prove each example in subtraction, by making it an example in addition of compound numbers.

b. Each example in multiplication should be verified by division, and each example in division should be verified by multiplication. c. Each step in the process should be fully and clearly explained by the pupils as they proceed with the operation.

d. To understand an explanation given in the book, or by the teacher, and to be able to give the explanation, unaided by the teacher, are quite different things. No pupil should be satisfied to simply understand what is explained to him; he ought to be able to give a good explanation himself, of every example or problem in a lesson, before leaving it.

e. Having acquired facility in performing the merely mechanical processes, and having mastered the logic of the process, before leaving the subject, the pupil should write out carefully a rule for performing the process.

REDUCTION OF DENOMINATE FRACTIONS.

254. A denominate fraction is one which expresses one or several of the equal parts of a denominate number.

255. A denominate fraction may be changed from a. One of a higher to one of a lower denomination. b. One of a lower to one of a higher denomination. c. A fraction to integers of lower denominations. d. Integers of a lower to a fraction of a higher denomination..

256. To reduce a denominate fraction from a higher to one of a lower denomination.

1. Reduce of an hour to an equivalent fraction of a lower denomination.

Suggestion.-What part of 1 minute is of 60 minutes?

What part of 1 second is 45 of 60 seconds?

2. Reduce

Then,

Then,

of an hour is what part of a minute? of an hour is what part of a second?

of a bushel to the fraction of a peck.

3. Reduce of a peck to the fraction of a pint.

257. To reduce a denominate fraction from a lower to one of a higher denomination.

1. Reduce of a pint to the fraction of a peck.

Suggestion.

2. Reduce

of a pint is what part of a quart, or 2 pints? of a quart is what part of a peck, or 8 quarts? Then, of a pint is what part of a peck?

of a pint to a fraction of a gallon.

3. Reduce of an inch to a fraction of a yard.

258. To reduce a denominate fraction to integers of a lower denomination.

1. Reduce of a sq. yd. to integers.

Suggestion. of a sq. yd. is of 9 sq. ft., or 6 sq. ft. of a sq. ft. is of 144 sq. in.

1. Reduce

Then, of a sq. yd. equals what?

of a mile to integers.

2. Reduce of a furlong to integers.

3. Reduce of an acre tò integers.

259. To reduce a denominate number to an equivalent fraction of a higher denomination.

1. Change 2 feet 3 inches to the decimal of a yard.

Suggestion.

3 inches is what decimal of a foot?

2.25 ft. is what part of a yard?
Why divide by 3?

2. Change 2 pints to the fraction of a peck.
3. Change 3 pints to the fraction of a bushel.
4. Change 8 sq. rds. to the fraction of an acre.
5. Reduce of a foot to rods.

6. One-eighth of an inch is what part of a rod? 7. One-fifth of a quarter is what part of a ton? 8. One-third of a grain Troy is what part of an ounce?

MISCELLANEOUS EXAMPLES.

1. Reduce of a mile to the fraction of an inch.
of a mile to integers of a lower de-

2. Reduce nomination.

3. Reduce 4. Reduce of a £ to the fraction of a farthing. 5. of a £ to integers of a lower denomination. 6. Reduce of a farthing to the decimal of a £. 7. What decimal of a yard is § of a foot? 8. What decimal of a day is g of a minute? 9. What fraction of a minute is of a day? 10. Reduce

of a pound to the fraction of a ton.

nomination.

of a cwt. to integers of a lower de

11. Reduce of a shilling to lower denominations. 12. Reduce .1357 of a yard to integers.

13. Reduce of a £ to the fraction of a farthing. 14. Reduce .4763 of £ to integers.