RULE. I. Divide the given number by the number of the scale that connects it with the next higher denomination; the remainder will be units of the same denomination as the dividend. II. Divide the quotient by the number that connects it with the next higher denomination; the remainder will be units of the denomination of the new dividend. III. Continue the operation till the required denomination is reached. 2. Reduce 11,911 grains to pounds Troy. Ans. 2 lbs. 16 dwts. 7 grs. 8. Reduce 876 dwts. to pounds Troy. 4. Reduce 1,511 grs. to ounces, apothecaries' weight. 5. Reduce 1,594 oz. avoirdupois, to quarters. Reduce 348 hrs. to wks. ? In 1794 rds. 6. Reduce 8,842 lbs. to tons. Reduce 4,412 lbs. to tons. 7. Reduce 7,620 minutes to days. 8. Reduce 687 hrs. to weeks. 9. How many yards in 786 in. ? 10. How many miles in 897 rds. 11. Reduce 2,875 in. to yards. 12. Reduce 510 pts. to bushels. 13. Reduce 352 qts. to bushels. 14. How many gallons in 840 pts.? 15. Reduce 8,532 gi. to gallons. Reduce 2,133 gi. to gal. 16. How many degrees in 8,844"? In 4,422'. 17. How many cubic yards in 162 cubic feet? 18. In 200 cord feet how many cords of wood? 19. Reduce 360 square chains to acres. ADDITION OF COMPOUND NUMBERS. 219. Addition of Compound Numbers is the cperation of finding the sum of two or more compound numbers. The principles are the same as in simple numbers. EXERCISES FOR ORAL WORK. 1. What is the sum of 9 inches and 11 inches? Of 22 in. and 13 in. ? Of 8 ft. and 17 ft.? Of 9d. and 16d. 2. What is the sum of 2 ft. 4 in., and 6 ft. 3 in.? 8. What is the sum of 2 yds. 1 ft., and 3 yds. 4 ft.? 4. What is the sum of 2 gals. 3 qts., and 3 gals. 3 qts.? 5. What is the sum of 3s. 8d., and 5s. 9d.? 6. What is the sum of 3 yds. 3 ft., 5 yds. 1 ft., and 7 yds.? 7. What is the sum of 2 wks. 3 das., and 3 wks. 4 das.? 8. What is the sum of 8 sq. ft. 16 sq. in., and 5 sq. ft.? 4 sq. in.? 9. Find the sum of 3 bush. 1 pk., and 4 bush. 2 pks. 10. What is the sum of 2° 3' 4", and 3° 1' 2", and 5° 2' 3"? OPERATION OF ADDITION OF COMPOUND NUMBERS. Let it be required to find the sum of £7 48.3d., £11 98. 8d. and £14 12s. 9d. ILLUSTRATION. £ S. d. 7 4 3 11 9 8 14 12 9 £33 6s. 8d. EXPLANATION.-We write the numbers so that units of the same denomination shall stand in the same column. We add the right hand column, and find its sum is 20d. = 18. 8d.; we write 8d. under the column in the place of the amount, and add 18. with the column of shillings, which amounts to 268. = £1 68.; we write 6s. under the column, and add £1 with the column of £s, which amounts to £33. The required sum is therefore £33 68. 8d. Hence, the following RULE. I. Write the numbers so that units of the same denomination shall stand in the same column. II. Add the units of the lowest denomination, and divide their sum by the number of the scale that connects this denomination with the next higher one; set down the remainder, and carry the quotient to the next column. III. Add the units of the second column thus increased, and proceed as before, continuing the operation till all the columns have been added. What is addition of compound numbers? What compound numbers can be added? Give the rule for addition of compound numbers. SUBTRACTION OF COMPOUND NUMBERS. 220. Subtraction of Compound Numbers is the operation of finding the difference between two compound numbers. The principles are the same as in subtraction of simple numbers. EXERCISES FOR ORAL WORK. 1. From 11 in. subtract 6 in. From 12 ft. subtract 9 ft. 2. What is the difference of 7 pks. and 4 pks.? 3. What is the difference between £3 4s., and £1 2s.? 4. What is the difference between 2s. 7d., and 1s. 4d.? 5. 8 yds. 2 ft. 6 yds. 1 ft. =? OPERATIONS OF SUBTRACTION OF COMPOUND NUMBERS. Let it be required to find the difference between £9 4s. 3d. and £2 18s. 6d. ILLUSTRATION. £ S. d. 9 4 3 £6 2 18 6 58. 9d. EXPLANATION.-We write the subtrahend under the minuend, so that units of the same denomination shall stand in the same column. We begin at the right. Since 6d. is greater than 3d. we add 12d. to 3d. making 15d., from which we subtract 6d., and write the remainder 9d. beneath. To compensate for 12d. added to the minuend, we add 18. equal to 12d. to the next number of the subtrahend, obtaining 198., which being greater than 4s., we add 20s. to 48., obtaining 248., from which we subtract 198., and write the remainder 5s. beneath. To compensate for 208. added to the minuend, we add £1 equal to 208. to the subtrahend, obtaining £3, which we subtract from £9, and write the remainder £6 beneath; hence, the remainder is £6 58. 9d. In like manner we treat all similar cases; hence, the following RULE. I. Write the subtrahend under the minuend so that units of the same denomination shall stand in the same column. II. Subtract each number in the subtrahend from the one above it in the minuend, and write the remainder in the line below. III. If any number in the subtrahend is greater than the one above it in the minuend, add to the latter as many units as make one of the next higher denomination, perform the subtraction, and add 1 to the next number in the subtrahend. |