EXERCISES. 1. Divide 9 x 5 x 27 x 8 by 3 × 25 × 8 × 4. V. When the dividend is a large number, or in calculations in which the same divisor must be frequently used, we may make a table of the product of the divisor into each of the nine digits, on a separate piece of paper; by this means, the process will be very easy, as the several quotient figures and products are obtained by inspection. [N. B. Before the learner proceeds farther, he should commit to memory the principal Tables of Money, Weights, and Measures, annexed to this Tract.] APPLICATION OF ADDITION, SUBTRACTION, MUL TIPLICATION, QUANTITIES. AND DIVISION, TO COMPOUND REDUCTION. REDUCTION is the application of Multiplication and Division, in bringing Money, Weights, and Measures, from one denomination to another, CASE I. To find how many of a lower denomination are contained in a given number of a higher denomination. RULE. Multiply the number of the highest denomination by as many of the next lower denomination as make 1 of the higher, adding mentally to the product the given number, if any, of that lower denomination. Then multiply the sum by as many of the next lower denomination as make 1 of this, adding mentally to the product the given number, if any, of the third denomination; and so on, till you come to the denomination required. The number last found will be the answer. 22 EXAMPLES. 1st. Reduce £48:14: 63 to 2d. Reduce 32 cwt. 1 qr. 15 lb. to lbs. farthings. £48:14:62 Cwt. 32: 1:15 20 974 shillings. 12 32 3243=1 qr. 15lb. 1037 4. 3627 lbs. Remark. Cwts. qrs. and lbs. are most easily reduced to lbs. by multiplying the cwts. by 112, adding to the product the lbs. of the odd weight. The mul tiplication by 112 is easily effected by merely placing the cwts. as in Method II. EXERCISES. 1. How many farthings in £145? 19. How many inches in 5 miles 1 fur. 17 yds. ? 30. How many seconds in 365 days 5 h. 48 min. 48 sec. ? 31. How many seconds of a degree in 5a 20° 45′ 15′′ ? CASE II. To find how many of a higher denomination are contained in a given number of a lower denomination. RULE. Divide the given number by as many of its denomination as make 1 of the next higher denomination; then divide the quotient by as many of its denomination as make 1 of the next higher; and so on, till you obtain the denomination required. The remainders, if any, are of the same denomination with the dividends from which they arise. EXAMPLES. 1. Reduce 7537 farthings to £'s. 2d. Reduce 1767 7bs. to crets. 1. How many pounds in 8175 shillings? 2. How many pounds in 9154 pence? 3. How many pounds in 31251 farthings? 4. How many pounds in 51273 halfpence? 5. How many pounds in 94187 sixpences? 6. How many pounds in 96537 fourpences 7. How many pounds in 59861 threepences? 8. How many pounds in 8395 twopences ? 9. How many pounds in 674 half crowns? 10. How many guineas in 17456 farthings? 11. How many pounds Sterling in £500 Scotch? 12. How many pounds Sterling in 1975 merks Scotch? 13. How many lbs. of silver in 76498 dwt. ? 14. How many lbs. of gold in 815731 grains? 15. How many cwt. in 325419 drams? 16. How many tons in 756975 lbs. ? 17. How many cwt. in 8653 lbs. ? 18. How many acres in 75767 square yards? 19. How many acres in 5834713 square ells? 20. How many roods of mason work in 74191 square feet? 27. How many chalders in 4362596 lippies ? 28. How many miles in a mean degree of latitude, or 4374556 inches? 29. How many days in 3:556928 seconds? 30. How many years of 365 days each in 78293767 seconds ? 31. How many degrees in 206264 seconds of a degree? CASE III. To find how many of one denomination are contained in a given number of another denomination, when the higher denomination does not contain an exact number of the lower. RULE. Reduce the given number, by multiplication, to a denomination which is contained exactly in that required; then reduce the product, by division, to the denomination required. Remark. When the multiplier is just 1 more or 1 less than the divisor, instead of multiplying and then dividing, we may divide by the divisor, and then subtract or add the quotient, according as the multiplier is less or greater than the divisor. Thus guineas may be reduced to pounds by adding go, and yards to English ells by deducting ; and so on. EXERCISES. 1. How many guineas in £473 ? 2. How many pounds in 756 guineas? 3. How many half guineas in 5897 half crowns? 4. How many pounds in 3258 half guineas? 5. How many pounds in 1649 dollars, each 4/6? 6. How many dollars, each 4/6, in 6968 guineas? 7. How many guineas in 8655 crowns ? 8. How many crowns in 4176 guineas? 9 How many lbs. troy in 100 lbs. avoirdupois ? 10. How many lbs. avoirdupois in 100 lb. troy? 11. How many lbs. of 16 oz. in 80 lb. of 171 oz.? 12. How many lbs. of 17 oz. in 64 lb. of 16 oz. ? 13. How many lbs. of 16 oz. in 96 lb. of 22 oz. ? 14. How many yards in 568 English ells? 15. How many English ells in 697 yards? 16. How many yards in 54 arsheens, each 28 inche 17. How many ale gallons in 877 wine gallons ? 18. How many wine gallons in 945 ale gallons ? 19. How many London chaldrons of coals in 100 Newcastle chal drons ? 20. How many barley bolls in 257 wheat bolls? 21. How many wheat bolls in 398 barley bolls? 22. How many pecks of 8 lb. each 174 oz. in a sack of flour? 23. How many sacks of flour in 540 barrels ? 24. How many barrels of flour in 350 sacks? ¶25. What is the value of 673 yards of Osnaburgs at 7d. ? 28. What is the value of 235 yards of broad cloth at 24/6 ? 32. When flax sells at 45 guilders (each 2/14) per cwt. what is the price per lb. ? 33. A labourer receives 2/2 a-day for every work-day from 4th March to 11th November, and 1/8 a-day during the rest of the year; how much do his wages amount to in a year? 34. How many miles in the circumference of the earth, the length of the mean degree of latitude being 4,374,556 inches? COMPOUND ADDITION. RULE. Place numbers of the same name under each other; find the sum of the right hand column, which divide by as many of that name as make one of the next higher; write the remainder, if any, under the column added, and carry the quotient to the next column : proceed in the same manner with the remaining denominations, till you come to the last, which add as abstract numbers. REMARKS. In adding the shillings, first run up the column of units, and put down the right hand figure of the sum, carrying the rest to the tens; then add up the tens, and divide their sum by 2, if I remain, put it down, and carry the quotient to the pounds." In D |