17. In 55799 grains, how many pounds? Ans. 9 lb. 8 oz. 1 dr. 2 sc. 19 gr. Long Measure. 21. The river Niagara, at the great cataract, falls nearly 163 feet down a perpendicular precipice; and the depth of the river at the foot of the falls is supposed to be at least 200 feet; which makes the whole height of the precipice about 363 feet. Reduce this number of feet to rods. Ans. 22 rods. 22. The highest mountain in Europe is Mont Blanc, in Switzerland; the summit of which is elevated about 15675 feet above the level of the sea. Reduce this number of feet to miles. Ans. 2 m. 7 fur. 30 rd. 23. The quantity of linen imported into the UnitedStates from Ireland, in the year 1806, was 2675619 yards. How many miles in length was the whole?. Ans. 1520 m. 1 fur. 36 rd. 1 yd. 24. Reduce 4735272960 barley-corns to miles. 4735272960÷190080-24912 miles, Ans. Cloth Measure. Ans. 4 yd. 3 qr. Ans. 75. Ans 39. 25. Reduce 19 quarters to yards. Square Measure. 28. Reduce 4779 sq. rods to acres. Ans. 29 A. 3 R, 19 sq. rd. 29. Reduce 7772 sq. inches to sq. yards. Ans. 5 sq. yd. 8 sq. ft. 140 sq. in. 30. Reduce 3048960 acres to sq. miles. Cubic Measure, 32. Reduce 687 cubic feet to cords. Ans. 5 C. 47 cub.ft. 33. Reduce 442368 cubic inches to cords. Ans 2. 34. Reduce 600 feet of round timber to tons. Ans. 15. Wine Measure. 35. Reduce 180 gills to gallons. Ans. 5 gal. 2qt. 1 pt. 36. Reduce 20160000 pints to pipes. 37. Reduce 504 pints to hogsheads. 38. Reduce 64 half gills to gallons. Dry Measure. Ans. 20000. Ans. 1. Ans. 1. 39. Reduce 2424 quarts to bushels. Ans. 75 bush. 3 pk. 40. Reduce 258 pints to bushels. Ans. 4 bush. and 1qt. 41. Reduce 360 bushels to chaldrons. Reduce 31556928 seconds to days. 2551443 seconds to days. 364 days to weeks. Ans. 10. Time. Ans. 365 da. 5h. 48m. 48 sec. 96 calendar months to years. Ans. 52. Ans. 8. Reduce 1831 years to centuries. 669138 days to Julian years. Ans. 18 cent. and 31 years. Circular Measure. Ans. 1832. 48. Reduce 47435" to degrees. Ans. 13° 10' .. 35". 49. Reduce 1020300" to signs. Ans. 9 S... 13° .. 25'. 50. Reduce 18048" to degrees. Ans. 5° and 48′′. QUESTIONS ON REDUCTION. 1. What is Reduction? 2. What is Reduction Descend' ing? 3. What is Reduction Ascending? 4. How is Reduction Descending performed when the given quantity consists of several denominations? 5. How is it performed when the given quantity consists of one denomination only? 6. How is Reduction Ascending performed? 7. How do you proceed when the divisor contains a fraction? 8. How are operations in Reduction proved? Note. It will be useful for Instructors to put various other questions to their pupils respecting the most usual denominations of money, weight and measure; viz. such as these: How many farthings make a penny? How many ounces in a pound, Avoirdupois? How are feet reduced to inches? How are square rods reduced to acres? &c. And learners ought not to leave Reduction until they are able to answer such questions correctly. COMPOUND ADDITION, Is the addition of numbers of different denominations, but of the same general nature. RULE. 1. Set down the given numbers in such a manner that *The reason of this rule is evident, from what has been said in Simple Addition and Reduction: For instance, the addition of Sterling money, as 1 in the pence is equal to 4 in the farthings; 1 in the shillings, to 12 in the pence; and 1 in the pounds to 20 in the shillings; therefore, carrying as directed, is nothing more than providing a method of placing the money arising from each column properly in the scale of denominations: and this reasoning will hold good in the addition of compound numbers of any denominations whatever. those of the same denomination may stand directly under one another; placing the lowest denomination of each quantity at the right hand, the next higher next, and so on; and then draw a line underneath. 2. Add together the numbers of the lowest denomination, as in Simple Addition, and divide the amount by a number which will (according to the Rule for Reduction Ascending) reduce it to the next higher denomination: Set down the remainder under the column* added, (or, if nothing remains, set down a cipher,) and carry the quotient to the column of the next denomination. Then add up the numbers of this denomination, together with the number (if any) carried from the first column, and reduce the amount to the next higher denomination; setting down the remainder under the proper column, and carrying the quotient to the next column, as before; and so proceed through all the denominations, setting down the whole amount of the last column. Then the amount of the last column, together with the several remainders (if any) of the lower denominations, will be the answer, or whole amount sought. PROOF. The method of proof is the same as in Simple Addition. EXAMPLES. Money. 1. What is the total sum of 477. 18s. 8d.+187. 19s.+ 177. 10d.+15s. 9d. and 11 d.? L. S. d. 47.. 18.. 8 18.. 19.. 17.. 0 0.. 10 15.. 9 Explanation.-I first write down the given quantities according to the Rule. Then I add up the column of pence, as in Simple Addition, and find the amount to be 38 pence. This sum I divide by 12, to reduce it to shillings, and the quotient is 3 shillings, and 2 pence remain: The remainder I set down under the column of pence, and the quotient I carry to the column of shillings. I next add up Ans. 84.. 15.. 2 Proof, 84.. 15.. 2 *By a column, is here meant a column of numbers of the same denomination; not a row of single figures, as in Simple Addition, the column of shillings, together with the 3 shillings carried from the pence, and the sum is 55 shillings. This sum I divide by 20, to reduce it to pounds; and the quotient is 2 pounds, and 15 shillings remain; which remainder I set down below the column of shillings, and carry the quotient to the pounds. I then add up the column of pounds and the 2 pounds carried from the shillings, and the sum is 84 pounds, the whole of which I set down below the column of pounds, because there are no more columns to add, and then the work is done. So, the answer, or sum total, is 84 l. 15 s. 2d.-Then, to prove the work, I add all the columns downwards, proceeding in other respects as before, and as I find the same sum total as before, I conclude the work is right. (3) 6.. 9.. 1 4.. 10.. 0 L. 2.. 6.. 2..0 Note. When the highest denomination mentioned in the question is not the highest of its kind, if the amount of that denomination in the answer be large, it may be reduced to a higher denomination, if necessary. Thus, in example 3d, the amount of the shillings is 46s., which being brought into pounds, is 21. 6s. 4. Required the amount of 3657. 14s.+18s. 9d.+361. 12s.767. 1s. 8d.+10d. 2q. |