SUBTRACTION OF DENOMINATE NUMBERS. RULE. Set down the numbers as in Addition, and commencing with the lowest denomination, subtract the lower quantity from that above it, if possible; but if the quantity above is too small, borrow a UNIT of the next higher denomination, and, having reduced IT, add ITs value to the number referred to in the minuend, and subtract from this SUM, setting the remainder immediately under the number subtracted, and, to balance the UNIT borrowed, add one to the next quantity, before subtracting it, and proceed in a like manner with all the other denominations, observing to set down the whole difference of the highest denomination, the denominate number thus formed, will be the ANSWER sought. EXAMPLES. 1. A certain field is 25 rods, 3 yards, 2 feet, 9 inches long, and 13 rods, 4 yards, 1 foot, 11 inches wide, how much longer is this field than it is wide? In the above question, we are, first, to take 11 from 9, which we cannot, hence, we borrow 1 foot to 12 inches, and 12+9=21 inches, from which we take 11, and 10 remains, carry 1 to 1, gives 2, from which if 2 be taken, nothing remains, and so with all the rest. 2. A merchant had in bank $1236.785, and drew out on check $307.875, how much was yet remaining? Here we place the integer and de cimal so that the like orders of units in each may fall exactly under each $ other, and subtract as in whole num- Thus: 1236.785 bers, which gives for the balance in 307.875 928.910 Ans. 1236.785 Proof. 3. A merchant shipped 2 boxes of specie, the first contained 327£. 11s. 9d. 1qr., and the second, 298£. 15s. 11d. 3qrs., how much more was in the first than in the second? Here we borrow 1d.=4fars. which we add to 1 far., making 5fars., from which we subtract 3fars., leaving 2fars., and by adding 1 to 11d., and proceed ing as directed, we have £ S. d. far. Thus: 327 11 9 1 298 15 11 3 28 15 9 2 Ans. 4. What is the difference between 46 rods, 3 yards, 1 foot, and 34 rods, 4 yards, and 2 feet. Here we borrow a yard to in crease the feet, also a rod, to in- Thus: 46 rods. yds. feet. 3 1 crease the yards, and subtracting, as directed in the RULE, we have 34 4 2 Add the difference to the less number, and we have 46 3 1 Proof. In the same manner solve the following QUESTIONS FOR EXERCISE. 1. A man gave his note for $346,875, and afterward paid $289,75, how much remained unpaid? 2. A merchant in Philadelphia bought a bill of goods of a house in London, amounting to 569£. 15s. 10d. 2qrs., on which he paid 287£. 19s. 11d. 1qr., how much was yet due? 3. Bought a lot of silver table spoons, weighing 25lbs. 9ozs. 16dwts. 22grs., and a lot of tea spoons, weighing 9lbs. 11ozs. 18dwts. 19grs., how much more did the table spoons weigh than the tea spoons? 4. The burden of a ship to England was 195Ts. 18cwts. 3qrs. 25lbs., and when she returned, she brought 108Ts. 19cwts. 1qr. 27lbs., how much more did she carry going than returning. 5. An apothecary mixed 2s. 83s. 43s. 19s. 14grs. of a certain kind of medicine, and sold 113s. 73s. 29s. 18grs., how much had he left? 6. What is the difference between 49bus. 1pk. 5qts. 1pt. 2 gills, and 36bus. 3pks. 7qts. 1pt. 3 gills? 7. Two ships sail from Portugal at the same time, one brings 26Ts. 25hhds. 49gals., and the other 18Ts. 12tier. 23gals., what was the difference in their cargoes? 8. What denominate number will show the difference between 87degs. 58 miles, 5 furlongs, 26 poles, 3 yards, 2 feet, 7 inches, and 53degs. 49 miles, 6furs. 29 poles, 2yds. 1ft.? 9. A man bought 2 lots of land, the first contained 84 acres, 1 rood, 28sq. rods, 7sq. feet, and the second, 59 acres, 3 roods, 36sq. rods, 8sq. feet, how much more was there in the first than in the second? 10. What is the difference between 27 cubic yards, and 27 cubic feet? how many cubic inches in this difference? What is the difference between a cubic yard and a cord? 11. A man bought 2 pieces of muslin, the first measured 34yds. 2qrs. 2nas., and the second, 25 ells E. 3qrs. 3nas., what was the difference in these pieces? 12. What is the difference between 6revs. 9s. 25°, 45', 36", and 8revs. 11s. 21°, 33', 22" ? 13. What is the difference between 25 years, 9 months, 27 days, and 24 years, 11 months, 29 days? 14. Charles was born May 5th, 1836, and William was born October 3d, 1841, what is the difference in their ages? i. e., what is the difference between 1841 years, 9 months, 3 days, and 1836 years, 4 months, 5 days? NOTE.-The subtraction of dates is a branch of knowledge so generally useful among men of all professions and pursuits, as to make it a subject of special attention. The later date including years, months, and days, will always form the larger number, or MINUEND, and the earlier date will give the less number, or SUBTRAHEND. To illustrate this subject further, we will suppose, the first date is the 9th of April, 1824, and the second (later,) is the 12th of November, 1847. In the first date we have 1824 years, 3 months, 9 days, which brings us to the 9th of April, 1824. In the second (latest,) date, we have 1847 years, 10 months, 12 days, which brings us to the 12th of November, 1847. Now, it is plain that if we subtract 1824 years, 3 months, 9 days, from 1847 years, 10 months, 12 days, (according to the RULE already given,) we shall have for the remainder 23 years, 7 months, 3 days, which is the time intervening between the proposed days. In the same manner the answer may be furnished to the questions which follow. 15. The war between ENGLAND and the AMERICAN COLONIES, commenced April 19th, 1775, and provisional articles of peace were signed November 30th, 1782, how long did the war continue? 16. The DECLARATION OF INDEPENDENCE was signed by the members of the CONTINEntal Congress, on the 4th of July, 1776, how long was it from the commencement of hostilities, April 19th, 1775, to the signing of the DECLARATION? how long from the signing of the DECLARATION to this time? 17. A note of hand, bears date June 12th, 1825, and the receipt against it, shows that it was paid on the 20th of March, 1834, how long was it from the time the note was given till it was paid? 18. How old are you? i. e., how many years, months, and days old are you, commencing with the date of your birth, and ending with the present time? 19. On the 3d of August, 1492, Columbus took command of three ships, and sailed on a voyage of discovery, in which (after a few weeks,) he discovered the island of Guanahani, how long ago is that? MULTIPLICATION OF DENOMINATE NUMBERS. RULE. First, set down the MULTIPLICAND, and place the multiplier on the right, under the lowest denomination, and draw a line under them. Second, begin with the lowest, and multiply each denomination separately, setting down and carrying, as in Addition, (page 153,) the DENOMINATE NUMBER, thus formed below the line, will be the ANSWER. EXAMPLES. 1. How much sugar in six hogsheads, each weighing 2cwts. 3qrs. 25lbs. 9ozs. Here we, first, multiply 9ozs. by 6, making 54ozs. = to 3lbs. 6ozs., we now set down 6ozs. and multiply 25lbs. by 6, making, with the 3lbs. reserved, 153lbs. = cwts. qrs. lbs. ozs. to 5qrs. 13lbs., which Thus: 2 we set down and reserve, as before, &c., till we find 6 17 3 13 6 Ans. 2. Bought 6 yards of broad cloth, at $4.875 per yard, what did it cost? The multiplication in this example is the same as in whole numbers, except that we cut off as many places for deci- Thus: 4.875 mals in the quotient as there are deci mals in the multiplicand, which gives 6 29.250 Ans. 3. In 12 boxes, each containing 125£. 15s. 6d. 3fars., what quantity of money is there? First, we say 12 times 3far. are to 36 fars. to 9d. Ofar., set down Ofar., and reserve 9d. Second, 12 times 6d. are 72d. and 9d. are 81d. to 6s. 9d., set down 9d. and carry 6s., and proceeding in Thus: 125 a like manner with the rest, we have. £. S. d. far. 15 6 3 12 1509 This process is very simple, and the above examples, if properly attended to, will sufficiently illustrate the principle for solving the following QUESTIONS FOR EXERCISE. 1. A draper sold 19 yards of broad cloth, at $4.875 per yard, what did it come to? what will 49 yards come to at the same rate? |