APPLICATIONS. 1. How many days are there in the twelve calendar months? January has 31, February 28, March 31, April 30, May 31, June 30, July 31, August 31, September 30, October 31, November 30, and December 31. Ans. 365 days. 2. A merchant on settling his accounts finds that he owes A 60 dollars, B 150 dollars, C 240 dollars, and to D 100 dollars. How much does he owe in all ? Ans. 3. What is the total weight of seven casks of merchandise : viz. No. 1, weighing 960 pounds, No. 2,725 pounds, No. 3, 830 pounds, No. 4,798 pounds, No. 5, 698 pounds, No. 6, 569 pounds No. 7, 987 pounds? Ans. 5567 pounds. 4. A man borrowed a sum of money and paid in part 267 dollars, and afterwards paid the remainder 325 dollars : How much did he borrow? Ans. dollars. 5. At the Custom House, on the first day of June, there were entered 1800 yards of linen; on the 10th, 2500 yards; on the 25th, 600 yards; on the day following, 7500 yards; and on the three last days of the month, 1325, yards each day: What was the whole amount entered during the month ? Ans. yards 6. A farmer has his live stock distributed in the following manner: in pasture No. 1, there are 5 horses, 14 cows, 8 oxen, and 6 colts; in pasture No. 2, 3 horses, 4 colts, 6 cows, 20 calves, and 12 head of young cattle; in pasture No. 4, 320 sheep, 16 calves, 2 colts, and 5 head of young cattle. How much live stock had he of each kind, and how many head had he altogether? Ans. 8 horses, 20 cows, 8 oxen, 12 colts, 36 calves, 17 head of young cattle, and 320 sheep. Total live stock, 421 head. 7. What is the interval of time between a transaction which happened 125 years ago, and one that will happen 267 years hence ? Ans. years. 8. An army consists of 4000 foot soldiers, 4006 cavalry or horse, 3093 artillery-men, 1224 riflemen, 1400 pioneers and 200 miners : What is the whole number of men in the army? Ans. 13923. 9. The mail route from Albany to New-York is 144 miles, from New-York to Philadelphia 90 miles, from Philadelphia to Baltimore 98 miles, and from Baltimore to Washington City 38 miles: What is the distance from Albany to Washington ? Ans. miles. 10. Suppose a man was born on the 1st of January, 1795: When will he be 85 years old ? Ans. In 1880. 11. A man dying leaves his only daughter nine hundred and ninety-nine dollars, and to each of three sons two hundred dollars more than he left the daughter. What was each son's portion, and what the amount of the whole estate? Each son's part dollars. dollars. 12. What was the whole number of inhabitants in the United States in 1840; there being in Maine 501,793; New Hampshire 284,574; Vermont 291,948; Massachusetts 737,699; Rhode Island 108,830; Connecticut 309,978; New-York 2,428,921; New-Jersey 373,306; Pennsylvania 1,724,033; Delaware 78,085; Maryland 469,232, Virginia 1,239,797; North Carolina 753,419; South Carolina 594,398; Georgia 691,392 ; Alabama 590,756; Mississippi 375,651 ; Louisiana 352,411 ; Tennessee 829,210; Kentucky 779,828; Ohio 1,519,467; Indiana 685,866; Illinois 476,183; Missouri 383,702; Arkansas 97,574; Michigan 212,267; Florida 54,477; Wisconsin Territory 30,945; Iowa Territory 43,112; District of Columbia 43,712; Naval Service 6,100 ? Ans. 17,068,666. Ans. Whole estate SUBTRACTION OF SIMPLE NUMBERS. $ 16. John has 6 apples and Charles has 4. How many more apples has John than Charles ? Ans. 2. Two is called the difference between the number of apples which John has, and the number of apples which Charles has. SUBTRACTION is finding the difference between two numbers. The larger of the two numbers is called the minuend, the lesser is called the subtrahend, and their difference is called the remainder. Q. What is Subtraction? What is the larger number called ? What is the smaller number called? What is the difference called ? § 17. James has 8 pears and gives 5 to William: how many has he left? Ans. 3. Q. Which number is the minuend ? Which the subtrahend? Which the remainder ? $ 18. The sign -, is called minus, a term signifying less. When placed between two numbers it denotes that the one on the right is to be taken from the one on the left. Thus, 6–4=2, denotes that 4 is to be taken from 6. Here 6 is the minuend, 4 the subtrahend, and 2 the remainder. When the numbers are small, their difference is apparent, and instead of saying, 6 minus 4 equals 2, we say, 4 from 6 leaves 2. Q. What is the sign of subtraction? What is it called? What does the term signify? When placed between two numbers what does it denote? When the numbers are small how do you read them, as 6–4 ? § 19. The following table should be committed to memory, and read, two from two naught remains; two from three, one remains, &c. SUBTRACTION TABLE, 2-2=0 3—2=1 4-2=2 5-2=3 6-2=4 7-2=5 8–2=6 9—2=7 10_2=8 11—2=9 12-2=10 3—3=0 4-3=1 5—3=2 6—3=3 7—3=4 8--3=5 9—3=6 10—3=7 11—3=8 12-3=9 13—3=10 4-4=0 5—4=1 6-4=2 7-4=3 8-4=4 9—4=5 10-4=6 11-4=7 12-4=8 13—4=9 1444=10 54530 6-5=1 7-5=2 8–5=3 9-5=4 104555 11-5=6 12-5=7 1345=8 14-5=9 15–5=10 1. From the number 869 subtract 327. We begin at the right hand figure OPERATION. of the lower line, and say, 7 from 9 869 Minuend. leaves 2: set down the 2 under the 327 Subtrahend. 7. Proceeding to the next column, 542 Remainder. we say, 2 from 6 leaves 4: set down the 4, and then say, 3 from 8 leaves 5. Thus, 542 is the remainder, or true difference between the numbers. 2. From 654 subtract 472. Beginning at the lower figure on the right we say, 2 from 4 leaves 2: set OPERATION. down the 2. At the next step we meet a difficulty; for, we cannot subtract 7 from 5. We avoid this difficulty, thus. Ten units in the second place are equal 654 5154 to one unit of the third place § 8. 472 4 72 Therefore, if we add 10 to the 5 and 182 1 82 diminish 6 by 1 the value of the upper line will not be changed. The numbers are so written at the right. hundreds. ertens to Orhundreds. itens units OPERATION. A osthous. os whuns. Now, instead of saying 7 from 5, we say, 7 from 15 leaves 8: set down the 8, and then say, 4 from 5 leaves 1. The remainder is, therefore, 182. Now, if instead of diminishing the 6 by 1, we had increased the 4 under it by 1, and subtracted 5 from 6, the remainder would have been the same. Therefore, When a figure of the subtrahend is greater than the one directly over it, suppose 10 to be added to the upper figure. Let the lower figure be then taken from the number thus arising, and add 1 to the next figure of the subtrahend before it is subtracted from the figure directly above it. This is called borrowing 10. Q. When a figure of the subtrahend is greater than the one of the minuend directly above it, what do you do? What is this called ? 3. From 6354 subtract 4627. In this example, we say, 7 from 14 leaves 7: 1 carried to 2 is 3, 3 from 5 leaves 2: 6 from 13 54 513414 leaves 7: 1 carried to 4 is 5, 5 from 4627 4 62 7 6 leaves 1. The remainder, there 1727 1 72 7 fore, is 1727. 4. From 60204 subtract 32861. In this example, we say, 1 from 4 leaves 3: 6 from 10 leaves 4: 1 carried 60204 to 8 is 9, 9 from 12 leaves 3: 1 carried 32861 to 2 is 3, 3 from 10 leaves 7: 1 carried 27343 to 3 is 4, 4 from 6 leaves 2. From these examples, we may deduce the following general RULE. $ 20. I. Set down the less number under the greater, so that units shall fall under units, tens under tens, hundreds under hundreds, &c., and draw a line beneath them. II. Then, beginning at the right hand, subtract each figure from the one directly over it, and set down the remainder. III. But if the upper figure be the least, suppose it to be increased by 10 : then make the subtraction, set down the remainder, and carry 1 to the next figure of the subtrahend. OPERATION, |