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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 sou’s portion, and what the amount of the whole estate?

dollars. Each son's part Ans. . Whole estate

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; Jowa Territory 43,112; District of Columbia 43,712 ; Naval Service 6,100 ?

Ans. 17,068,666.

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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 24.ers.

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.

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SUBTRACTION TABLE,

2-2=0 3-2=1 4-2=2 5-2=3 6-2=4

-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
hy -3=4
8--3=5
9-356
10-3=7
11-3=8
12-3=9
13--3=10

4-4=0
544=1
6-4=2
by_4=3
8—4=4
3-4-5
10—4=6
11-457
12-4=8
13-4=9
14-4=10

5-5=0 6-5=1 7-5=2 8-5=3 9_5=4 10-555 11-5=6 12-5=7 13-5=8 14-5=9 15-5=10

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When the numbers are small, as in the above examples, they may be subtracted in the mind, without writing them down. When the numbers are large, we write one number under the other, and then make the subtraction by parts.

1. James has 27 apples, and gives 14 to John : how many will he have left? The 27 is made up of 7 units and 2

27 Minuend. tens; and the 14, of 4 units and 1 ten.

14 Subtrahend. . If then we subtract the units from each other, 3. units will remain, and if we

13 subtract the tens also, one ten will remain. Hence, the remainder is 13.

2. What are the remainders in the following examples.

Minuends,
Subtrahends,
Remainders,

(1) 874 642 232

(2) 972 631

(3) 999 367

(4) 8197 7487 1010

3. A farmer has 378 sheep, and sold 256 : how many had he left ? We first write the number 378, and then

378 the 256 under it, so that units shall fall under

256 units, tens under tens, and hundreds under

122 hundreds. We then take 6 units from 8, 5 tens from 7 tens, and 2 hundreds from 3 hundreds, leaving for the remainder 122.

4. A merchant has 578 dollars in cash, and pays 475 dollars for goods : how much has he left ?

Ans. 103 dollars. 5. What are the remainders in the following examples.

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(1) 62843 51720 11123

(2) 278846 167504

(3) 894862 170641

6. What is the difference between 4 units and 1 ten.

10 We write the ten, and then place the 4

4 under the units' place. Then we say, 4 from ten leaves 6.

6

7. What is the difference between 2 tens and 6 units ?

Here we may say, 6 from 20 leaves 14.

20

6 14

14

8. What is the difference between 14 and 8?

Having written the 8 under the 14, so that units shall stand under units, we see that 8 8 cannot be subtracted from 4, but we can say,

6 8 from 14 leaves 6.

9. What is the difference between 3 tens and 7 units ? What is the difference between 4 tens and 2 tens? What is the difference between 5 tens and 1 ten ?

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