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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. 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. 550 dollars. 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. 592 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. 16375 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,

Ives, 2 colts, and 5 head of young cattle. How

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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 transa action which happened 125 years ago, and one that will happen 267 years hence ?

Ans. 392 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. 370 miles. 10. Suppose a man were born on the 1st of January, 1795: when will he be 85

years

old ?

Ans. In 1890. 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 1199 dolls.

4596 dolls. 12. What was the whole number of inhabitants in the United States in 1830; there being in Maine 399,955; New Hampshire 269,328; Vermont 280,652; Massachusetts 610,408; Rhode Is? 97,199, Connecticut 297,675; New York 1,9

Ans. {Whole estate

New Jersey 320,823; Pennsylvania 1,348,233 ; Delaware 76,748; Maryland 447,040; Virginia 1,211,405; North Carolina 737,987; South Carolina 581,185; Georgia 516,823; Alabama 309,527; Mississippi 110,357; Louisiana 215,739; Tennessee 681,904; Kentucky 687,917; Ohio 937,903; Indiana 343,031;

Ilinois 157,445 ; Missouri 140,455; Michigan Territory 31,639; Arkansas 30,388; Florida 34,730; District of Columbia 39,834; Naval Service 5,602.

Ans. 12,810,540.

SUBTRACTION OF SIMPLE NUMBERS.

§ 19. 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.

Ø 20. Subtraction is finding the difference between two unequal numbers.

§ 21. The larger of the two numbers is called the minuend, the lesser is called the subtrahend, and their difference is called the remainder.

§ 22. 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 she remainder.

23. When the numbers are small, their differ

ence is apparent, and instead of saying, 6 minus 4 equals 2, we say, 4 from 6 leaves 2. The following table is to be so read, and committed to memoTy.

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SUBTRACTION TABLE. 2-2=0 543=2 9-455 9-6=3 32=1 63=3 10_4=6 10-6=4 4-2=2

743=4 55=0 7--7=0 52=3 83=5

6-5=1 87=1 6--2=4 9-3=6

7-5=2 9—7=2 742=5 10-3=

8-5=3 1047=3 2=6 4450 9-5=4

88=0
9_2=7 514=1 .10-5=5

9-8=1
10_2=8
6_4=2

6-6=0 10-8=2
33=0 7-4=3

7-6=1

9-9=0 4-3=1 &4=4

86=2

10_9=1

12-2=10
12-3= how many ?
15~4= how many?
11-6= how many ?
189= how many ? ?
25-85 how many?.

1747= how many ? 16-8= how many ? 19-9= how many ? 20 4= how many? 1347= how many 14-2= how many ?

?

Ex. 1. From 869 take 327.

869 minuend Write the numbers 327 subtrahend

542 remainder.

We begin at the right hand figure of the lower line, and say, 7 from 9 leaves 2: set down the 2 under the 7. Proceeding to the next column, 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.

Ex. 2. From 654 take 472.

o hundreds.

tens
units

Metoda a hundreds.

tens

upper line

Minuend

654 5 15 4 Write the Subtrahend

47 2 4 7 2 Remainder

182 182 Beginning at the lowest figure on the right, we say, 2 from 4 leaves 2: set 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 to one unit of the third place, $ 10. Therefore, if we add 10 to the 5 and diminish 6 by 1 the value of the will not be changed. The numbers are so written at the right.

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.

Ø 24. 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 page ure 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.

Ex. 3. From 6354 take 4627.

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vaunits

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Minuend

13414 Write the Subtrahend 462 7 4 627

Remainder. 1725 1727

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