14. Add together the numbers 8, 43, 201, 5278, 35, and 71507.

Ans. 77072. 15. Add together the numbers 26, 60, 782, 2548, 92812, 913, and 83. Ans. 97224. 16. What is the sum total of 287, 34, 8210, 304, 510258, 83000, and 7? Ans. 602100. 17. What is the sum total of 90032, 1320, 2870, 4855, 875, and 48? Ans. One hundred thousand. 18. What is the sum total of 362, 88735, 9542, 521, and 100850? Ans. Two hundred thousand, and ten. 19. What is the sum total of the following numbers, viz. Five hundred and twenty-eight,

Three thousand two hundred,

Seven thousand nine hundred and fifty,

Forty-two thousand,

Three hundred twelve thousand, four hundred

and thirty-one?

Ans. 366109.

20. Required the sum of the following numbers, viz.

Five hundred and sixty-eight,

Eight thousand eight hundred and five,
Seventy-nine thousand six hundred,

Nine hundred and eleven thousand,

Nine hundred ninety-nine millions and twenty-six.

Ans. 999999999.

PRACTICAL QUESTIONS.

1. A merchant, on settling his accounts, finds that he owes A 415 dollars, B 38 dollars, C 1248 dollars, and D 52 dollars: What is the amount of all these debts?

Answer, 1753 dollars.

2. The contents of five boards are as follows: The first board contains 24 square feet, the second 19, the third 22, the fourth 13, and the fifth 11. How many square feet do Ans. 89.

they all contain?

3. A man built a dwelling house, a barn, a grist mill,

and a shed. The dwelling house cost 1520 dollars, the barn 218 dollars, the mill 1432 dollars, and the shed 75 dollars. What did all those buildings cost?

Ans. 3245 dollars.

4. A man borrowed of his neighbor thirty dollars, at one time; three hundred and five at another; and four thousand and twenty at another. What do all these sums amount to? Ans. 4355 dollars.

5. In the year 1821, the number of inhabitants in England was 11260555, in Wales 717108, in Scotland 2092014, and in Ireland 6847000. How many inhabitants were there in all of those countries? Ans. 20916677.

6. From the creation of the world to the general deluge, was 1650 years; from this time to the call of Abraham was 427 years; from that to the departure of the Israelites out of Egypt, 430; from that to the building of the temple by Solomon, 479; from that to the founding of Rome, 266; from that to the birth of our Saviour Jesus Christ, 752; and it is now 1831 years since the birth of Christ. How many years since the creation? Ans. 5835.

7. The four largest cities in Europe, are London in England, Paris in France, Constantinople in Turkey, and Naples in Italy. London contains about one million two hundred and twenty-five thousand inhabitants; Paris seven hundred and fifteen thousand; Constantinople five hundred thousand; and Naples three hundred and thirty thousand. What is the whole number of inhabitants in these four great cities? Ans. 2770000.

8. The population of the World is estimated as follows: Europe, one hundred and eighty millions; Asia, three hundred and eighty millions; Africa, fifty millions; America, thirty-eight millions; Austral Asia and Polynesia, two millions: How many in all?

Ans. Six hundred and fifty millions.

9. The Hudson and Erie canal, in the State of NewYork, extends from the Hudson river at Albany, to Buffalo on Lake Erie. The distances on this canal are as follows, viz. From Albany to Schenectady 30 miles; from thence to Utica 80 miles; from thence to Syracuse 61; from thence to Rochester 99; and from thence to Buffalo 93. There are, in this canal, 26 locks between Albany and Schenectady, 25 between Schenectady and

C

Utica, 25 between Utica and Rochester, and 6 between Rochester and Buffalo. How long is the canal, and how many locks does it contain?

Ans. The canal is 363 miles long, and it contains 82 locks.

QUESTIONS ON THE FOREGOING.

1. What are the fundamental rules of Arithmetic? 2. Why are they so called? 3. What is addition? 4. What is simple addition? 5. When you would add together several numbers, how do you write them down? 6. Which column of figures do you add first? 7. Do you begin at the bottom, or at the top of the column? 8. When you have added up the column of units, what do you do with the amount? 9. How then do you proceed? 10. When you have added up the last column, what do you do with the amount? 11. How is addition proved?

SUBTRACTION,

Is taking a less number from a greater, so as to find their difference.

The greater number is called the Minuend; the less number, the Subtrahend; and their difference, or what is left after the subtraction is performed, is called the Remainder.

Subtraction is either simple or compound.

SIMPLE SUBTRACTION,

Is taking a less whole number from a greater of the same denomination; as 2 dollars taken from a sum of 5 dollars, will leave a remainder of 3 dollars: Or, it is simply subtracting a less whole number from a greater, without regard to their signification; as 4 taken from 7, leaves 3.

SUBTRACTION TABLE.

2-2-0 6-3-3

3-2=1 7-3-4 5-5-0 7-7=0
8-3-5 6-5-1 8-7=1
5-2-3 9-3=6

4-2-2

6-2-4 10-3=7 8-5-310-7-3

7-5-2 9-7-2

5-3-210-4-6 | 10-6=4

This Table may read thus, 2 from 2 leaves 0; 2 from 3 leaves 1; 2 from 4 leaves 2, &c.

When the numbers are small, as in the foregoing table, the subtraction of the less number from the greater may be readily done in the mind, without writing down the numbers. When the given numbers are large, their dif ference may be found by the following

RULE.

1. Set the subtrahend, or less number, under the minuend, or greater number,* so that units shall stand under units, tens under tens, &c. as in Addition, and draw a line underneath.

2. Begin with the right hand figures, and take, if possible, the lower figure from the upper, and set down the remainder underneath, or if nothing remains, set down a cipher; and in like manner proceed with all the other figures when the figures in the lower number are all less than the corresponding figures in the upper number.

3. But, if any figure in the lower number be greater than the one above it, borrow 10, which add to the upper figure,

Although it is usual, and generally most convenient, to write the subtrabend below the minuend, it is by no means essential; and it may be well for the student, in solving some of the following questions in Subtraction, to write the subtrahend above the minuend, and so perform the subtractions downwards, in order that be may be able to perform subtraction in this manner, when it may happen, in complex operations, that the numbers are so arranged.

and from the amount subtract the lower figure, and set down the remainder below. Then carry 1, (as an equivalent to the 10 borrowed,) and add it to the next figure to the left, in the lower number, and proceed as before.*

To prove Subtraction.

Add the remainder, or answer, to the subtrahend; and, if the work be right, the amount will be equal to the minuend.

EXAMPLES.

1. Subtract 315 from 457.

Operation.

Minuend, 457
Subtrahend, 315

Explanation. I first write down the numbers as directed in the 1st article of the Rule. Then I subtract as follows: I begin with the right hand figures, and Remainder, 142 say, 5 from 7 leaves 2; which I set down underneath: then, 1 from 5 leaves 4, 457 which I set down: then, 3 from 4 leaves 1, which I set down, and the work is done. So, the whole remainder, or answer is, 142.—Then, in order to prove the work, I add the remainder to the subtrahend; and the sum being equal to the minuend, I conclude the work is right.

Proof,

* Demonstration -When all the figures in the subtrabend are less than their corresponding figures in the minuend, the difference of the figures in the several like places, must,all taken together, make the true difference sought; because, as the sum of the parts is equal to the whole, so must the sum of the differences, of all the similar parts, be equal to the difference of the whole.

2. The reason of the method of proceeding when any figure in the subtrahend is greater than the corresponding figure in the minuend, may be shown as follows: If any two given numbers be increased equally, by the addition of any one number to each of them, their difference, when thus increased, will still be the same as before. Thus, if to each of the numbers, 6 and 4, we add 10, or any other number, their difference, after being thus increased, will evidently be the same as before, viz. 2. Now, in performing subtraction, according to the above Rule, when any figure in the subtrahend is greater than the corresponding figure in the minuend, we, in effect, add 10 to each of those figures; for instead of adding 10 to the figure in the subtrahend, we add 1 to the next place to the left, which, by the nature of notation, is equal to ten units in the former place: Therefore, we increase the minuend and subtrabend equally, by adding the same number to both, and hence their difference remains the same The reason of the method of proof is evident; for if the difference of two numbers he added to the less number, it must manifestly make up a sum equal to the greater number.