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it under the column; if it be ten or any number of tens, write a cipher; if there be an excess over ten or tens, write down this excess, and carry as many units to the next column, as there are tens; and thus proceed with each remaining column, writing the whole sum under the last.

Proof.-Draw a line below the upper number, and add the remaining numbers as shown in the rule ; add the sum thus found and the upper number together, and if the sum be equal to the first addition, the work is right. Or, begin at the top number, add downwards, and carry as beforé; if the two sums come alike, the work is probably right.

EXAMPLES.
1.
2.

3.
2178
567842

321674
4216
143469

92167
3945
782107

8547
2763
695213

26
1684
203169

2141

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6.

Miles. 4734746 3474352 4634324 .7369138 3543468 4733246 4743447 3752612 7426984

7. Leagues. 46434733 74265374 52652754 35374205 74447352 47345264 74167574 43526526 38573452

8. Years. 347312484 368126312 758612691 731674591 323473276 471266198 323634712 271254712 312844795

APPLICATION.

1. What is the sum of 37, 509, 7126, 17630, and 459273 yards?

2. Required, the sum of 3579, 41, 96120, 725, 11, 1820, 5, and 720139 bushels.

3. What is the sum of 2591, 720396, 14, 259, 6, 370214, 9740, 53, 1692, and 137 dollars ?

4. How many days are in the 12 calendar months, in a leap year?

5. A person dying left to his widow 1500 dollars, to his eldest son 30500, to each of his other two 3406 ; also 2700 to each of his three daughters, besides 751 dollars in other small legacies ; what did his estate amount to?

6. If the distance from Hallowell to Portland be fifty six miles, thence to Portsmouth fifty-four miles, thence to Boston sixty-four miles, thence to Hartford ninety-eight miles, thence to New-York one hundred and eleven miles, thence to Philadelphia ninety miles, thence to Baltimore ninety-nine miles, and thence to Washington thirty-eight miles; what is the whole distance between Hallowell and the city of Washington ?

7. John, James, and Paul counting their prize-money, John had one thousand, three hundred and seventy-five dollars ; James had just three times as much as John : and Paul had just as much as both the others; pray how many dollars had Paul ?

SIMPLE SUBTRACTION. SUBTRACTION is finding the difference of two numbers, by taking the less from the greater. It is simple subtraction if the numbers are of one denomination; as, 5 feet taken from 8 feet, will leave 3 feet.

The greater number is called the minuend, or substra tum; the less, the subtrahend; and the number found by the operation, the difference, or remainder.

Rule.Write the less number under the greater, placing units under units, tens under tens, &c. and draw a line under them. Begin at the right, and take each figure in the subtrahend from its corresponding one in the minuend, setting down the remainder straight under it below the line. If the lower figure be greater than the one above it, add ten to the upper figure, from which sum take the lower, and set down the remainder, carrying one to the next lower figure; and thus proceed until the whole is finished.

Proof.--Add the remainder to the subtrahend, and if the sum be equal to the minuend, the work is right.

EXAMPLES. 1.

2. From 67216 the minuend, 46132941 Take 43792 the subtrahend. 17316257

3. 71290 46172

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16

10. 100200300400 98087076065

11. 10000000 9999991

APPLICATION.
1. From 360418 tons, take 293752.
2. From 100046 acres, take 10009.
3. What is the difference between 1735, and 1897348

bours ?

4. How much do 540312 days exceed 7953 ?
5. How much are 30491 gallons less than 57321469 ?

6. If the distance from Hallowell to Savannah, through Washington, be 1268 miles and that from Washington to Savannah, 658 miles; how far is Washington from

7. From Hallowell to the city of New-York is 383 miles. Now, if a man should travel 10 days from Hal

Hallowell ?

8. If a farmer kills six hogs, which weigh two hundred

Jowell towards New-York, at the rate of thirty-six miles each day; how far would he then be from that city ? and fifty-four, one hundred and ninety-seven, two hundred and sixteen, two hundred and forty-nine, three hundred and twelve, and three hundred and sixty-three, and markets one thousand weight of pork; what quantity does he reserve for his own use?

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SIMPLE MULTIPLICATION. MULTIPLICATION is finding the amount of any given

number, by repeating it any proposed number of times;
as, 4 times 7 are 28.

The number to be multiplied is called the multiplicand.
The number which multiplies is called the multiplier.

product.

The number arising from the operation is called the

The multiplicand and multiplier are called factors; and if these are of one denomination it is called Simple

Multiplication.

MULTIPLICATION AND DIVISION TABLE.

1 2 3 4 5 6 7 8 9 10 11 12 2 4 6 8 10 12 14 16 18 20 22 24 31 6 9 12 15 1821 24 27 30 33 36 41 8|12|16|20|2428|32| 36| 40| 44 48 5/10 15 20 25/30/35,401 45 50 55 60 6|12|18|24|30|36|42|48| 54 60 66 72 7 14 21 28 35 42 49 56 63 70 77 84 8|16|24/32 40 48 56 64 72 801 88 96 9 18 27 36 45 54,63 72 81 90 99 108 10 20 30 40 50 60 70 80 90 100 110 120 11 22 33 4455 66 77 88 99 110 121132 12/24|36|48,60 72 84,96 108/120/132/144

Use of the TABLE in MulTIPLICATION. Find the multiplier in the left hand column, and the multiplicand in the uppermost line; and the product is in the common angle of meeting, or against the multiplier, and under the multiplicarid.

To use the above Table in Division, seek your divisor in the left hand column; then run your eye along the line, to the right hand, till you come to your dividend; and the figure in the top line, of the same column, will be the quotient, or number of times the divisor is contained in the dividend. Case I.- When the multiplicr is not more than twelve.

RULE.-Multiply each figure in the multiplicand by the multiplier, beginning at the right hand side, and setting down the whole of such products as are less than ten; but for such as are just equal to a certain number of tens, write down 0, and carry 1 for each ten to the next product; and for such as exceed a certain number of tens, set down the excess, and carry for the tens as before.

EXAMPLES. 1. What number is equal to 4 times 365 ? Thus

2. 365 Multiplicand.

5124167 4 Multiplier.

3

a

Ans. 1460 Product.

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