Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

Let the pupil be required to answer the following ques

tions:

4+3 how many?

2+5+1=how many ? 5+6+7+2 how many?

8+9+2+1+7=how many?

6+7+5+4+3+2=how many ? 1+2+4+3+5+7+6=how many ?

EXAMPLES.

1. Where the sums of the several columns are less than

ten ;

Add together 2432, 3343 and 4122. Set the numbers under each other: units under units; tens under tens; hundreds under hundreds; thousands under thousands. Draw a line below the whole.

Add first, the column of units. Set the sum 7 under the column of units; next add the tens; set the sum 9 under the column of tens-next add the hundreds; set the sum 8 under the column of hundreds. Lastly, add the thousands, and set the sum 9 under the column of thousands. The whole amount is, then, nine thousand eight hundred and ninety-seven.

Add 6264, 2532 and 1203.

Add 4132, 1001 and 1423.

OPERATION.

∞Thousands.
- ∞ Hundreds.

[blocks in formation]

3 3 4 3

4

2 2

7

9 8 9

Ans. 9999.

Ans. 6556.

2. Where the sums of the several columns equal or exceed ten;

What is the sum total of the following numbers: 3758, 4903, 7006, 3713, 3721.

Place the numbers as directed in the preceding example. The sum of the numbers in the units' column is 21-that is, 2 tens and 1 unit. Set the 1 under the units' column, and carry the 2 to the next or tens' column. The sum of the tens' column thus increased is 10

OPERATION.

Ten Thousands.

∞∞∞ Thousands.

44064 Hundreds.

Tens.

∞∞∞ Units.

4 9

371

2 3

3

2 1

1

0 1

tens; that is, 1 hundred and no tens. Place a zero under the tens' column, and carry the 1 to the hundreds' column. The sum of the hundreds' column, so increased, is 31 hundreds; that is, 3 thousands and 1 hundred. Set the 1 under the hundreds' column, and carry the 3 to the thousands' column. The sum of this column, so increased, is 23 thousands, or 2 tens of thousands and 3 thousands. Set the 3 under the thousands' column, and carry the 2 to the tens of thousands' place; or, what is the same thing, set down the whole of the sum of the last column.

10. From what has now been explained, we know that ten units are equal to one ten, ten tens are equal to one hundred, ten hundreds are equal to one thousand, and so on; ten of any order are equal to one of the next superior order. Hence, for adding numbers of the same denomination, we deduce this

RULE.

I. Place the numbers to be added under each other, so

that units may stand under units, tens under tens, hundreds under hundreds, and so on for the higher orders.

II. Commencing at the right, find the sum of the numbers in the column of units; if this sum is less than ten, place it immediately under the unit column; but if it equals or exceeds ten, see how many tens it contains, and how many units over; write down the units under the units' column, and carry the tens to the next, or tens' column. In this way proceed with each column, observing to carry for every ten contained in such column, one to the column of the next higher denomination. When we reach the last column, its whole amount must be set down.

How do you write the numbers for addition? Where do you commence to add? If the sum is expressed by a single digit, how do you dispose of it? When it equals or exceeds ten, how do you proceed? What is the rule with regard to carrying? How do you proceed when you come to the last column?

[blocks in formation]

11. The method of proving, or testing the work of addition, is generally to commence at the top of the respective columns and add downwards, carrying one for every ten as before; if the sum is the same as when the columns were added upwards, the work is then supposed to be correct.

This proof is not infallible, since mistakes

may occur in both operations, which shall balance each other.

How is the work of addition generally proved? Is this method of proof infallible? Why not?

[blocks in formation]

8. Add 123405, 2354210, 794327, and 36547, together.

Ans. 3308489. 9. Add 275602, 345607, 4567801, and 365, together. Ans. 5189375. 10. Add 100375, 406780, 4673005, 4112, and 2478, together.

Ans. 5186750.

11. Add 1034001, 78954, 379205, 367001, and 45637, together.

Ans. 1904798. 12. What is the sum of the following numbers: Three thousand six hundred and fifty, seven thousand eight hundred and thirty-two, eleven thousand five hundred and sixty-seven, ten thousand and fifty-six, four hundred and seventy-two? Ans. 33577.

13. What is the sum of the numbers, four thousand three hundred and seventy-three, three thousand one hundred and fourteen, one thousand two hundred and twentythree, six hundred and fifty-four? Ans. 9364.

14. Find the number of days in a year, the days of the respective months being as follows: January,31, February, 28, March, 31, April, 30, May, 31, June, 30, July, 31, August, 31, September, 30, October, 31, November, 30, December,31.

Ans. 365 days.

15. A man drew five loads of bricks; in the first load he had 1209, in the second load 1453, in the third load 1101, in the fourth load 1212, and in the fifth load 1303. many bricks were there in all?

How

Ans. 6278 bricks.

16. If there are shipped from the United States, 15624 barrels of flour to Sweden, 250 barrels to Holland, 205154 barrels to England, 6401 to Texas, 19602 to Mexico, what is the whole amount? Ans. 247031 barrels.

17. In 1837 the United States exported 100232 hogsheads of tobacco; in 1838 they exported 100592; in 1839 they exported 78995; in 1840 they exported 119484; in 1841 they exported 147828. How many hogsheads of tobacco were exported during these five years?

Ans. 547131 hogsheads. 18. If the cotton crop of the United States is estimated at 1360532 bales for the year 1839, 2177835 bales for the year 1840, 1634945 bales for the year 1841, and 1683574 bales for the year 1842, how many bales will the four years' crops amount to? Ans. 6856886 bales. 19. In 1839 the Onondaga Springs produced 2864718 bushels of salt; in 1840 they produced 2622305 bushels; in 1841 they produced 3340769 bushels; in 1842 they produced 2291903 bushels. What is the whole number of bushels during the above four years?

Ans. 11119695 bushels.

« ΠροηγούμενηΣυνέχεια »