36. To add when the numbers are large, and the amount of each column is less than ten.

Ex. 1. A farmer sold 234 bushels of corn, 423 bushels of oats, and 141 bushels of wheat; how many bushels of grain did he sell?

OPERATION.

234

423

141

Sum 798

Having for convenience arranged the numbers so that units stand under units, tens under tens, etc., add the units; thus, 1 and 3 are 4, and 4 are 8, and set the 8 under the column of units. Then, add the tens;

thus, 4 and 2 are 6, and 3

are 9, and set the 9 under the column of tens, and so proceed till all the columns are added. Thus we find that the entire sum is 7 hundreds, 9 tens, and 8 units, or 798 bushels the answer.

36. How are numbers arranged for addition? Why? Which column is added first? What is done with the sum?

In like manner add the numbers in the following examples:

16. In 1850 the population of Virginia was 1,421,661, and that of Vermont was 314,120; what was the total population of Virginia and Vermont in 1850? Ans. 1,735,781.

17. In 1860 the population of Massachusetts was 1,231,065 and that of Kentucky was 1,155,713; what was the total population of Massachusetts and Kentucky in 1860 ?

Ans. 2,386,778.

18. A gentleman paid $135 for a horse, $243 for a chaise, and $121 for a harness; what did he pay for all?

19.

Add 2316, 3120, 1201, and 2002. 20. Add $35.41, $21.24, $1.32, and $2.01. 21. Add 43216, 20431, 14030.

22.

Ans. 8669.

Ans. $59.98.

Ans. 77,677.

What is the sum of 3241 + 2312 + 1203 + 3120? 23. What is the sum of 1325 + 2312 + 1321 + 4031? 24. What is the sum of 1242 + 2123 + 1312+ 2112? Ans. 6789. What is the sum of 3124 +1232 + 2113 + 1220? What is the sum of 23102 +52454 + 24342? What is the sum of 15323 +32354 + 41302?

25.

26.

27.

37.

or more.

To add when the amount of any column is ten

28. A farmer raised 473 bushels of potatoes, 285 bushels of onions, 568 bushels of carrots, and 359 bushels of turnips; how many bushels of vegetables did he raise? Ans. 1685.

OPERATION.

473

285

568

359

Having arranged the numbers so that units stand under units, tens under tens, etc., as in example 1, add the numbers in the column of units; thus, 9 and 8 are 17, and 5 are 22, and 3 are 25 units, (= 2 tens and 5 units). The 5 units are set under the column of units and the 2 tens are added to the tens given in the example; thus, 2 and 5 are 7 and 6 are 13, and 8 are 21, and 7 are 28 tens (= 2 hundreds and 8 tens). The 8 tens are set under the tens, and the 2 hundreds are added to the hundreds in the example, giving 16 hundreds, or 1 thousand and 6 hundreds, which, written in their proper places, give 1685 for the

Ans. 1685

answer.

38. In the same manner, add the numbers in the following short columns, and also add across the page, as suggested by the signs.

29. 38462843 + 63542 + 35842 + 91326 + 73241 82735 12600 82145 38642

30. 8305

31.9160

21311

3654

32. 34621538 + 56421 +36245 + 35496 +82437 33. 1354 6242 91367 24687 23549

43621

39. In solving the foregoing examples, the learner has already become familiar with all the operations in addition; but to enable him readily to tell how to add, we give the following

RULE. Write the numbers in order, units under units, tens under tens, etc. Draw a line beneath, add together the figures in the units column, and if the sum be less than ten set it under the column; but if the sum be ten or more, write the units as before, and add the tens to the next column. Thus proceed till all the columns are added.

40. PROOF. The usual mode of proof is to begin at the top and add downward. If the work is right, the two sums will be alike.

NOTE 1. By this process, we combine the figures differently, and hence shall probably detect any mistake which may have been made in adding upward.

39. Why is a Rule for addition given? Repeat the Rule. If the amount of any column is 10 or more, where is the right-hand figure of the amount written? Why? What is done with the left-hand figure or figures? Why?

40. How is addition proved? Why not add upward a second time? In addition is it desirable to name the figures as we add them? Why not?

Ex. 44. In adding upward we say 4 and 6 are 10, and 5 are 15, and 8 are 23, etc.; but in adding downward, we say 8 and 5 are 13, and 6 are 19, and 4 are 23, etc.; thus obtaining the same result, but by different combinations..

ILLUSTRATION.

53468

72635
24376
27594

Sum, 178073

Proof, 178073

NOTE.

If we do not obtain the same result by the two methods, one operation or the other is wrong, perhaps both, and the work must be carefully performed again.

In adding it is not usually desirable to name the figures that we add; thus, in Ex. 44, instead of saying 4 and 6 are 10, and 5 are 15, and 8 are 23, it is shorter and therefore better to say, 4, 10, 15, 23; and then setting down the 3, say 2, 11, 18, 21, 27, etc.

45. A grain dealer bought 3756 bushels of wheat of A, 2347 bushels of B, 1346 bushels of C, and 5468 bushels of how many bushels of wheat did he buy? Ans. 12917.

D;

46. I paid $3465 for a farm, $15000 for a mill, $ 6795 for a lot of wool, and $ 4620 for 40 shares of railroad stock; how much did I pay for all this property? Ans. $29880. 47. Bought 3 city lots for $15345, and sold them so as to gain $ 3639; what sum did I receive for them?

Ans. $18984.

48. A man commenced trade with $5345, and in one year he gained $3462; what was he worth at the end of the year?

49. Add three hundred and twenty-five; two thousand one hundred and fifty-four; two hundred and fourteen; twentythree thousand five hundred and forty-one; and three hundred and seventy-five. Ans. 26609. 50. What is the sum of thirty-four thousand five hun