38. It is obvious that numbers can be added only when they refer to the same things. Five oranges and three books when "put together" are still 5 oranges and 3 books, and not 8 oranges or 8 books.

It is also obvious that digits can be added only when they refer to the same order of units. Nine hundreds and eight tens when put together are still 9 hundreds and 8 tens, and not 17 hundreds or 17 tens.

Care must be taken, therefore, in writing numbers to be added, that all the units' digits shall fall in one column, all the tens' digits in the next column (to the left), and all the hundreds' digits in the next column, and so on.

39. To add columns of digits with absolute accuracy and great rapidity is a real accomplishment, and the operation of addition should be continued until both these results are secured. The beginner, however, will need some test of the accuracy of his work. One test is to begin at the bottom of the right-hand column in adding, and write on a piece of waste-paper the entire sum of each column; then to begin at the top of the left-hand column and write also the entire sum of each column; finally, to add the sums obtained in the first addition, and the sums obtained in the second addition, and compare the results.

The study of an example will make the process understood.

By comparing the results we find each sum to be

3,135,006, and so infer that the operation is correct.

2. 483, 1000, 8000, 648, 3750, 9840.

3. 15, 603, 1145, 6342.

4. 41, 725, 60, 425, 7000, 4900, 398.

5. 39, 876, 5742, 3000, 478, 9873.
6. 327, 4960, 5000, 749, 3000, 7849.

7. 4284, 32, 679, 43, 5006, 7897.

8. 325, 6007, 983, 4050, 678, 9874.

9. 856, 9193, 8765, 4287, 6696, 9185, 979.

10. 7964, 5000, 303, 9784, 5673, 9004.

11. 9007, 34, 6876, 400, 9344, 7879.

12. 45,678, 96, 375, 4784, 9673, 11,980.

13. 7865, 3586, 4321, 8576.

14. 900,542308,970 + 555,674 + 498,785.

15. 456,789304,590 +600,792 + 480,893 +514,763. 16. 357,963478,497 +323,484 + 596,372 +300,409. 17. 706,96378,405 +907,342 +503,476.

18. A man bought a sleigh for $142, a carriage for $325, and a pair of horses for $476. What was the cost of all?

19. A man collected on Monday, $1290; on Tuesday, $340; on Wednesday, $1008. How much was collected in all?

20. A lady paid $912 for a piano, $342 for furniture, $187 for linen, $46 for silver. What did she pay for all? 21. A farmer had in one flock of sheep, 407; in another, 96; and in a third, 2584. How many had he in all?

22. A man owns four houses; the first is worth $47,050; the second, $9106; the third, $1492; the fourth, $512. What is the value of them all?

23. Five loads of flour weighed as follows: 3500 pounds, 4967 pounds, 3974 pounds, 7982 pounds, 7963 pounds. What was the weight of the whole?

24. A house was bought for $7895; repairs amounted to $1500; new fences, $97; repairs on stable, $463; furniture, $1285. What was the cost of the whole? towns is: 1674, 9008, 3769, 4000, 7096, 3784. Find the whole population. 26. A house-lot cost $675; for building the house and fur

25. The population of six

nishing materials the carpenters were paid $2245,

the masons $540, the painters $320. What was expended on house and lot?

27. A merchant bought carpets to the amount of $4670; curtains, $300; paper-hangings, $1275; matting, $9765. What was the cost of the whole?

28. Find the sum of three hundred thousand six hundred fifty, seven thousand eight hundred thirty-two, eleven thousand five hundred sixty-seven, ten thousand fiftysix, four hundred seventy-two.

29. Find the sum of one hundred sixty-seven thousand, three hundred sixty-seven thousand, nine hundred six thousand, two hundred forty-seven thousand, ten thousand, seven hundred thousand, nine hundred seventy-six thousand, one hundred ninety-five thousand, ninety-seven thousand.

30. Find the sum of two hundred seven, three hundred

sixty-two, nine hundred forty-five, two thousand three hundred forty-three, fifteen thousand six hundred twenty-two, forty-five thousand eight.

31. Add 3 thousand 4 hundred 92, one thousand four, 6 thousand 5 hundred seventy, 42 hundred eleven. 32. Add 386 million 591, 546 million 311 thousand 122, 796 thousand 351, 84 hundred 1, 9 thousand, 86 thousand 521, 3 hundred fifty-eight thousand 6 hundred, 8 million 888 thousand eight hundred eightyeight, 1 hundred million.

33. Find the sum of six million sixty thousand six, seven million nine hundred fifty thousand ninety-nine, ten

million nine thousand eight hundred seven, three hundred sixty-seven thousand forty-five.

34. Find the sum of 200 million 302 thousand, 200 thousand two hundred, 50 million 50 thousand 50, 25

million 860 thousand, 47 million 467 thousand, 202 million 6367.

35. What is the sum of eighteen thousand three hundred twenty, seventy-four thousand five hundred six, ten hundred seventeen thousand nine hundred twentyone, fifty-three thousand seven hundred eleven, five hundred seventy-six thousand three hundred four, six hundred fifty thousand forty-four?

36. A man drew five loads of bricks; in the first load there were 4068; in the second, 1342; in the third, 3927; in the fourth, 1694; in the fifth, 2009. How many in all the loads?

37. What is the united population of the following cities: Utica, 28,804; Lowell, 40,928; Lynn, 28,236; Salem, 24,100; Erie, 19,500; Auburn, 17,225?

38. A fruit-grower sent to market the produce of six peach orchards; from the first, 7000 baskets; from the second, 6973; from the third, 1004; from the fourth, 3276; from the fifth, 1594; from the sixth, 3976. How many baskets in all?