How is addition proved? What is the reason for this proof? Ans. The same error, if any, is not likely to be repeated, when the same numbers are added in a different order.

Why do we find it convenient to begin with units to add? Ans. Because, if the sum of any column is greater than nine of the order added, we can readily add the number denoted by its lefthand figure or figures with the next column.

31. What is the sum of 9401, 105, and 47?

Ans. 9553.

32. What is the sum of 324 + 643 + 201 +46 ?

Ans. 1214.

33. What is the sum of 5684 +340 + 7006 +309 + 824?

34. 170640 +126+123 +11= how many?

Ans. 1070.

35. 36320+708 +17+3= how many?

Ans. 1084.

36. Find the sum of 31, 114, 3047, and 57183. 37. Find the sum of 19, 119, 11919, and 9191. 38. A farmer has four fields; the first yields 1109 bushels of corn, the second, 301, the third, 516, and the fourth 613; how many bushels do the four fields yield? Ans. 2539 bushels.

39. George Washington was born in the year 1732, and lived 67 years. In what year did he die?

When the sum of a column is ten or more, why is the right-hand figure of the sum written underneath? Ans. Because it expresses units of the order added.

40. In January there are 31 days, February 28, March 31, April 30, May 31, and June 30; how many days are there in these six months? Ans. 181 days.

41. I have bought six lots of coal, consisting of 210, 317, 258, 610, 516, and 311 tons, respectively; how many tons are there in all? Ans. 2222 tons.

42. What is the sum of nine hundred three, four thousand fourteen, fifteen, sixty-three, and three thousand three hundred two? Ans. 8297.

43. What is the sum of fifteen thousand fifteen, one thousand six hundred one, ten thousand one hundred ten, and seven hundred seventeen? Ans. 27443.

44. Paid for a farm 6715 dollars, for having it fenced 635 dollars, and for having a barn built upon it 500 dollars. For how much must it be sold to gain 200 dollars? 45. What is the extent of the British Isles, if Scotland has 30000 square miles, England 51200, Wales 7200, and Ireland 32500? Ans. 120900 square miles.

46. The United States is 3385000 square miles in extent, Brazil 3000000, Russia in Europe 2100000, France 204800, and Austria 259300; what is the extent of all these countries? Ans. 8949100 square miles.

Why is the number expressed by the left-hand figure or figures of the sum of a column added in with the next column at the left? Ans. Because ten units of the order added are one of the order next higher.

LONG COLUMNS.

Practise upon the following examples, until the numbers of each can be added correctly and rapidly, by

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REVIEW. What is a unit? (1.) What is Quantity? (10.) What are Numbers? (11.) What are Figures? (16.) What is Notation? (32.) What is Numeration? (36.) What is Addition? (39.) What is the result in Addition called? (40.) Recite the Rule for Addition. (42.)

43. 1. If John should have 6 trouts and his brother 4, how many more will John have than his brother?

2. Six trouts less 4 trouts are how many?

3. Six less 4 are how many?

4. Four and how many are six?

44. Subtraction is the process of finding the difference between two numbers of the same kind.

The DIFFERENCE, or REMAINDER, is the number left after the subtraction is performed. Thus,

The difference between 8 apples and 6 apples is 2 apples.

The SUBTRAHEND is the number subtracted.

The MINUEND is the number subtracted from.

The DIFFERENCE between two numbers is such а number as added to the smaller will equal the larger.

What is Subtraction? The Difference? The Subtrahend? The Minuend? The Difference between two Numbers?