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3. Required the sum of the following numbers:

11. 6, 9, 7, 5, 8, 4.
12. 7, 4, 1, 6, 3, 8.
13. 3, 9, 2, 7, 5, 1.
14. 9, 6, 5, 2, 8, 7.
15. 5, 6, 4, 7, 1, 8.
16. 5, 2, 8, 6, 3, 4.
17. 7, 3, 5, 8, 6, 1.
18. 9, 5, 9, 4, 6, 8.
19. 3, 6, 8, 5, 6, 3.

1. 4, 5, 2, 4, 8, 6.

2. 7, 6, 4, 8, 5, 3.
3. 9, 3, 5, 6, 4, 2.
4. 8, 6, 8, 5, 2, 3.

5. 4, 3, 8, 6, 5, 4.

6. 8, 9, 3, 1, 9, 4.

7. 6, 7, 9, 4, 5, 6.

8. 4, 9, 3, 6, 8, 2.

9. 7, 3, 4, 8, 2, 5.

10. 4, 7, 5, 6, 2, 4.

20. 7, 4, 9, 4, 9, 3.

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WRITTEN PROBLEMS.

1. A book-agent sold 3 books every day for six days. How many books did he sell in the six days?

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NOTE. Let the pupil indicate the solution of each problem in this

way.

2. In a family are six children; the youngest is 2 years old. Each of the other five is 2 years older than the one next younger. What is the age of the oldest?

3. A tree was broken off 9 feet from the ground; 8 feet of the piece broken off lies upon the ground, and the remaining 7 feet of it lies in water. How high was the tree?

4. A book-case contained 5 shelves. The librarian removed 9 books from the fifth shelf, 8 books from the fourth, 5 books from the third, 7 books from the second, and 4 books from the first. How many books did he remove from the case?

5. A man on examining his purse found therein 5 dimes, 4 quarter-dollars, 3 dollars (silver), 2 half-dollars, and one eagle. How many pieces of money had he?

6. I have three different measures: gill, pint, quart. The pint contains 4 gills, the quart 8 gills. How many gills do the three measures contain?

7. If a pint of water weighs one pound, and 2 pints equal 1 quart, and 8 pints equal 1 gallon, how much does the water in a pint, a quart, and a gallon measure weigh?

8. John, James, George, and Henry were solving problems. John solved 5, James solved 4, George as many as both John and James. Henry copied the 4 that James did. How many problems were solved?

9. A room is 9 feet long, 9 feet wide, and 8 feet high. How long a line would measure twice across the width of the room and then up to the ceiling?

10. Some articles on my desk measure as follows: A pen-holder, 7 inches; a steel ink-eraser, 7 inches; a pair of dividers, 6 inches; a lead-pencil, 5 inches; a paper-cutter, 8 inches; and a fountain-pen, 7 inches. Find the combined length of the six articles.

11. On a wintry holiday 6 boys and 4 girls, set free from school, went skating; 7 girls and 5 boys went coasting; 4 boys built a snow man, and 2 a snow fort. Find the number of boys, the number of girls, and the number of pupils the school contained.

12. A street-vender sold to some boys 4 apples for 8 cents, 3 oranges for 9 cents, 2 pears for 6 cents, 5 lemons for 9 cents, and 2 peaches for 4 cents. How many units of fruit did he sell, and how many cents did he receive?

13. A school-girl wrote in her copy-book 7 lines on Monday, 8 lines on Tuesday, 6 lines on Wednesday, 5 lines on Thursday, and 7 lines on Friday. How many lines did she write during the week?

14. Find the sum of 1, 2, 3, 4, 5, 6, 7, 8, 9.

15. Change to Arabic numerals the following Roman numbers, and find their sum: III., IX., VIII., V., IV., VI.

ORAL EXERCISES.

1. How many are:

1. 10 cents and 10 cents?

10 and 10?

2. 10 dollars and 20 dollars? 10 and 20?

3. 10 tops and 30 tops? 10 and 30?

4. 30 books and 10 books?

30 and 10?

35 and 10?

10 and 40?
40 and 10?
40 and 8?
10 and 18?

5. 35 books and 10 books?
6. 10 books and 40 books?
7. 40 men and 10 men?
8. 40 men and 8 men?
9. 10 men and 18 men?
10. 20 ships and 16 ships?

2. Count by:

1. 10's from 0 to 100.
2. 10's from 5 to 95.
3. 10's from 7 to 97.
4. 10's from 8 to 98.
5. 10's from 9 to 99.
6. 20's from 0 to 100.
7. 20's from 2 to 102.
8. 20's from 3 to 103.
9. 30's from 5 to 95.
10. 30's from 10 to 100.

20 and 16?

From 2 to 92.
From 4 to 94.
From 3 to 93.
From 19 to 90.
From 1 to 101.
From 5 to 85.
From 6 to 86.
From 7 to 87.
From 8 to 98.

From 9 to 99.

Addition of Several Columns.

WRITTEN EXERCISES.

1. Find the sum of $357, $470, $534.

Process.

$357

470

534

Explanation.

Explain, speaking thus: "Since the numbers express the same kind of thing, they are like numbers, and their sum can be found. In accordance with the same principle, we write units of the same order in the same column, and proceed thus: 4 units + 7 units = 11 units 1 ten and 1 unit; 1 ten 3 tens +7 tens + 5 tens 16 tens = 1 hundred and 6 tens; 1 hundred + 5 hundred 4 hundred + 3 hundred hundred 1 thousand and 3 hundreds. Hence, the sum is $1361."

$1361

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Repeat the principle on which your work depends.

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What is a unit? What is the unit of each of the numbers added? What is the unit of their sum?

Can the unit of the numbers added and the unit of their sum ever be different?

Brief directions are:

1. Write units of the same order in the same column. 2. Begin at the right to add.

3. Add the columns separately.

4. When tens of any order appear, carry them to the next column.

5. Write the entire sum of the last column.

6. Prove by adding each column in reverse order.

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When dollars and cents are written in columns, do not the

decimal points form a column?

Did you place a decimal point in each sum directly under

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4. Add 4795, 3084, 3970, 6952, 7964.

5. Add 5968, 3075, 493, 3980, 77.

6. Add 2325, 2642, 5236, 8230, 3616, 21.

7. Add 4836, 658, 816, 636, 1158, 6.

8. Add 52055, 3650, 62055, 4268, 13670, 231. 9. Add 46632, 5056, 64645, 5565, 66646, 54532. 10. Add $75.32, $27.25, $76.37, $27.54, $72.37. 11. Add $617.64, $763.55, $377.07, $767.76, $735.67. 12. Add $767.37, $54.76, $67.54, $476.71, $32.55.

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