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DEFINITIONS AND PRINCIPLES.

ART. 30.—Addition is the process of uniting two or more numbers into one.

ART. 31.—The Sum or Amount is the number obtained by addition. Thus, when 6 and 5 are added, the sum or amount is 11.

ART. 32.—The Sign of Addition (+) is called plus, and means more. When placed between two numbers, it shows that they are to be added. Thus, 7 + 6 is read ng plus 6, and means that q and 6 are to be added ; 9 + 3 + 2. is read 9 plus 3 plus 2, and means that 9, 3 and 2 are to be added.

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ART. 33.-The Sign of Equality (=) is read equals. It shows that the expression on the left of the sign is equal to the expression on the right of that sign. Thus, 10 + 6 16, is read 10 plus 6 equals 16, and means that when 10 and 6 are added, the sum is 16; 12 + 9 21, is read 12 plus 9 equals 21, and means that when 12 and 9 are added, the sum is 21.

The dollar sign ($) is placed before the number to which it belongs. Thus, for convenience, 275 dollars is written $275.

Cents written either alone or with dollars, occupy two places on the right of dollars, from which they are separated by a period called the decimal point. Thus, 24 dollars 36 cents, is written $24.36; 75 cents is written $.75.

ART. 34.–Principles. 1. Only like numbers can be added.

2. The sum or amount is of the same kind as the numbers added.

ORAL EXERCISES.

ART. 35.-1. Richard paid $8 for a coat and $7 for a pair of trousers : how much did the garments cost ?

Solution.—They cost the sum of $8 and $7, or $15.

2. Susan paid $14 for a sacque and $3 for a doll : how much did the two cost ?

3. Samuel paid $90 for a bicycle and $8 for his knickerbockers : how much did he pay for both ?

4. Johnson gave $30 to the missionary cause and $25 to the tract society : what was the amount of his contributions ?

5. A horse cost $120 and a carriage $80 : what was the cost of both ?

6. Thomas paid $.50 for a book and $. 75 for a knife : how much did the two cost ?

7. James rode 15 miles on the cars and 20 miles on the steamboat: how far did he ride ?

8. If there are 40 lines on one page of a book, how many lines are on two such pages ?

9. It is 14 miles from A to B and 18 miles beyond B is C: what is the distance from A to C ?

10. A merchant sold 24 yards of cloth on Monday and 36 yards on Tuesday : how many yards did he sell in the two days ?

11. John gave to his mother 8 apples, to his brother 6, and to his sister 5: how many did he give to the three ?

12. George has 10 cents in one pocket, 15 cents in another, and 20 cents in another : how many cents has he ?

13. Helen spelled 14 words on Wednesday, 14 on Thursday, and 12 on Friday : how many words did she spell?

14. Horace studied 15 minutes one afternoon, 25 another, and 30 another: how many minutes did he study during the three afternoons ?

15. Jenkins spent $.25 in one store, $.35 in another, and $.45 in a third : how much did he spend ?

16. James earned 18 cents on Monday, 15 cents on Tuesday, and 16 cents on Wednesday : how many cents did he earn ? 17. A farmer had three grape-vines.

The first produced 32 pounds of grapes, the second 40 pounds, and the third 48 pounds : how many pounds did all produce ?

18. A drover bought 37 sheep of one man, 35 of another, and 38 of a third : how many sheep did he buy ?

19. The price of a horse was $98, of a carriage $72, and of a harness $20 : what was the cost of all ?

20. An orchard contains 60 peach trees, 35 plum trees, and 25 pear trees : how many trees in the orchard ?

21. A lady paid $38 for a dress, $18 for a shawl, and $8 for a bonnet : how much did she pay for all ?

22. A pole is 22 feet in the air, 19 feet in the water, and 11 feet in the earth : what is the length of the pole?

23. There are 45 pupils in one school-room, 48 in another, and 53 in a third : how many pupils in the three rooms ?

24. Mr. Harper was 47 years old 12 years ago : how old will he be 9 years hence ?

25. A horse was sold for $120, which was $15 less than it cost : for what should it have been sold to gain $25 ?

26. John has 45 cents and Mary 35 cents : if each had 15 cents more, what would be the sum possessed by both

WRITTEN EXERCISES.

ART. 36.-1. What is the sum of 482, 324, 473, and 638 ?

Process. Analysis.—We write the numbers so that units

of the same order stand in the same column, draw 482

a line underneath, and begin at the right to add. 324 473

Beginning with the order of units, we add each 638

column separately. Thus, 8 + 3 + 4 + 2 = 17 units,

equal to 1 ten and 7 units. We write 7 in the units' 1917

place and add the 1 ten with the column of tens.

One ten from the units' column + 3 + q + 2 + 8 = 21 tens, equal to 2 hundreds and 1 ten. We write 1 in the tens' place and add the 2 hundred with the column of hundreds.

Two hundred from the tens' column + 6 + 4 + 3 + 4 = 19 hundreds, equal to 1 thousand and 9 hundreds, which we write in their proper places.

Therefore, the sum of 482, 324, 473, and 638 is 1917.

NOTE.-In adding, name results only. Thus, instead of saying 8 and 3 are 11 and 4 are 15 and 2 are 17, say 8, 11, 15, 17.

ART. 37.-Rule for Addition.— Write the numbers SO that units of the same order stand in the same column, draw a line underneath and begin at the right to add.

If the sum of any column is less than 10, write it under the column. added ; and if 10 or more, write the units' figure under the column added, and add the ten or tens with the next column. Write the total sum of the last column.

Proof.-Begin at the top and a ld each column downward. If the sums agree, the work is probably correct.

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14. Add seven thousand forty-nine; eighty-eight thousand six hundred ; three million four hundred thirtytwo thousand ninety-nine ; sixteen million six hundred thousand six hundred.

15. Add nineteen million thirty-eight thousand twenty-five; four hundred thousand eight hundred eight; one billion one hundred twenty-four thousand ninetytwo; three hundred thousand two hundred eighty-five.

16. What was the total amount of taxes received by the city of Trenton during the week in which the receipts were as follows: Monday, $13,845.50; Tuesday, $9,842.28; Wednesday, $6,584.90 ; Thursday, $11,094; Friday, $10,956.51 ; Saturday, $17,328.48 ?

17. The mariner's compass was invented in China 1120 years before Christ, and America was discovered 1492 years after Christ : how many years between the dates ?

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