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§ 22. ADDITION consists in finding the sum or aggregate

amount of two or more numbers.

Thus the sum of 4 and 5 is 9; or 5 added to 4 makes 9.

What is the sum of 7 and 3? Of 6 and 4? Of 8 and 5?

The Sum found may be regarded as a whole, of which the given numbers are the parts.

What is the sum of 4, 6 and 8?

Then what is the whole, and what

are its parts? What is the sum of 10, 4, and 3?

whole, and what are its parts?

Then what is the

$ 23. The whole is equal to the sum of all its parts.

Recite the elementary sums of numbers; thus 1 and 1 are 2; 1 and 2 are 3; &c.-2 and I are 3; 2 and 2 are 4; &c., as given from left to right in the

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are 77 are 88 are 99 are 10 are 76 are 870 are 98 are 109 are 11

414

are 5|5

are

616 are 7

54.

are

6|5

are 8 86 are 917 are 10 8 are 119 are 12

are 5/3 are 6/4 are

are

6|3 are 74

are

7/3

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are

7/5

85 are 9 9/6 are 10 7 are 118 are 129 are 13

are 84 are 95 are 106 are 11 are 12 8 are 139 are 14

are

9/4 are 10/5 are 11 6 are 127 are 13 8 are 14 9 are 15

7 and 1 are 8 82 are 9 93 are 10 4 are 115 are 126 are 137 are 14 8 are 15 9 are 16 Sand 1 are 92 are 10 3 are 11 4 are 125 are 136 are 147 are 15 8 are 16 9 are 17 9 and 1 are 10/2 2 are 11 3 are 12 4 are 135 are 14|6 are 1517 are 16 8 are 17 9 are 18 10 and 1 are 11 2 are 123 are 134 are 145 are 15/6 11 and 1 are 122 are 13/3 are 14 4 12 and 1 are 132 are 14|3 are 15/4

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Sign of Addition.

$ 24. The sign +, called plus, placed between numbers, signifies that the numbers are to be added together.

Thus 5+4, 5 plus 4, signifies 5 and 4 added together.

What is the sum of 4+3+2? Of 6+4+8? Of 7+3+4+6? Sum of Concrete Numbers.

$ 25. The sum of similar concrete numbers, is a concrete number of the same kind.

Thus, the sum of 5 cents and 4 cents is 9 cents.

What is the sum of 6 pounds + 5 pounds? Of 7 days + 3 days + 5 days? Of 10 miles 9 miles? Of 12 pints + 6 pints+2 pints?

$ 26. Dissimilar concrete numbers cannot be united in one number.

Thus we cannot add 5 cents and 3 days together.

RULE III.

$27. To Add two or more Numbers together.

1. Set the numbers one under another, with units under units, tens under tens, &c.

2. Proceeding from right to left, add up each column of figures, and under each set its amount, if less than 10.

3. If the amount be 10 or more, set down its right hand figure, and add the left figure or figures to the next column. Set down the whole amount of the last column.

EXAMPLE.

To find the Sum of 930+6754+8621

930

6754

8621

16305

Having set units under units, tens under tens, &c., we say 1 and 4 are 5, and set 5 under the units' column.

Then, 2 and 5 are 7, and 3 are 10. We set the 0 under the tens' column, and add or carry the 1 to the next column; thus 1 and 6 are 7, and 7 are 14, and 9 are 23. We set 3 under that column, and say 2 and 8 are 10, and 6 are 16.

The left hand figure in the amount of any column, denotes the number of tens in that amount; and these tens are so many units when carried to the next column on the left. (§ 11.)

In the preceding example, the amount of the tens' column is 10 tens. But 10 tens being 1 hundred, we set down no tens, and add 1 to the hundreds' column,-which makes 23 hundreds, or 2 thousands and 3 hundreds. The 3 is put in the hundreds' place, and the 2 is added to the thousands' column, making 16 thousands.

By thus carrying one for every ten, from right to left, we find the number belonging to each distinct order of units in the sum of the several numbers. The whole is equal to the sum of all its parts.

The Operation Proved.

§ 28. Addition may be verified or proved, by adding the several columns of figures downwards; the Sum must be the same as when they are added upwards.

Thus to prove the operation in the preceding example, we begin at the top, and say 4 and 1 are 5; then 3 and 5 are 8, and 2 are 10. Setting down the 0, and carrying the 1, we say 1 and 9 are 10, and 7 are 17, and 6 are 23; then 2 and 6 are 8, and 8 are 16.

The Sum found is the same as before.

EXERCISES.

1. John has 95 chestnuts, Thomas has 180, and Charles 270; what number have they all together?

The whole number of chestnuts will be found by adding together 95, 180, and 270. Answer, 545 chestnuts.

2. A farmer being asked how many sheep he had, replied: "in one field I have 410, in another 500, in another 602." How many had he? Ans. 1512 sheep.

3. A merchant bought cloth for 375 dollars, linen for 83 dollars, silk for 234 dollars, and calico for 75 dollars. What sum did he expend for the whole ? Ans. 767 dollars.

4. A gentleman bought a carriage for 350 dollars, a pair of horses for 240 dollars, and a set of harness for 100 dollars. What did the whole amount to? Ans. 690 dollars.

5. Going out to collect money, I received from one person 13 dollars, from another 124 dollars, from another 89 dollars, and from another 20 dollars. What was the whole sum collected? Ans. 246 dollars.

6. Suppose a man should raise on the several fields of his farm the following quantities of grain, viz: 685 bushels, 97 bushels, 330 bushels, and 1000 bushels,-how many bushels would he raise altogether? Ans. 2112 bushels.

7. Allowing a person's estate to be estimated as follows, viz: real estate 9000 dollars, personal property 1375 dollars, recoverable debts 875 dollars, and cash 300 dollars,-what would be the value of his estate? Ans. 11550 dollars.

8. Admitting I bought of A 500 bushels of wheat, of B 934 bushels, of C 83 bushels, and of D 125 bushels,-how many bushels did I buy in all ? Ans. 1642 bushels.

9. Three persons deposite flour in the same warehouse; the first, 43 barrels; the second 150 barrels; and the third, 89 barrels. What quantity do they all deposite? Ans. 282 barrels.

10. A merchant bought four pieces of cloth; the first for 225 dollars, the second for 310 dollars, the third for 279 dollars, and the fourth for 95 dollars. What did the whole cost him?

Ans. 909 dollars.

11. If a merchant buy a stock of goods for 5000 dollars, for what sum must he sell the goods so as to gain by them 475 dollars? Ans. 5475 dollars.

For

12. Bought a barrel of sugar for 15 dollars, a barrel of molasses for 13 dollars, and a sack of coffee for 20 dollars. what sum must the whole be sold to gain 10 dollars?

Ans. 58 dollars.

13. A person on a journey travels, the first week 255 miles ; the second, 240 miles; the third and fourth, each 200 miles. How far did he travel in the four weeks? Ans. 895 miles.

14. Four persons, A, B, C, and D, engage in speculation. A gains 75 dollars, B 100 dollars, and C and D each 235 dollars; what sum was gained by all together? Ans. 645 dollars. 15. A farmer bought three plantations for 3750 dollars each, and sold them again so as to make 1000 dollars on the whole. For what sum did he sell the three. Ans. 12250 dollars.

16. A draper sold four bales of linen; the first and second contained each 480 yards; the third and fourth each 542 yards. How many yards did he sell? Ans. 2044 yards.

17. Bought of A 325 bushels of wheat; of B, 280 bushels; of C as much as from A; and of D as much as from B. What quantity of wheat did I buy in all? Ans. 1210 bushels.

18. A merchant bought at one time 375 barrels of flour, for 1875 dollars; and at another 400 barrels for 2000 dollars. What quantity of flour did the merchant buy, and for what sum ? Ans. 775 barrels, for 3875 dollars.

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Ans. 11035.

Ans. 5552.

Ans. 6424.

19. Find the Sum 345+480+2346+7864.
20. Find the Sum 201+342+4000+1009.
21. Find the Sum 804+4364+25+1231.
22. Find the Sum 58603+75+49+2400.
23. Find the Sum 73846+37+63+9000.
24. Find the Sum 7+43+479+8+3703.
25. Find the Sum 9+60+340+4+8264.
26. Find the Sum 5+50+600+8+8900.
27. Find the Sum 6+10+100+9+1000.

Ans. 61127.
Ans. 82946.
Ans. 4240.
Ans. 8677.

Ans. 9563.

Ans. 1125.

28. A lends to B 2500 dollars; to C 3000; and has 5325 dollars left. What sum had A at first? Ans. 10825 dollars.

29. A speculator bought stock at one time for 325 dollars; and at another time for 705 dollars. In selling the whole, he realized a gain of 175 dollars; for what sum did he sell?

Ans. 1205 dollars. 30. A gentleman is 15 years older than his wife, and she is 20 years older than their eldest son, who is 29 years of age. Required the gentleman's age, and the age of his wife?

Ans. His age is 64 years; hers 49. 31. A, B, and C form a partnership in trade. A puts in 4250 dollars; B, 2000 dollars; and C as much as A and B together; what is their whole stock in trade? Ans. 12500 dollars.

32. Bought at one time 75 yards of cotton, and 100 yards of linsey; at another, 37 yards of cotton, and 87 yards of linsey; and at another, 125 yards of cotton, and 9 yards of linsey. What quantity of each kind did I buy?

Ans. 237 yards of cotton, and 196 of linsey. 33. A merchant bought cloth for 375 dollars, and silk for 95 dollars. In selling, he gained 50 dollars on the cloth, and 45 dollars on the silk; for what sum did he sell the whole ?

Ans. 565 dollars.

34. A grocer paid 300 dollars for sugar, 174 dollars for coffee, 85 dollars for rice, and 56 dollars for tobacco. He sold the sugar at a profit of 25 dollars, and the other articles at cost; what did he get for the whole? Ans. 640 dollars.

35. A father bequeaths to his only daughter 2500 dollars, and to each of his two sons, 500 dollars more than to his daughter. What sum did each son receive, and what was the amount of the several bequests? S Each son, 3000 dollars, Amount, 8500 dollars.

Ans.

36. Several persons contributed towards the establishment of a library. A gave 200 dollars, and B 50 dollars more than A; C gave 300 dollars, and D 25 dollars more than C. What was the whole amount contributed? Ans. 1075 dollars.

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