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22. Find the sum of 36875+28764+3128+6785+3876+ 38521+46212.

Ans. 164161. 23. Find the sum of 41287, 32104, 80010, 678910, 136710, 896343. 257856.

Ans 2123220 24. Find the sum of 67851, 21856, 38214, 621857, 36724, 128705, 1250641.

Ans. 2165848. 25. Find the sum of 20875, 318764, 287656, 318567, 208725, 387124, 411403.

Ans. 1953114. 26. Find the sum of 218765, 865432, 896, 32481, 2879823, 8128765, 1759824.

Ans. 13885986. 27. Find the sum of 61857, 30876, 14687, 318572, 856, 30876, 12345, 678910, 328764.

Ans. 1477743.

MENTAL EXERCISES.

1. Rose gave 15 cents to her brother and 8 cents to her sister; how much did she give to both ?

SOLUTION.-If Rose gave 15 cents to her brother and 8 cents to her sister, to both she gave 15 cents plus 8 cents, which are 23 cents.

2. What is the cost of a suit of clothes if the material cost $25 and the making cost $10?

3. If a boy has 12 cents and then earns 15 cents, how many cents will he then have ?

4. The head of a fish is 6 inches long, the tail 8 inches, and the body 12 inches; what is the length of the tish?

5. How many are 18 and 6? 17 and 8? 21 and 7? 25 and 8? 36 and 8? 42 and 77 48 and 67 57 and 7?

6. How many are 8 and 24? 9 and 26? 7 and 35? 6 and 48 ? 5 and 477 4 and 48? 3 and 68?

7. How many are 105 and 6? 108 and 7? 115 and 8? 124 and 61 135 and 59 140 and 77 155 and 8?

8. How many are 6 and 135? 5 and 206? 7 and 208? 4 and 2121 7 and 234? 8 and 326? 300 and 400?

9. Howard shot 11 robins, Howell shot 12 robins, and Hoyt shot 13 robins ; how many robins did they all shoot ?

10. A boy bought a robin for 10 cents, a jay for 20 cents, and a wren for 30 cents; what did they all cost ?

11. A lady gave 6 cents for needles, 12 cents for thread, and 25 cents for some muslin ; what was the entire cost?

12. What is the sum of 28 and 37?

SOLUTION.-28 and 30 are 58, and 7 are 65.

13. What is the sum of 25 and 38? 27 and 36? 45 and 28? 47 nud 05? 67 and 487 73 and 48 ?

14. What is the sum of 29 and 46? 28 and 38? 76 and 46? 85 and 917 83 and 48? 96 and 69? 125 and 437 173 and 205?

15. Add by 7's from 7 to 98; from 1 to 99; from 2 to 100; from 3 to 101. Add by 8's from 8 to 120; from 2 to 122; from 3 to 123.

16. Add by 9's from 0 to 108; from 1 to 109; from 2 to 110; from 3 to 111. Add by 11's from 0 to 132; from 1 to 133; from 2 to 134.

17. Add by 12’s from 0 to 144; from 1 to 145; from 2 to 146; from 3 147; by 13's from 13 to 130; from 1 to 131; etc.

18. Add aiternately by 4 and 5 till the sum exceeds 100; by 5 and 6; by 6 and 7; by 8 and 9; by 9 and 10; by 11 and 12.

19. A merchant sold some rice for $15, some sugar for $17, and some flour for $22; what was the amount of the sale?

WRITTEN EXERCISES.

OPERATION

1. A farmer raised 857 bushels of wheat, 372 bushels of rye, 720 bushels of oats, and 876 bushels of

corn; bow

many bushels of grain did he raise ?

SOLUTION.-If he raised 857 bushels of wheat, 372 bushels of rye, 720 bushels of oats, and 876 bushels 857 of corn, he raised in all the sum of 857 bushels, 372

372 bushels, 720 bushels, and 876 bushels, which we find 720 by adding, to be 2825 bushels.

876

2825 2. A lady owns a farm worth $8326, a house worth $6575, a barn worth $3818, and $7584 in State bonds; what is she worth?

Ans. $26303. 3. A grocer paid $897 for flour and $759 for sugar; for what must both he sold that the grocer may gain $125 on the transaction?

Ans. $1781. 4. In a graded school there are 29 pupils in the first sec. tion, 42 in the second, 38 in the third, 45 in the fourth, 51 in the fifth, and 63 in the sixth ; how many pupils are there in the whole school?

Ans. 268 pupils. 5. A merchant “checked” out of bank $2560 one day, $3065 the next, $2780 the next, and then had $5760 in bank: how much had he in bank at first?

Ans. $14165 6. A dealer bought 450 barrels of wheat flour for $2700, and 286 barrels of rye flour for $1416; how many barrels did be buy and wbat was the whole cost? Ans. $4116.

7. A gentleman dying left his eldest son $7286, the next younger son $9111, and the youngest as much as both the others; what was the fortune?

Ans. $32794. 8. Bought calico for a dress for $2, a neck-tie for $0.45, a parasol for $3.50, a pair of boots for $4.25, and a pair of gloves for $1.75; what was the whole cost? Ans. $11.95.

9. A speculator bought three city lots for $5750 each; for what must he sell them that he may gain $2367 by the investment?

Ans. $19617. 10. Mr. Bowman paid $628 for flour, $382 for sugar, and $125 for potatoes; how much did he receive for all if he sold them at a gain of $324 ?

Ans. $1459. 11. A boy bought an arithmetic for 95 cents, a grammar for 65 cents, a history for 75 cents, a geography for $1.88, a piece of India-rubber for 5 cents, and a pencil for 3 cents; wbat was the whole cost?

Ans. $4.31. 12. A merchant pays his book-keeper $1500 a year, three salesmen $750 each, a porter $450, and a boy $200; what amount of salaries does he pay?

Ans. $4400. 13. A young man paid $450 for a borse, $115 for a sleigh, $137.50 for a harness and bells, and $33.35 for a robe; what was the cost of the whole outfit?

Ans. $735.85. 14. At an auction a woman bid off a marble-topped bureau at $19.50, a dozen cane-seat chairs at $15.00, a carpet at $31, a small rug at $1.50, and a dozen china dinner plates at $1.75; what was her bill?

Ans. $68.75. 15. A schooner sailed from Milwaukee to Erie, having on board 12391 bushels new No. 3 Milwaukee wheat, 11420 bushels Mixed Spring Minnesota wheat, and 1239 bushels common Winter Red Western wheat; of how many bushels did her cargo consist ?

Ans. 25050 bushels. 16. A dry goods merchant, in purchasing his stock, paid $650 for silks, $875 for woolens, $345.75 for cotton dress goods, and $795.45 for other goods; what did his stock cost?

Ans. $2666.20. 17. Mr. Anthony's balance in bank on Monday morning was $1546.75; that day he deposited $500; Tuesday be

deposited $350; Wednesday, $ 764.75; Thursday, $250; Friday, $640; Saturday, $54; how much did he have on deposit on the next Monday morning? Ans. $4105.50.

18. A builder bought a lot for $450, built upon it a house costing $3545, and a barn and carriage-house costing $847.50, fenced it at a cost of $127.50, and graded it at a cost of $77.25; for what must be sell the property in order to gain upon it $540?

Ans. $5587.25. 19. A Normal school paid, in 1875, $18,622.17 for salaries of professors and teachers, $1350 for salaries of other officers, $34,721.03 for board, washing, etc., $11,806.95 for servants! hire, and $7159.15 for other expenses; what were the

expenditures for the year?

Ans. $73,659.30 20. In erecting an academy, the trustees paid $250 for digging the cellar, $580 for laying the foundation walls, $12,575 for the brickwork, and $10,650 for the woodwork, plastering, etc.; what was the entire cost? Ans. $24,055.

21. Mr. Johnson's house cost for brick $450; for lumber, $780; other materials, $350 ; digging the cellar, $87.50; masons' and bricklayers' work, $425; carpenters' work, $789.75; painting, glazing, etc., $350; what was the whole cost of the house?

Ans. $3232.25. 22. In the year ending June 1, 1875, Pennsylvania expended for school-houses, $2,059,464.83; for teachers' wages, $4,746,875.52; for fuel and contingent expenses, $2,448,315.78; for other expenses, $109,270.94 ; $77.324.32 extra appropriation to city of Pittsburg; $85,815.84 for Normal schools; and $423,693.76 for Soldiers' Orphan schools; wbat was the wbole amount expended that year for education by the State ?

Ans. $9,950,760.99. 23. The cash value of farms in New York in 1870 was $1,272,857,766 ; in Pennsylvania, $1,043,481,582; in New Jersey, $257,523,376 ; in Ohio, $1,054,465,226; in Indiana, $634,804,189; in Illinois, $920,506,346; in Missouri, $392,908,047; in Wisconsin, $300,414,064; and in Michigan, $398,240,578; what is the total value of the farms in these States ?

Ang $6,275,201,174.

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CONTRACTIONS IN ADDITION. 60. Contractions in Addition are abbreviated methods of adding

61. There are several methods of abbreviating the process of addition, a few of which will be stated :

1. In adding omit naming the numbers added; merely name the results.

2. When two or more terms of a column can be easily grouped together, use their sum instead of adding each separately; combining with especial reference to TENS.

3. When a term is repeated several times in a column, multiply it by the number of times it is repeated, and use the result.

1. What is the sum of 8752+3687+2573+8576+2857 +6872 ?

1st METHOD.-We add thus: 2, 9, 15, 18, 25, 27; OPERATION. write the 7 and carry the 2; 2, 9, 14, 21, 28, 36, 41; 8752 write the 1 and carry the 4; etc.

3687 20 METHOD.—Thus: 9, 15, 25, 27, in which the 3

2573 and 7 are grouped and used as 10. We may also group 8576 2 and 6, 7 and 3, and then 7 and 2; thus, 8, 18, 27, etc.

2857 3D METHOD.-In the second column, we may take

6872 the three 7's, then the two 5's, and then the 8; thus, 21,

33317 31, 39, etc.

WRITTEN EXERCISES.
(2)
(3)
(4)
(6)

(6) 67854 41235 32106 $875.67 $365.75 61387 47368 21876 321.08 406.26 57854 47376 52382 345.67 57.38 87543 51847 36875 891.01 693.84 78587 63529, 42356 121.31 746.38 18234 17152 52873 415.16

25.06 34387 50381 61874 178.20

8.72 21857 27596 18027 222.32

45 50 31242 38273 25718 425.26 482.38 82356 54368 43281 272.82

29 45 14181 70305 25728 930.35

8.65 82815 75056 71890 363.73 682.50 71281 18293 12134 839.46 14.75 85427

52738 51617 876.54 937.18 18315 25382 82365 324.36

8.28 61038 32728 57634 484.95 473.54

442

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