WRITTEN EXERCISES.

15.-1. What is the sum of 65 and 87?

PROCESS. 65 87

152, Ans.

For convenience we write the numbers with units under units and tens under tens, and begin at the right to add. The sum of 7 units and 5 units is 12 units, which equal 1 ten and 2 units; we write the 2 units under the column of units, and add the 1 ten to the column of tens.

The sum of 1 ten, 8 tens, and 6 tens is 15 tens, which equal 1 hundred and 5 tens; we write the 5 tens under the column of tens, and place the 1 hundred on the left in the place of hundreds.

2. What is the sum of 455, 789, and 347?

PROCESS.

455

789

347

1591, Ans.

In practice we name results only in adding; thus, we say 7, 16, 21; write 1 and carry 2.

Then 2, 6, 14, 19; write 9 and carry 1.

Then 1, 4, 11, 15; write 15.

PROOF.-Begin at the top and add downward; if the two

results agree, the work is probably correct.

387 205 562

785

3.72 4.67 8.71

12. The cost of tuition of the public schools of Pennsylvania for 1892 was $7,766,657.16, and the cost of fuel for the same year was $3,301,159.51; what was the difference between the cost of tuition and the cost of fuel?

13. Philadelphia paid for teachers' salaries during the year 1892, $1,738,637.25, for school buildings $574,845.31, and for fuel, etc. $351,126.05; how much more did the city pay for teachers' salaries than for buildings and fuel?

14. The population of New York in 1880 was 5,082,871, and of Pennsylvania 4,292,891. In 1890 the population of New York was 5,997,853, and of Pennsylvania 5,258,014; how much more did Pennsylvania gain in ten years than New York?

15. The receipts and expenditures of the United States government for the last six months of 1893 were as follows:

Receipts.

July, $30,905,776.19

Aug., 23,890,885.30

Sept., 24,582,756.10

Oct., 24,553,394.97

Nov., 23,079,400.81

Dec., 22,312,027.00

Expenditures.

$39,675,888.60

33,305,228.48

25,478,010.17

29,588,892.34

31,302,026.41

83-102. Add each group by columns and by lines

341 + 467 +508 + 632 = 263 + 821 + 700 + 216 = 567 + 463 + 436 + 348 = 873 + 562 + 321 + 516 = 142 + 702 + 786 + 922 = 378 + 433 + 105 + 483 ==

421 + 322 + 234 + 621 = 812 + 444 + 423 + 578 = 287 + 555 + 342 + 760 = 359 + 666 + 167 + 420 = 614 + 777 + 761 + 706 = 786 + 888 +504 + 933 =

103. What is the sum of 80965 + 6789 + 1940 + 2071 + 8900 + 6886 + 904 + 17895 + 7907 +999 + 90899.

PRACTICAL PROBLEMS.

1. A farmer bought three horses: the first cost $275, the second $360, and the third $416; what did they all cost?

2. The distance from Harrisburg to Hagerstown is 74 miles, from Hagerstown to Roanoke 240 miles, from Roanoke to Bristol 150 miles, from Bristol to Chattanooga 242 miles; how far from Harrisburg to Chattanooga by this route?

3. A bought 7590 pounds of pea coal, 3765 pounds of nut coal, 6834 pounds of stove coal, and 2505 pounds of bituminous coal; how much coal did he purchase?

4. A dealer in eggs packed 1080 eggs in a barrel, nine hundred in a second, 1008 in a third, and eleven remained; how many eggs had he altogether?

5. How much money did four harvest-hands earn if Mr. Jones earned $23.16, Mr. Piper $22.02, Mr. Herr $30.30, and Mr. Binkley $14.40?

6. A florist sold eleven pinks for $1.10, forty roses for $5, thirteen lilies for $3.25, and two hundred geraniums for $10; how many flowers did he sell, and how much money did he receive for them?

7. A hunter shot 21 pheasants, one hundred and twenty-two pigeons, 300 rabbits, three wild turkeys, 33 wild ducks, and 10 snipe in a season; how many animals did he shoot?

8. Harold bought a wagon for $25, a sleigh for $10.50, a lap robe for $1.75, and a whip for $1.25; what was his bill?

9. A lady bought an extension-table for $12, a stove for $17.50, an oil-cloth for $2.25, bed-room suite for $95, a rockingchair for $11.15, some dishes for $45, carpet for $37.50, a lamp for $3.75, and a piano for $375; what was the entire bill?

10. A owes his grocer $7.95, his butcher $14.59, his tailor $16.78, his baker $6.37, his hired help $28: he also owes a coal-bill of $25.25, a wood-bill of $3.38, and school-tax of $2.12; how much does he owe?

11. In 1890 in New York City there were 312,706 families, in Chicago 220,320, in Philadelphia 205,135, in Brooklyn 170,970, in St. Louis 91,756, in Boston 86,716, in Baltimore 86,654, in Cincinnati 63,530, in Cleveland 53,052, and in San Francisco 52,535; how many families in these ten cities?

12. The superintendent of a factory received $1800 a year, the engineer $800, the fireman $600, the book-keeper $750, the fuel cost $1500, the raw material $111,000, and the pay-roll of the other employés amounted to $50,000; what were the expenses of the factory for the year?

13. Four men, A, B, C, and D, entered into partnership: A put into the business $1650, B put in $75 more than A, C put in $150 more than B, and D put in as much as A and C; what was the amount of money invested?

14. B paid $650 for a lot, on which he built a house for $5785, the fence around the lot cost $167, the pavement cost $243, and the plumbing cost $315. He sold the property and cleared $1200; what did he receive for it?

15. The number of immigrants coming into the United States in 1882 was 788,992; in 1883, 603,322; in 1884, 518,592; in 1885, 395,346; in 1886, 334,203; in 1887, 490,109; in 1888, 546,889; in 1889, 444,427; in 1890, 455,302; in 1891, 560,319; and in 1892, 623,084. How many immigrants arrived in the eleven years?

WRITTEN EXERCISES.

CASE I.

24. When the multiplier is one figure.

1. Multiply 396 by 7.

PROCESS.

Multiplicand, 396
Multiplier, 7

Product,

2772, Ans.

We write the multiplier under the units figure of the multiplicand, and begin at the right to multiply.

7 times 6 units are 42 units, or 4 tens and 2 units. We write the 2 units under the units column and add the 4 tens to the next product.

7 times 9 tens are 63 tens, plus the 4 tens are 67 tens, or 6 hundreds and 7 tens. We write the 7 tens under the tens column and add the 6 hundreds to the next product.

7 times 3 hundreds are 21 hundreds, plus the 6 hundreds are 27 hundreds, or 2 thousands and 7 hundreds, which we write in their proper places.

2. Multiply 956 by 8.

PROCESS.

In practice we say, 8 times 6 are 48; write 8 and carry 4. 8 times 5 are 40, and 4 are 44; write 4 and carry 4. 8 times 9 are 72, and 4 are 76; write 76.

956

8

7648, Ans.

3.

8. 3216 3

15-122. Multiply each of the following numbers by 4. By