year, 189 in the sixth year, 178 in the seventh year, and 157 in the eighth year.

pupils in the school?

How many

10. At an auction the following named sales are made stove for $15; chairs for $12.75; rugs for $45; pictures for $15.75; piano for $275; books for $24.50; table for $3.75; writing desk for $10.50; sofa for $7.50. What was the total

amount of the sales?

11. The railroad distance from New York to Albany is 144 miles; from Albany to Buffalo, 298; from Buffalo to Cleveland, 183; from Cleveland to Toledo, 109; from Toledo to Springfield, 365; from Springfield to St. Louis, 95 miles. What is the distance from New York to St. Louis by this route?

12. A man commenced farming in the West, and raised the first year 724 bushels of corn; the second year 3498 bushels; the third year 9872 bushels; the fourth year 9964 bushels; the fifth year 11078 bushels. How many bushels did he raise in the five years?

13. How many men in an army consisting of 52714 infantry, 5110 cavalry, 6250 dragoons, 3927 light-horse, 928 artillery, 250 sappers, and 406 miners?

14. A fruit dealer in Florida shipped for New York in one week 2464 boxes of oranges, 1632

boxes of pineapples, 1948 boxes of lemons, and

850 boxes of cocoanuts.

number of boxes shipped?

What was the entire

15. The area of Maine in square miles is 33040; of New Hampshire, 9305; of Vermont, 9565; of Massachusetts, 8315; of Rhode Island, 1250; of Connecticut, 4990. What is the area of the New England states in square miles?

CHAPTER III

SUBTRACTION

41. 1. What is the difference between 5 and 3¢? The answer to the above question may be found in two different ways:

1st. By adding to the smaller number until it equals the larger, as business men do in making change.

2d. By taking away the smaller number from the larger and noting what remains.

2. Mary is 13 years old and her brother is 8 years old. What is the difference in their ages?

3. A boy had 24 marbles and lost 16 of them.

4. A man had 15 bushels of potatoes and sold 5 bushels. How many bushels had he left?

5. Bought coffee for 754 and gave the clerk $1. How much change should I receive?

$1.00

- .75

The business man has learned to add

to the 75 as he counts out the change,

$ ? until he makes $1.

This method is much easier to learn, and also one by which we are much less likely to make mistakes. Begin at the 5, and reading down add as you read, saying 5 and 5, writing in the 5, are 10; then carry as in addition, and say, 8 and 2, writing the 2, make 10. You have written in 25, which is the right change.

6. Mr. Smith bought 18 tons of coal. How much was left after he had used 7 tons?

Proof: 7 tons that he used + 11 tons left make 18 tons, which he had at first.

7. From 925 subtract 476.

925 By the old-fashioned plan of subtrac476 tion, this was a long and hard example. 449 It was explained as follows: "The subtrahend is written under the minuend, and we begin at the right to subtract.

"Since 6 units cannot be subtracted from 5 units, one of the tens, which is equal to 10 units, is united with the 5 units, making 15 units. 6 units from 15 units leave 9 units, which are written under the units.

"Since one of the tens was united with the units, there is but 1 ten left. Because 7 tens cannot be subtracted from 1 ten, 1 hundred, which is equal to 10 tens, is united with the 1 ten, making 11 tens. 7 tens from 11 tens leave 4 tens, which are written under the tens.

"Since one of the hundreds was written with the tens, there are but 8 hundreds left. 4 hundreds. from 8 hundreds leave 4 hundreds, which are written under the hundreds. Hence the remainder is 449. Proof: 449, the remainder, plus 476, the subtrahend, equals 925, the minuend. Hence the result is correct."

By the additive plan, we work as follows:

925 Begin at the right-hand figure of the 476 lower number, and read down, adding in