add it to the 3 units, making 13 units, which sum we place in brackets over the 3 and mark out the 3. We can now subtract the 7 from the 13. We next seek to subtract the 6 from the 4, which we cannot do. We must then seek one from the hundreds' place to be added to the 4. But there are no hundreds there. We then go to the thousands' place. Taking one from the 8, we have 7 left. Place the 7 in brackets over the 8 and mark out the 8. The 1 thousand we carry to the hundreds' place, where it counts 10 hundred; place the 10 over the zero and mark out the 0. Then take 1 hundred from the 10 in the brackets, leaving 9, which, place in second brackets above, and mark out the 10; then add the 1, counting it as 10 tens, to the 4, and you have 14 tens, which place within second brackets over the 4 and mark out the 4.

Now we proceed with the subtraction; 6 from 14 leaves 8; 9 from 9 leaves 0; 4 from 7 leaves 3.

It will be noticed that the minuend appears in three different forms; yet the sum is the same in all. Thus, in the minuend proper, the sum is 8 thousands, 0 hundreds, 5 tens, 3 units; in the minuend in the first brackets, the sum is 7 thousands, 10 hundreds, 4 tens, 13 units; in the second brackets, 7 thousands, 9 hundreds, 14 tens, 13 units each form being equal to 8053,

NOTE. The preceding explanations are intended to show the reasons of the process. The pupil should perform similar operations without writing down the steps.

From 8275 subtract 7189.

From 6044 subtract 5272.

From 90000 subtract 1

Ans. 1086.

Ans. 772. Ans. 89999.

There is another mode, shorter and more practical, for performing subtraction, when figures in the subtrahend are larger than corresponding figures in the minuend.

Add, then, 10

tens cannot be subtracted from the 5 tens. tens to the 5, making 15 tens, and then say 7 from 15 leaves 8; having added 10 tens to the 5 of the minuend, we restore the balance by adding 1 hundred to the 9 of the subtrahend, making 10. But we cannot subtract 10 from 0. Then we add 10 hundred to the 0, and say 10 from 10 leaves 0. Before subtracting the thousands, we must add 1 to the 4 thousands to compensate for the 10 hundred added to 0, then say 5 from 8 leaves 3.

Ans. 25485.

From 64281 subtract 38796.

From what has been done, we deduce this

RULE.

I. Place the subtrahend under the minuend, so that units

may stand directly under units, tens under tens, &c.

II. Then commencing at the right, subtract each figure of the subtrahend from the corresponding figure of the minuend; observing, when a figure of the subtrahend is greater than the corresponding figure of the minuend, to increase the minuend by 10 before subtracting, and then to carry to the next figure of the subtrahend.

How do you place the numbers for subtraction? Where do you commence to subtract? Explain the method of subtracting when the figure in the subtrahend exceeds the corresponding figure of the minuend.

13. If the operation is rightly performed, the difference added to the subtrahend must equal the minuend.

10. From seven million three hundred and sixty-five thousand, two hundred and thirty-nine, take three hundred and forty-two thousand and thirteen.

Ans. 7023226.

11. From one million and eleven, subtract thirteen.

Ans. 999998.

12. From three hundred and sixty-five thousand, take three hundred and sixty-five

Ans. 364635.

13. America was discovered in 1492. How many years from that time to the year 1844?

Ans. 352 years.

14. If a man receive 11345 dollars, and pay out of it 9203 dollars, how much will he have remaining?

Ans. 2142 dollars.

15. In 1842 the Onondaga Salt Springs yielded 2291903 bushels of salt, and in 1826 they yielded 827505 bushels. How many more bushels were produced in 1842 than in 1826 ?

Ans. 1464398 bushels.

16. In 1842 the United States shipped to England 205154 barrels of flour, to Scotland 3830 barrels. How many more barrels were sent to England than to Scotland? Ans. 201324 barrels.

17. Two men start together from the same place, and travel in the same direction; one goes 63 miles each day, and the other goes 37 miles. How far apart will they be at the end of the first day?

Ans. 26 miles.

18. George Washington was born in the year 1732; he died in the year 1799. To what age did he live?

Ans. 67 years.

35

19. At an election 12572 votes are taken, of which the successful candidate received 7391. How many votes did the other candidate receive?

Ans. 5181 votes.

20. And what was the first one's majority?

Ans. 2210 votes.

21. The coinage of the United States mint for 1843 was in value 11967830 dollars, and in 1846 it was 6633965 dollars. How much greater in value was the coinage in 1843 than in 1846?

Ans. 5333865 dollars.

22. The total number of pieces coined in 1843 was 114640582, and in 1844 it was 9051834. How many more pieces were coined in 1843 than in 1844?

Ans. 105588748 pieces.

23. In the year 1846, the value of the gold coin produced at the mint was 4034177 dollars; the value of the silver coin was 2558580 dollars; and the copper coin was 41208 dollars. How much greater was the value of the gold than the silver, and how much greater the copper? Also, how much did the silver exceed the copper?

24. In 1835, the number of post offices in the United States was 10770; extent of post roads 112774 miles; in 1845, the number of offices was 14183; and extent of roads 143940 miles. How many offices were added during these 10 years, and how many additional miles of road were added?

Ans.

S3413 post offices. 31166 miles of road.

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