EXAMPLES.

1. In which no figure of the subtrahend is larger than the corresponding figure in the minuend.

From 796 subtract 375.

Place the subtrahend directly

under the minuend, so that units may stand under units, tens under tens, hundreds under hundreds.

OPERATION.

Hundreds.

Tens.

Units.

6 minuend.

5 subtrahend.

7

4 2

1 difference.

Then commence at the units' column and subtract— 5 from 6 leaves 1; place the one under the units' column, and so proceed with each suc

2. In which some of the figures of the subtrahend are larger than the corresponding figures of the minuend. From 867 subtract 496.

OPERATION.

Hundreds.

7 hundred, 16 tens, and 7 units, [7][16]:

=8 hundred, 6 tens, and 7 units, $

Tens.

Units.

67 minuend.

Place the minuend and subtrahend as in the preceding example. Begin at the units' column; 6 from 7 leaves 1. Passing to the tens' figure of the subtrahend, which is 9, we see that it cannot be subtracted from the corresponding figure of the minuend. But we know (ART. 10,) that 1 of any order is equal to 10 of the next lower order. We therefore take 1 from the hundreds' figure, leaving that figure 7, (which we place in brackets over the 8, marking out the 8,) and counting the 1 hundred as 10 tens, we add it to the 6 tens, making 16 tens, which sum we place in brackets over the 6 and mark out the 6. We now say 9

from 16 leaves 7; 4 from 7 leaves 3.

From 959 subtract 678.

From 767 subtract 349.

From 8965 subtract 7774.

From 52475 subtract 19304.

Ans. 281.

Ans. 418.

Ans. 1191.

Ans. 33171.

3. We will now give an example of a more difficult

ing out the 5,) and counting the 1 ten as ten units, we

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.

tens cannot be subtracted from the 5 tens. Add, then, 10 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.

11. 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 figure by 10 before subtracting, and then to carry 1 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.