tens above it; but we here find a difficulty, since the 4 is greater than the 2, and cannot be subtracted from it. We therefore add 10 to the 2, which makes 12 tens, and then subtract the 4 from the 12, and 8 tens remain, which we write below. Then to compensate for the 10 thus added to the 2 in the minuend, we add 1 to the 3 in the next higher place in the subtrahend, which makes 4 hundreds, and subtract the 4 from the 6, and 2 hundreds remain; and thus find the remainder to be 282.
NOTE 1.---This operation depends upon the self-evident truth, That, if any two numbers are equally in creased, their difference remains the same. In working the example 10 tens, equal to 1 hundred, were added to the 2 tens in the upper number, and I was added to the 3 hundreds in the lower number. Now, since the 3 stands in the hundreds place, the 1 added was in fact 1 hundred. Hence, the upper and lower numbers being equally increased, the difference is the same.
NOTE 2.-- In the operation, instead of adding 10 to 2 in the minuend, 1 of the 6 hundreds can be joined to the 2 tens, thus forming 12 tens; then 4 tens from 12 tens leaves 8 tens; and 1 of the 6 hundreds having been taken, there remain only 5 hundreds; and 3 hundreds from 5 hundreds leaves 2 hundreds, and the result is the same as by the other process.
§ 31 RULE.- Place the greater number above, and the less number under it. Place units under units, tens under tens, &c. Commence at the right hand and subtract each figure of the subtrahend from the figure above it in the minuend.
If any figure in the subtrahend is langer than the fig- ure above it in the minuend, add 10 to that figure in the minuend before subtracting; then, after subtracting, add 1 to the next figure of the subtrahend.
S 32. Second Method of Proof.—Subtract the remainder from the minuend, and the result will be like the subtrahend, if the work is right.
