Avas. 12330 1.1

§ 2. Simple Subtraction.

SIMPLE SUBTRACTION is the taking of a less number from a greater of the same denomination, so as to shew the difference or remainder; as 5 taken from 8, there remains 3.

THE greater number (8) is called the Minuend, the less number(5) the Subtrahend, and the difference(3) or what is left after Subtraction,the Remainder.

RULE.

"PLACE the less number under the greater, units under units, tens under "tens, and so on. Draw a line below: then begin at the right hand, and "subtract each figure of the less number from the figure above it, and place the remainder directly below. When the figure in the lower line "exceeds the figure above it, suppose 10 to be added to the upper figure; "but in this case you must add 1 to the under figure in the next column be you subtract it. This is called borrowing ten.”

"fore

PROOF.

ADD the remainder and subtrahend together, and if the sum of them car. respond with the minuend, the work is supposed to be right.

Minuend

6 5

3

Subtrahend 5 2 7
Remainder 3 3 8
Proof.

1

2

6 5 3

EXAMPLES.

THE numbers being placed with the larger uppermost, as the rule directs, Ibegin with the unit or right hand figure, in the subtrahend, and say, 1 from 3 and there remain 2, which I set down, and proceeding to tens, or the next figure, I say 7 from 5 I cannot, I therefore borrow, or suppose 10 to be added to the upper figure (5) which make 15, then I say, 7 from 15 and there remain 8, which I set down; then proceeding to the next place, I say, 1 which I borrowed to 2 is 3, and 3 from 6 and there remain 3, this I set down, and in the next place say 5 from 8 and there remain 3, which I set down and the work is done. PROOF. I ADD the remainder to the subtrahend, on finding the sum just equal to the minuend, suppose the work to be right.

I

NOTE. THE reason of borrowing ten, will appear if we consider, that, when two numbers are equally increased by adding the same to both, their difference will be equal. Thus, the difference between 3 and 5 is 2; add the number 10 to each of these figures (3 and 5) they become 13 and 15, still the difference is 2. When we proceed as above directed, we add or suppose to be added, 10 to the minuend, and we likewise add 1 to the next higher place of the subtrahend, which is just équal in value to 10 of the lower place.

2 2 1 0 7 1 7

0 9 1 2 3 Remainder.

3 2 7 8 6 3 3 2 1 4 6 5

6. From 3 7 5 1 dollars, take 1 6 7 4 dollars.

WRITE the less number under the greater, with units under units &c. as

the rule directs.

Thus, 3 7 5 1

8. From 10000000

Subtract

1 4 8 9 3 2 2494143

9999999

0000001

THE distance of time since any remarkable event, may be found by subtracting the date thereof from the present year.

SUPPLEMENT to Subtraction.

QUESTIONS.

1. WHAT is Simple Subtraction ?

2. How many numbers must there be given to perform that operation? 3. How must the given numbers be placed?

4. WHAT are they called?

5. WHEN the figure in the lower number is greater than that of the upper number from which it is to be taken, what is to be done?

6. How does it appear, that in subtracting a less number from a greater, the occasionally borrowing of ten, does not affect the difference between these two numbers ?

7. How is subtraction proved?

8. WHEN, and how may Subtraction be of use to a man engaged in the pursuits of life?

NOTE. In case of borrowing ten, it is a matter of indifference, as it respects the operation, whether we suppose 10 to be added to the upper figure, and from the sem subtract the lower figure and set down the difference ; or, as Mr. PIKE directs, first, subtract the lower figure from 10, and adding the difference to the figure above, set down the sum of this difference and the upper figure. The latter method may, perhaps, be thought more easy, but it is conceived, that it does not lead the understanding of youth so direct ly into the nature of the operation as the former.

6. From 3 7 5 1 dollars, take 1 6 7 4 dollars.

WRITE the less number under the greater, with units under units &c. as the rule directs.

7. From 2673105, the minuend;

take

178932, the subtrahend.

OPERATION.

Minuend

Subtrahend

8. From 10000000.

THE distance of time since any remarkable event, may be found by subtracting the date thereof from the present year.