Here are six balls,

Now, if we put a bit of paper, or the edge of a book, or our hand, on the lower three, how many remain ?-Why, three, Then you see, that if you take 3 from 6 there remain 3.

Sum 2.-Now take eight from ten, how many remain ?

Put down the highest number
Now put 8 under the units

10

8

Eight from ten and there remain 2

Here are ten stars, we will cut off 8 of them on the left hand by a stroke, and then you will see that 2 only remain.

Sum 3.-Take 9 from 12, how many remaiu?

Here are 12 pens, and we will take away 9 by putting a finger on them, and we shall then see how many remain.

4*

Now take 9 from the bottom, counting upwards, you then come to the line drawn across, above which are the other 3 which remain out of the 12. This we do thus,

12

9

Take 9 from 12, and there remain 3

12

Now to prove your sum correct, and all other sums in subtraction, add the two bottom lines together, and see if they come the same as the top; if so the sum is right, if not, it is

wrong. You took away 9 from 12, and left 3 behind; you put the 9 and the three again together, and they will again make 12.

Sum 4.--Take 11 from 12, how many remain ?

Sum 5.-Take 8 from 10, how many remain?

Sum 6.--Take 2 from 12, how many remain? Put down 12 pins, or peas, or marbles on the table, and take 2 from them, and you will see how many remain. But you ought now to begin and do without these helps.

Sum 7.--Take 6 from 11, how many remain?

Sum 8.-Take 30 from 35, how many remain? Here put down the highest number first,

35

Now put down under it

30

Now take 30 from 35, and there remain 5

This you do this way; say if we take nothing from 5, why 5 still remain. If we have 5 apples on the table and take none away, why 5 apples still remain. Then say 3 from 3 and nothing remains; for if I take 3 apples when there are only 3 to take from, I leave none behind. So in all cases you can never have any remainder if you take the same num

ber from the same.

For if you take 7 from 7,

of course you take all away and nothing remains: so with 6 from 6, and 8 from 8, and the rest.

Sun 9.-Now take 12 from 29, how many remain ?

Greater number

Less number

29
12

—

17

Here say 2 from 9 and there remain 7, and put down 7 under the 2; then say 1 from 2 and there remains 1.

You have here 2 units to take from 9 units; and 1 ten from 2 tens, which is the same thing as taking 2 from 9 and 1 from 2, and your remainder is 1 ten by taking 1 from 2, and 7 units by taking 2 from 9. This is easier than taking 12 from 29.

Sum 10.--Take 27 from 39, how many remain? Here let the little pupil first do the sum in the same way as the last, and so for the next three sums.

Sum 11.--Take 39 from 59, how many remain? Mind here that if you take 9 from 9, being the same figures, nothing remains.

Sum 12.-Take 25 from 35, how many remain?

Sum 13.--Take 42 from 59, how many remain ?

Sum 14.--Take 37 from 41, how many remain? Here let the little learner observe, that

although we cannot take a large number from a small one, as for instance, we cannot take 20 apples from 10, and therefore the large number must always be at the top, and the small one at the bottom which we substract from it, yet there are small figures that must sometimes be above larger ones, for which we have a remedy.

Now we put down 41 the greater number, 37 the less number.

And

-

4

But when we come to subtract, 7 is larger than 1. Therefore we cannot take 7 from 1, but we say 7 from 1 I cannot, but 7 from 11, and there remain 4; this we call borrowing, for we are supposed to take ten from the next column which is tens, and one of which makes ten of that we want, and we add it to the top figure, by which we make the larger number to enable us to subtract. Therefore in all cases where the upper figure is less than the bottom, borrow ten and add to it, and then subtract the bottom one from it. Now we have borrowed ten from the tens, but that we must pay, and therefore we go to the next figures and say, 1 I borrowed I pay to the 3 is 4, now 4 from 4 and nothing remains; this being the last left hand figure and 0 being of no value, it is not put down, but a blank is left, and the sum stands 4.