knife for 21 cents and another for 12 cents; what was the difference in price? 11 taken from 19, how many will remain? 8 from 19? 10 from 19? 7 from 19? 11 from 19? 6 from 19 12 from 19? 5 from 19? 13 from 19? 4 from 19? 14 from 19? 3 from 19? If 9 be taken from 18, how many will remain? 8 from 18? 10 from 18? 7 from 18? 11 from 18? 6 from 18? 12 from 18? 5 from 18? 13 from 18? 4 from 18? 14 from 18? 3 from 18? 15 from 18? 2 from 18? 16 from 18? 1 from 18? 17 from 18? If 10 be taken from 20, how many will remain? 9 from 20? 11 from 20? 8 from 20? 12 from 20? 7 from 20? 13 from 20? 6 from 20? 14 from 20? 5 from 20? 15 from 20? 4 from 20? 16 from 20? 3 from 20? 17 from 20? 2 from 20? 18 from 20? 19 from 20? 11 from 21? 10 from 21? 12 from 21? 9 from 21? 13 from 21? 8 from 21? 14 from 21? 7 from 21? 15 from 21? 6 from 21? 16 from 21? 5 from 21? 17 from 21? 4 from 21? 18 from 21? 3 from 21? 19 from 21? 2 from 21? 11 from 22? 10 from 22? 12 from 22? 9 from 22? 13 from 22? 8 from 22? 14 from 22? 7 from 22? 15 from 22? 6 from 22? 16 from 22? 5 from 22? 17 from 22? 4 from 22? 18 from 22? 3 from 22? 19 from 22? 2 from 22? 12 from 23? 11 from 23? 13 from 23? 10 from 23? 14 from 23? 9 from 23? 15 from 23? 8 from 23? 16 from 23? 7 from 23? 17 from 23? 6 from 23? 18 from 23? 5 from 23? 19 from 23? 4 from 23? 20 from 23? 3 from 23? 21 from 23? 2 from 23? 22 from 23? 1 from 23? 12 from 24? 11 from 24? 13 from 24? 10 from 24? 14 from 24? 9 from 24? 15 from 24? 8 from 24? 16 from 24? 7 from 24? 17 from 24? 6 from 24? 18 from 24? 5 from 24? 19 from 24? 4 from 24? 20 from 24? 3 from 24? 21 from 24? 2 from 24? 22 from 24? 1 from 24? 23 from 24?

16 boys went on a sailing excursion, only 7 of them returned; the others were drowned; how many were lost? If from a pile of 20 apples, I take away 13, how many will be left? A man started on a journey of 23 miles; after he had traveled 16 miles, he stopped to feed his horse; how far had he then to travel? A man having 22 chickens, killed 13 of them; how many were left? From a stick of timber 19 feet long, 7 feet were cut off; what was the length of the remainder? 19-7-how many? 21-9-how many? 17-9 how many? 23-5-how many? 15-7-how many? 24-9-how many? 11-7-how many? 22-16=how many? 12-7 how many? 13-5-how many? 14

?

7=how many y? 15-9 how many ? 16-9 how many 17-8 how many? 18-7-how many? 19-11-how many? 20-9 how many? 21-7-how many? 22-9 how many? 23-13-how many?

From the preceding table and examples, the scholar will comprehend the nature of Simple Subtraction; his next step will be to practice with his slate and pencil. It will already have been observed, that only two numbers are employed in a single operation of subtraction. The larger of these two numbers is called the minuend; and the smaller, the subtrahend. The object of the rule is to find the difference between the two; that is, to find how much will remain of the larger after the smaller is taken from it. The number obtained by the operation, is called the remainder.

The scholar may be guided by the following rule:

RULE.-1st. Write the less of the two numbers under the greater, with units under units and tens under tens, &c. and draw a line beneath them.

2d. Commence with the right hand figure of the lower line or subtrahend, and take it from the figure which stands directly above it, if practicable. Do the same with the remaining figures in the subtrahend, if practicable, and the operation will be completed.

3d. But whenever this cannot be done, that is, when the lower figure is the larger, 10 should be added to the upper figure and the lower one taken from the sum.

4th. Whenever 10 is added to an upper figure, 1 must be carried or added to the next lower figure; that is, 1 is to be carried whenever 10 is borrowed..

5th. To prove the work, add the remainder to the subtrahend, and if the work be right, the amount will correspond with the

minuend.

The scholar will easily comprehend the nature of this rule, unless he should find difficulty in understanding why, when we borrow 10, we are required to carry only 1. He must however remember, that by the addition of this 10 to the upper number, he has increased the value of that number 10 units, 10 tens, 10 hundreds, or 10 thousands, according to the place the figure occupies. If he add it to the units, the value of the addition is 1 ten; if to the tens, the value is one hundred, because 10 units make one ten, and 10 tens, one hundred, &c. Now by the rule, if 10 be borrowed, 1 must be carried to the

next lower figure; by which operation, one more will be taken from the figure in the minuend; and this one more, which is thus removed, is just equal in value to the 10 that was added, for it is taken from a figure one degree farther to the left. But this subject will be more clearly comprehended, when illustrated by example. Take the following sum:

From 6 3 5 428

Take 3 8 2 5 1 6

Rem. 2 5 291 2

In this example, it is evident that if 6 be taken from 8, 2 will remain; and if the 1 ten be taken from 2 tens, 1 ten will remain. But how is 5 in the place of hundreds to be taken from the 4 above it? Evidently by the third section of the rule; that is, 10 is added to the 4 in the minuend, by which addition, it will become 14 hundred, from which if 5 hundred be taken, 9 hundred will remain, which is the third figure in the remainder. But by this operation the minuend has been increased 10 hundred; if therefore I add 1 to the 2 thousand, it will become 3 thousand, and consequently, when subtracted from the figure 5 above it, will take one thousand more from the minuend, so that only 2 will remain. If therefore 10 hundred was in one instance added to the minuend, in the other, 1 thousand, its equal, has been taken from it. The same reasoning is applicable to the 8; 10 is added to the 3, which increases it to 13; the 8 is taken from the 13, and 5 remains. There is then one to carry to the 3, which thus increased is taken from the 6, and 2 re

mains. The whole remainder therefore is 252912.

Now if this remainder be added to the lower number or subtrahend, the amount will be the minuend; which proves that the operation is correct, thus:

23. A was born in 1679; how old was he in 1777 ? Ans. 98 years.

24. From 1600000 take 900000, and from the remainder take 699999, and how much will remain? Ans. 1.,

25. A man has two flocks of sheep; in the one there are 693, and in the other, 499; what is the difference in these flocks? Ans. 194.

26. A man has in his possession property to the amount of $15728, and he owes $7869; how much will remain in his hands, when his debts are paid? Ans. $7859.

27. America was discovered in 1492. How long will it have been discovered in 1846 ? Ans. 354 years.

28. A man being asked how old he was when his eldest son was born, said that his own age was 79 years, and his son's 42 years; what was his age at the birth of his son? Ans. 37 years.

29. The amount of A's debts was 2356 dollars; the amount of his property, 5672 dollars. How much had he left after his debts were paid? Ans. $3316.

30. A merchant bought a quantity of cloth for $572, and sold it for $526. Did he gain or lose, and how much? Ans.

Lost $46.

31. To what number must I add 576 to make the amount 1726? Ans. 1150.

32. Bought cotton in one month to the value of $572896; and sold the same for $600027. How much did I gain? Ans. $27131.

33. If the sum of two numbers be 2793, and one of those numbers, 1892, what is the other? Ans. 901.

34. A merchant bought 742 yards of cloth and sold all but 7 yards. How much did he sell? Ans. 735 yards.

35. A man paid 1182 dollars for a house, and sold the same for 1069 dollars. How much did he lose? Ans. $113.

36. A farmer purchased a farm, for which, including the buildings, he paid $6782; the buildings were worth $2896; what was the value of the land? Ans. $3886.

37. A person owed a merchant $999, and paid him all but $179. How much did he pay him? Ans. $820.

Sums requiring in their solution, the application of both Addition and Subtraction.

38. I hold in my

is due $70 interest.

possession a note for $560, on which there On the back are two endorsements; one, $320, and the other, $260. What is now due? Ans. $50. 39. There are $1000 in four different purses; in the first there