17. Add 2 to itself, till the sum is a hundred.

18. Add 3 to itself, till the sum is a hundred and two. 19. Add 5 to itself, till the sum is a hundred and ten. 20. Add 4 to itself, till the sum is a hundred and twelve. 21. Add 10 to itself, till the sum is a hundred and twenty. 22. A man bought a sheep for 3 dollars, a cow for 21 dolfars, and a calf for 5 dollars: how much did he pay for the whole?

23. A shopkeeper sold a dress to a lady for 15 dollars, a muff for 10 dollars, and a bonnet for 6 dollars: what was the amount of her bill?

24. A drover bought 16 sheep of one farmer, 9 of another, 10 of another, and 6 of another: how many sheep did he buy of all?

25. Harry gave 31 cents for his arithmetic, 10 cents for a writing-book, 8 cents for a ruler, and 6 cents for a lead pencil: how many cents did he pay for all?

26. What is the sum of 10 and 12 and 5 and 4?

27. William bought a pair of boots for 26 shillings, and a cap for 9 shillings: how much did he pay for both?

28. Susan bought a comb for 17 cents, a purse for 8 cents, and a spool of cotton for 5 cents: how much did she pay for all?

29. A farmer sold a ton of hay for 18 dollars, a cow for 10 dollars, and a cord of wood for 3 dollars: how much did they all amount to?

30. A merchant sold 15 barrels of flour to one man, 5 to another, and 7 to another: how many barrels of flour did he sell?

81. In a certain school there are 60 boys and 30 girls: how nany scholars does that school contain?

Analysis.-60 is the same as 6 tens, and 30 the same as 3 tens; now 6 tens and 8 tens are 9 tens, and 9 tens are 90. Therefore the school contains 90 scholars.

32. A mechanic sold a wagon for 30 dollars, and a sleigh for 20 dollars: how much did he get for both?

33. 40 is how many tens? 60? 20? 30? 70? 80? 50? 90? 100 ?

34. 7 tens and 2 tens are how many? 7 tens and 4 tens?

35. 6 tens are how many? 8 tens? 9 tens? 10 tens? 11 tens? 12 tens? 13 tens? 14 tens? 15 tens? 16 tens? 17 tens? 18 tens? 19 tens? 20 tens?

36. 8 tens and 3 tens are how many? 5 tens and 8 tens? 7 tens and 8 tens? 6 tens and 9 tens? 9 tens and 8 tens? 10 tens and 6 tens?

37. In a certain orchard there are 80 apple-trees, and 40 peach-trees: how many trees does it contain?

38. A traveler rode 90 miles in the cars, and 60 miles in stages: how many miles did he travel?

39. A man gave 60 dollars for his horse, 30 dollars for his harness, and 20 dollars for his cart: how much did he pay for all?

40. A man bought a horse for 98 dollars, and a wagon for 65 dollars: how much did he give for both?

Analysis.-98 is composed of 9 tens and 8 units, and 65 is composed of 6 tens and 5 units. (Art. 7. Obs. 3.) 9 tens and 6 tens are 15 tens, or 1 hundred and 5 tens; 8 units and 5 units are 13 units, or 1 ten and 3 units; now 1 ten added to 5 tens, makes 6 tens or 60, and 3 units are 63, which, added to the hundred, makes 163. He therefore paid 163 dollars.

OBS. In adding large numbers mentally, it is more convenient and expeditions to begin with the highest order.

41-45. How many are 68 and 25? 56 and 23 and 5? 83 and 72 and 4 and 6? 72 and 25 and 10 and 2? 63 and 24 and 12 and 10 and 7?

46. Bought a pound of tea for 60 cents, an ounce of popper for 8 cents, and a quart of molasses for 10 cents: what does my bill amount to?

47. The price of a geography is 55 cents, and the price of a grammar is 42 cents: what is the cost of both?

48. Paid 7 dollars for a barrel of flour, 17 dollars for a ton of hay, and 30 dollars for a cow: what is the cost of all?

49. In January there are 31 days, and in February 28 days : how many days are there in both months?

50. A man, having three sons, gave 50 dollars to the oldest, 40 dollars to the second, and 30 dollars to the youngest: how many dollars did he give to the three?

2

EXERCISES FOR THE SLATE.

ART. 17. In each of the preceding examples it will be observed, we have two or more numbers given, and from these it is required to find a single number, which is equal to the several given numbers united together. The operation by which this number is found, is called Addition. Hence,

18. ADDITION is the process of uniting two or more numbers

in one sum.

The answer, or number obtained by addition, is called the sum, or amount.

OBS. When all the numbers to be added are of the same kind, or denomination, as all books, all yards, &c., the operation is called Simple Addition.

18. a. SIGNS. The relations of numbers, and the operations which are performed with them, are often denoted by certain characters, called signs.

19. The sign of addition is a perpendicular cross (+), called plus, and shows that the numbers between which it is placed, are to be added together. Thus, the expression 6+8, signi、 fies that 6 is to be added to 8. It is read, " 6 plus 8," or "6 added to 8."

66

Note.-The term Plus is a Latin word, originally signifying more. In Arithmetic, it means added to.

20. The sign of equality is two horizontal lines (=), and shows that the numbers between which it is placed, are equal to each other. Thus, the expression 5+3=8, denotes that 5 added to 3 are equal to 8. It is read, "5 plus 3 equal 8,” or “the sum of 5 plus 3 is equal to 8." So 7+5=8 +4=12.

Read the following expressions: 3+4+1=3+5. 17+3+12=15+7+10. 13+6+2+3=7+5+12. 25+6+17+3=26+3+2+20. 36+9+5=24+8+3+15.

65+10+12+20+16+41+7=40+35+15+17+25+39.

QUEST.-18. What is addition? What is the answer called? Obs. When the numbers to be added are all of the same denomination, what is the operation called? 18. a. How are the relations of numbers and their operations Sometimes denoted? 19. What is the sign of addition? What does it show? Note. What is the meaning of the term plus? 20. What is the sign of equality? What does it show? How is the expression 5+3=8, read? Bow.7+5=8+4=19 °

CASE I.- When the sum of a column does not exceed 9. ART. 21. Ex. 1. A man bought 436 pounds of tea, and 253 pounds of coffee: how many pounds of both did he buy?

Suggestion.-Write the numbers un

Operation.

hund.

tens

units

4 3 6 tea 253 cof. Ans. 689 pounds.

der each other, units under units, tens under tens, &c., and draw a line beneath them, as in the margin. Then, beginning at the right hand, proceed in the following manner: 3 units and 6 units are 9 units. Set the 9 in units' place under the column added because it denotes units. (Art. 8.) Next, 5 tens and 3 tens are 8 tens. Write the 8 in tens' place, because it denotes tens. Finally, 2 hundreds and 4 hundreds are 6 hundreds. Write the 6 in hundreds' place, because it denotes hundreds. He therefore bought 689 pounds of both.

22. In the solution above it is important to observe, that units are added to units, tens to tens, &c. Hence, universally, Figures of the same order must be added to each other.

The reason is, that figures of different orders express units of different values; consequently, if added together, the amount would neither be of one order nor another. (Art. 8.) Thus, 3 units and 3 tens will neither make six units, nor six tens, any more than 3 apples and 3 oranges will make 6 apples, or 6 oranges. In like manner, it is plain that 5 tens and 4 hurdreds will neither make 9 tens, nor 9 hundreds.

OBS. The object of writing units under units, tens under tens, &c., is to prevent mistakes which might occur from adding different orders to each other.

Solve the following examples in a similar manner:

2. A butcher purchased two droves of sheep, the first conaining 436, and the second 243: how many sheep did both droves contain? Ans. 679 sheep.

3. A man found two purses of money, one containing 425 dollars, the other 361 dollars: how many dollars did both purses contain?

QUEST.-21. Explain the solution of the first example from your slate. 22. What orders of figures do you add together? Why not add figures of different orders to each other?

4. A man bought two tracts of wild land, one containing

3261 acres, and the other, 5428 acres: how many acres of land

did he buy?

CASE II. When the sum of a column exceeds 9.

ART. 23. Ex. 13. A man bequeathed 5876 dollars to his oldest child, 4629 dollars to the second, and the balance of his estate, which was 3548 dollars, to the youngest: what was the amount of his property?

5876

4629

8548

14053 Ans.

Suggestion. Having set down the numbers, and Operation. added the units' column as before, we find the sum is 23. Now 23 units are equal to 2 tens and 3 units, for every ten in a lower order makes one in the next higher. (Art. 9.) We therefore set the 3 or right hand figure under the units, and reserving the 2 or left hand figure, add it to the next column. Thus, 2 tens (which were reserved) added to 4 make 6 tens, and 2 are 8, and 7 are 15 tens, which are equal to 1 hundred and 5 tens. Set the 5 or right hand figure under the column added, and add the 1 or left hand figure to the next column as before. Now 1 hundred added to 5 makes 6 hundreds, and 6 are 12, and 8 are 20 hundreds, which are equal to 2 thousands and 0 hundreds. Set the 0 or right hand figure under the column alded, and add the 2 to the next column. In like manner we find the sum of the thousands' column is 14; and as this is the last column, we set down the whole sum. Therefore the amount of his property was 14053 dollars.

QUEST.-23. Describe the solution of the 13th example. 24. What is meant by currying the tens?