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Note. It is an interesting and profitable exercise for young pupils to recite tables in concert. But it will not do to depend upon this method alone. It is indispensable for every scholar who desires to be accurate either in arithmetic or business, to have the common arithmetical tables distinctly and indelibly fixed in his mind. Hence, after a table has been repeated in order by the class in concert, or individually, the teacher should ask many promiscuous questions, to prevent its being recited mechanically, from a knowledge of the regular increase of numbers.

Ex. 11. How many are 12 and 10? 22 and 10 ? 32 and 10? 42 and 10? 52 and 10? 62 and 10? 72 and 10? 82 and 10? 92 and 10?

12. How many are 24 and 10? 36 and 10? 48 and 10 53 and 10? 67 and 10? 91 and 10? 86 and 10? 78 and 10? 69 and 10? 97 and 10?

13. How many are 19 and 4? 29 and 4? 39 and 4? 79 and 4? 59 and 4? 89 and 4? 99 and 4? 69 and 4? 49 and 4?

14. How many are 17 and 8? 27 and 8? 47 and 8? 67 and 8? 57 and 8? 97 and 8? 87 and 8?

15. How many are 16 and 7? 26 and 7? 56 and 7? 86 and 7? 76 and 7? 96 and 7?

16. How many are 14 and 6? 24 and 6? 84 and 6? 74 and 6? 54 and 6? 64 and 6? 94 and 6?

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

OBS. This and the next four examples may be recited in concert. Thus, 2 and 2 are four, and 2 are 6, and 2 are 8, &c.

18. Add 3 in the same manner, till the sum is a hundred and two.

19. Add 5 in the same manner, till the sum is a hundred and ten.

20. Add 4 in the same manner, till the sum is a hundred and twelve.

21. Add 10 in the same manner, till the sum is a hun

dred and twenty.

22. A man bought a sheep for 3 dollars, a cow for 21 dollars, 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?

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 many shillings did he give 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 he receive for all?

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?

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

Analysis.-60 is 6 tens, and 30 is 3 tens; (Art. 7. Obs. 2 ;) 6 tens and 3 tens are 9 tens, and 9 tens are 90. Ans. 90 scholars.

32. A mechanic sold a wagon for 30, 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. 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?

35. 7 tens and 2 tens are how many? Ans. 9 tens, or 90.

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 the orchard contain?

38. A traveler rode 90 miles in the cars and 60 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, joined with the hundred, makes 163. Ans. He paid 163 dollars. 41. How many are 63 and 24? Ans. 87. 42. How many are 68 and 25 ?

43. How many are 56 and 23 and 5?

44. How many are 83 and 72 and 4 and 6? 45. How many are 72 and 25 and 10 and 2?

46. Bought a pound of tea for 60 cents, an ounce of pepper 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 ?

17. The learner will perceive that the solution of each of the preceding examples consists in finding a single number which will exactly express the value of the several given numbers united together.

18. The process of uniting two or more numbers together, so as to form one single number, is called ADDITION. The answer, or the number thus found, is called the sum, or amount.

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

19. Signs. Addition is often represented by the sign +, which is called plus. It consists of two lines, one horizontal, the other perpendicular, forming a cross, and shows that the numbers between which it is placed are to be added together. Thus the expression 6+8, signifies that 6 is to be added to 8. It is read, "6 plus 8," or "6 added to 8."

OBS. Plus is a Latin word, originally signifying "more," hence "added to."

20. The equality between two numbers, or sets of numbers, is represented by two parallel lines, called the sign of equality. It 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.

QUEST.-17. In what does the solution of the preceding examples consist? 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? 19. What is the sign of addition called? Of what does it consist? What does it show? Obs. What is the meaning of the word plus? 20. How is the equality between two numbers represented?

EXERCISES FOR THE SLATE.

21. The preceding examples are designed to be performed mentally. This is the most convenient way of adding small numbers; but when the numbers are large, the operation may be facilitated by setting them down upon a slate or black board. The manner of doing this will now be explained.

OBS. Pupils not unfrequently seem to infer, that when they take up the slate and pencil, they can lay aside thinking; that the hands are to solve the question without the aid of the intellect. Hence operations upon the slate are often a merely mechanical effort, as listless and mindless as the singing of a parrot, or the trudging of a dray-horse. This is a sad mistake. It is sure to render the study of arithmetic irksome, and to destroy the progress of the learner.

It is not the object in using the slate to supersede thinking and reasoning, but to assist the memory in retaining the numbers and the several steps of the operation, while the intellect is carrying on the process of thinking and reasoning.

The hands simply write down the figures or the result of the operation, but it is the mind, and the mind only, that performs the addition and all other arithmetical calculations, whether we use the slate or not. Hence, whoever wishes to become a proficient in arithmetic, must never allow his mind to become inactive when using his slate, nor pass a single solution without understanding the reason of the several steps.

Ex. 1. A man bought a pound of tea for 63 cents, and a pound of coffee for 24 cents: how much did he pay for both?

Directions. Write the numbers under each other, so that units may stand under units, tens under tens, and draw a line beneath them. Then, beginning at the right hand or units, add each column separately in the following manner: 4 units and 3 units are 7 units.

tens

units

Operation.

6 3 price of tea.
24
66 of coffee.

87 cts. price of both.

QUEST.-What does the sign of equality show? How is the expression 5+3=8 read? How 7+5=8+4=12? 21. How are the preceding examples to be performed? What is the most convenient way for adding small numbers? What for large ones? Obs. Does the slate supersede thinking and reasoning?

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