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or 944 cents. The interest of 37 dollars for 60 days would be 37 cents, and for 20 days f of 37 cents, or 12 cents. The whole interest is 18 dollars and 95cents.

146. They would both together dog of the work in 1 \lay, and it would take them of a day to do the other Ans. 1} day.

149. They both together consume 4 of a bushel in a week, but the woman alone consumes only 1 of a bushel in a week. That is, they both together consume I in a week, but the woman alone only foi consequently, the man alone would consume B; and a bushel would last him 3} weeks.

152. A and B can build of it in 1 day; A, B, and C, can build } of it in 1 day; the difference between 1 and 1 is ; therefore C can build of it in 1 day; and it would take him 131 days to build it alone.

164. Find how much they might eat in a day, in order to make it last 1 month, and then it will be easy to find how much they may eat in a day, to make it last 11 months.

167. The money is 7 parts of the whole, and the purse one part; consequently the money is į and the purse of 16.

170. He gave one part for the apple, 2 parts for the orange, and 4 parts for the melon. These make 7 parts. The apple 3 cents, the orange 6 cents, and the melon 12 cents.

175. If to a number half of itself be added, the sum is f of that number; hence subtract 2} from 100, and the remainder is of the number of geese that he had.

180. This must be reduced to 6ths. 1 half is, and is , and the number itself is . If therefore to the whole number its half and its third be added, the sum will be *; hence, 77 is 1 of the number.

181. is *; therefore if to a number 1 and 4 of itself be added, the whole number will be ; but when 18 more is added to , the first number is doubled ; that is, the number is sy of the first number; therefore 18 is of the number.

ARITHMETIC.

PART III.

WRITTEN ARITHMETIC.

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Notation and Numeration. 1. Instead of writing the names of numbers, it is usuar to

express them by particular characters, called figures. One

is written 1 | Twenty-six is written 26 Two

2 Twenty-seven Three 3 Twenty-eight

28 Four 4 Twenty-nine

29 Five 5 Thirty

30 Six 6 Thirty-one

31 Seven 7 Forty

40 Eight 8 Fifty

50 Nine 9 | Sixty

60 Ten 10 Seventy

70 Eleven 11 Eighty

80 Twelve 12 Ninety

90 Thirteen 13 One hundred

100 Fourteen

14 One hundred Fifteen

15
and one

101 Sixteen

16 One hundred Seventeen

and two

102 Eighteen

18 One hundred Nineteen

19
and ten

110 Twenty

20 One hundred Twenty-one

21
and twenty

120 Twenty-two 22 Two hundred

200 Twenty-three

23 | Three hundred " 300 Twenty-four 24 One thousand

1000 Twenty-five

25 | Ten thousand “ 10,000

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2. When several figures stand side by side, the value of each figure depends on its place as counted from the right towards the left. A figure standing in the first place signifies so many units, or ones; the same figure, in the second place, signifies so many tens; in the third place, hundreds ; in the fourth place, thousands ; in the fifth place, tens of thousands ; and in the sixth place, hundreds of thousands. Therefore every time a figure is removed one place to the deft, its value is made ten fold, as may be seen in the following table.

A Hundreds of thousands.

Tens of thousands.
Thousands.
Hundreds.
Tens.
Units.

111,111, read One hundred and eleven thousand, one hundred and eloven.

4 " Four. 49 o Forty-nine. 496 Four hundred and ninety-six. 4,965 " Four thousand nine hundred and sixty-five. 49,652 Forty-nine thousand, six hundred and fifty-two. 496,527 " Four hundred and ninety-six thousand, five hundred and

twenty-seven.

3. Let the pupil read the following numbers:1. 34 5. 142 9. 6,744 | 13. 1,504 2. 76 6. 279 10. 8,329 | 14. 50,603 3. 68 7. 758 ) 11. 4,960 | 15. 124,769 1. 95 8. 423 | 12. 9,080 | 16.

784,984 4. Let the pupil express the following numbers in figures : – 1. Seventy-eight. 2. Ninety. 8. One hundred and fifty-six. 4. Three hundred and eight.

5. One thousand, four hundred and sixty-nine.
6. Five thousand and two.
7. Seventy-seven thousand and eighty-four.
8. Forty thousand, seven hundred and twenty-two.
9. Five hundred and sixty-six thousand, one hundred

and fifty.
10. Six hundred thousand.

ADDITION.

Tens.

5. 5 and 4 and 7 are how many? This is called a question in addition. We put together or add the numbers, 5, 4, and 7 to find their sum or amount. Thus, the sum of 5 and 4 and 7 is 16. Ex. 1. What is the sum of 46 and 37 ?

It is most convenient to write the numbers in order, units under units, tens under tens, &c.; then begin

ning with the units, we find that 6 units and 7 units 46

are 13 units, or 1 ten and 3 units. We write down 37

the 3 units under the units and add the 1 ten to the

other tens; 1 (ten) and 4 (tens) and 3 (tens) make 8 83 (tens) which written with the 3, makes 83. Ex. 2. What is the sum of 736 and 875 and 394 ?

Adding the units we find 6 and 5 are 11, and 4 are 15, or 1 ten and 5 units. Writing the 5 under the column of units, we reserve the i ten and add

it to the tens of the next column ; thus, 1 and 3 are 8 7 5

4, and 7 are 11, and 9 are 20 (tens) or 2 hundreds, 3 94

and 0 tens. We write the under the column of

tens, and add the 2 (hundreds) to the column of 2005 hundreds ; thus 2 and 7 are 9, and 8 are 17, and 3 are 20 (hundreds), which being the sum of the last column we write down. The answer, therefore, is 2005. 6. Add the following:

7.

10. 15 33 8 7 19 28 45 56 69 4 9 5 7 8 7

5

Hundrede.
Tens.

736

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7. 40. Add together 39, 67, 92, 43, 84, 51. 41. Add together 270, 489, 126, 46.

42. Add together 2368, 235, 496, 1736.

43. Add together 66,476, 801, 4009, 32, 127, 8. 44. A merchant bought 4 pieces of cloth; for the first piece he gave 53 dollars; for the second, 78 dollars; for the third, 68 dollars; and for the fourth, 67 dollars. How much did he give for the whole ?

45. In an orchard there are 22 peach-trees, 95 appletrees, 17 pear-trees, and 56 plum-trees. How many trees in the orchard ?

46. A man bought four horses; for the first he gave 84 dollars;

for the second, 150 dollars; for the third, 475 dollars; and for the fourth, 526 dollars. How much did be give for all the horses ?

47. In the Boylston school there are 810 scholars; in the Brimmer, 597 scholars; in the Dwight, 956 scholars ; in the Elliot, 776 scholars; in the Franklin, 572 scholars; and in the Hancock, 731 scholars. How many scholars in these six schools ?

48. A gentleman, building a house, paid the mason 2,964 dollars, the carpenter 5,723 dollars, the plasterer 625 dollars, and the painter 354 dollars. How much did the whole house cost?

[See page 173.]

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