cents.

or 94 cents. The interest of 37 dollars for 60 days would be 37 cents, and for 20 days of 37 cents, or 12 cents. The whole interest is 18 dollars and 95 146. They would both together do of the work in 1 day, and it would take them of a day to do the other Ans. 1 day.

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

10

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 and is; therefore C can build of it in 1 day; and it would take him 13 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 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 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 11; hence, 77 is of the number.

181.is; therefore if to a number and 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 of the first number; therefore 18 is of the number.

ARITHMETIC.

PART III.

WRITTEN ARITHMETIC.

Notation and Numeration.

1. Instead of writing the names of numbers, it is usual to express them by particular characters, called figures.

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 left, its value is made ten fold, as may be seen in the following table.

Hundreds of thousands.

Tens of thousands. Thousands.

Hundreds.

Tens.
Units.

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

Four.
Forty-nine.

Four hundred and ninety-six.

Four thousand nine hundred and sixty-five.
Forty-nine thousand, six hundred and fifty-two.

Four hundred and ninety-six thousand, five hundred and
twenty-seven.

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.

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.

46

37

1888

83

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 beginning with the units, we find that 6 units and 7 units are 13 units, or 1 ten and 3 units. We write down 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 (tens) which written with the 3, makes 83.

Ex. 2. What is the sum of 736 and 875 and 394 ?

Hundreds.

Tens.

736

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, and 0 tens. We write the 0 under the column of tens, and add the 2 (hundreds) to the column of 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.

394

2005

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 he 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 173.1