31. 4 is 21, and 98 is 48. Now 48 times, and 21 is contained only consequently only 2 or 24.

is contained in 48 part as many times,

B. 1. is; consequently 5 pounds can be bought for of a dollar.

3. is, and is. If he had given only apiece, be could have given it to 9 persons; but since he gave, he could give it to only 1 half as many, or 4 persons.

5. is, and is 14. If a pound had cost of a dollar, 14 pounds could be bought for of a dollar; but since it costs, only as many can be bought; that is, 4 pounds.

9. is 18, and 1ğ is 8. If a bushel had cost of a dollar, 65 bushels might have been bought; but, since it cost 18, only part as much could be bought; that is, 4 bushels.

12. is, and is 1; 1 is contained in 1§ 15 times, but is contained only as many times; that is, 3 times

Miscellaneous Examples.

5. of a penny is of 4 farthings. 6. of 12 pence. Ans. 10 pence. 7. of 4 quarters is 2 quarters and of a quarter is 1 of 4 nails, which is quarters, 1g nails.

13. of 24 hours is 15 hours.

Ans. 2g farthings

of a quarter 18 nails, ins

14. of 24 hours is 14 hours and of an hour; 2 of 60 minutes is 24 minutes. Ans. 14 hours, 24 minutes. 28. There being 4 farthings in a penny, 1 farthing is

20

of a penny.

of a shilling, because there are 12

of a shilling.

of a pound.
of a pound.

part of a penny. 30. 3 farthings is 31. 1 penny is pence in a shilling. 34. 5 pence is 41. 1 shilling is 43. 3 shillings is 48. 1 farthing is 49. 2 farthings is of a shilling. 51. 1 penny is to of 1 pound. 7 pence is of £1. 59. 38. 5d. is 41 pence, which is of £1.

of one shilling.

, or

of a shilling. 5 farthings is

89. 1 oz. is 91. 1 lb. is

of a yard.

of 1 lb. 15 oz. is 18 of 1 lb.
of 1 quarter. 9 lbs. is

miles

of 1 quarter. 100. At the end of 1 hour they would be 7 and apart. In 7 hours, 7 times 74, which is 548 miles. 121. This is the principle of fellowship; 3 shillings were paid; one paid, the other .

122. One paid, the other .

123. 20 dollars were paid in the whole; one paid, another, and the third.

126. 3 and 4 and 5 are 12. The first put in; the second; the third.

129. 4 dollars for 2 months is the same as 8 dollars for 1 month; 3 dollars for 3 months is the same as 9 dollars for 1 month; and 2 dollars for 4 months is the same as 8 dollars for 1 month. The question is the same as if A had put in 8 dollars, B9 dollars, and C 8 dollars. A must have, B, and C, of 100 dollars.

131. A's money was in 4 times as long as C's. It is the same as if A had put in 8 dollars for the same time, and B 8 dollars for the same time. A must have, B, and O, of 88 dollars.

The examples 127, 128, 129, 130, and 131, are double or compound fellowship.

139. The interest of 50 dollars for 1 year and 6 months is 4 dollars and 50 cents, and for 1 month it is 25 cents. The interest of 7 dollars for 19 months (a dollar is of a cent a month) is 663 cents. The whole amounts to 5 dollars and 41 cents.

140. The interest of 200 dollars for 11 years is 16 dollars. The interest of 67 dollars is 67 cents for every 2 ‣ months, for 16 months it will be 8 times 67 cents, which are 5 dollars and 36 cents. The whole interest is 21 dollars and 36 cents.

143. The interest of 100 dollars for 21 years is 13 dollars and 50 cents. The interest of 100 dollars for 60 days would be 1 dollar, the interest for 20 days will be of a dollar, or 33 cents. The interest of 1 dollar for 21 years is 13 cents; for 10 dollars the interest would be 1*dollar and 35 cents, and for 30 dollars, 4 dollars and 5 cents. The interest of 7 dollars for 2 years is 7 times 13 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 951 cents.

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

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 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 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 21 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 11 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

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

196

49,652

Four.
Forty-nine.

Four hundred and ninety-six.

4,965 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.

496,527 "