The Elements of Arithmetic, Oral and Written

11. How many barrels of flour at 9 dollars a barrel can be bought for 175 dollars?

12. There are 320 rods in a mile. How many rods in half a mile? In one-fourth of a mile?

13. Two men start from the same place and travel in the same direction-one travels XXV miles a day; the other XVIII miles a day. How far apart are they in a week?

14. Bought 13 cows, at 40 dollars each; 16 sheep at 2 dollars each; a horse for 250 dollars, and a wagon for 97 dollars. How many months would it take to pay for them, in monthly payments of 18 dollars each?

15. A farmer raised 1500 bushels of oats, and sold then for 32 cents a bushel. How many acres of land could he buy, at 20 dollars an acre, with the proceeds?

16. A man received 574 dollars of interest in 7 years. What was that a year?

17. A man has an income from salary, of 75 dollars a month; from interest, of 28 dollars a month; from rents, of 62 dollars a month. It costs him 300 dollars a year for board and 18 dollars a year for taxes. How much will he have at the end of 2 years?

18. How many barrels of flour at 7 dollars a barrel, will pay for 30 tons of coal, at 4 dollars a ton, and 44 cords of wood, at 3 dollars a cord ?

19. If a field containing 42 acres produce 1659 bushels of wheat, what will be the number of bushels per acre? 20. A farmer sold 15 tons of hay at 9 dollars a ton, and 25 cords of wood at 4 dollars a cord, and wished to divide the amount equally among 5 creditors; how much would each receive?

21. If 42864 pounds of cotton be packed in 94 equal bales, what is the weight of each bale?

22. If you deposit 216 cents each week in a savings bank, and take out 89 cents a week, how many cents will you have in bank at the end of 36 weeks?

23. A man sold 6 horses at 125 dollars each, 25 head of cattle at 30 dollars each, and with the proceeds bought land at 25 dollars an acre; how many acres did he buy? 24. A room is 40 feet wide, its length is twice its width, and its height, one-fifth its length. How high is it?

25. Bought 150 barrels of flour for 1050 dollars, and sold 107 barrels of it at 9 dollars a barrel, and the remainder at 7 dollars a barrel; did I gain or lose, and how much?

DRILL EXERCISES.

50. 1. 36, 36, 36, 36, 36, 36, 18, 38.

Let the pupils recite in the following manner,-36 is 36 times 1, 18 times 2, 12 times 3, 9 times 4, etc. In like manner, treat each of the products of the multiplication table as given on Page 31..

2. Double, numbers as in exercises 2, 3 and 4, Page 32, and reverse the process by halving the final products; thus, Half of 8192, Half of 4096, etc.; the pupils naming the successive quotients.

3. 8, × 9,÷12, +3, × 5, +10,÷11, × 8, +20,÷12, +4, ×7,-3=?

Let the pupil read the successive results, as in the last exercise on Page 32.

4. 427, x5, +6, -8,÷4, × 9, -3, ÷ 10, +12, ÷ 9. × 11=?

From right to left. From left to right. This affords over 1000 different exercises in addition.

To 1 add each number in column A. To 2, 3, etc., to 10. Same with each column. By columns give the sum of each number and the one below it. By lines give the sum of each number and the

one to right of it.

By column give the difference of each number and the one below it. By lines give difference of each number and one to right of it. In column A, give difference of each number and 1.

20.

Same with each column.

2, 3, etc., to

Also 3,

By column give product of each number and the one to right of it. In column A, give product of each number and 2. 4, etc., to 9. Same with each column.

Divide 10 by each number in column A, naming only quotient and remainder. Also 11, 12, etc., to 25. Same with each column. Begin at the left and divide the product of any two numbers in columns A and B by the number at the right in column C; then of the columns B and C by the numbers in column D, etc. In the same manner begin with the two columns on the right.

Also beginning at the top, divide the product of the numbers in any two lines by the number in next line below; then in same manner begin with the two lines at the bottom, and divide by the numbers in the next line above.

This table and similar tables, placed upon the blackboard, will afford abundant exercise for months. In no case should more than five minutes daily be given to this kind of work.

FRACTIONS.

51. A Unit is one, or a single thing. (Art. 1.) 52. Numbers that express or represent equal parts of a unit or whole thing are called Fractions.

A fraction is usually expressed by two numbers, called the Numerator and Denominator, one written over the other with a line between them. When so written, they are sometimes called Common Fractions; thus,

Thus, in the fraction }, 4 is the denominator or namer, and shows that the unit is divided into four equal parts, named fourths.

54. The number above the line is the Numerator. Thus, in 2, 3 is the numerator or numberer, and shows that 3 of the 4 equal parts are taken, or expressed, by the fraction.

55. The numerator and denominator of a fraction are called the Terms of the Fraction.

Thus, 3 and 4 are terms of the fraction .

Read the following fractions, and name the terms: