plicand, and the product of the units, separately; add the tens of each number to the units of the preceding number; thus: (Ex. 1.), 8, 63, 49; 1479: 6, 21, 9; 819: 4, 26, 12; 672: &c.

EXERCISES.

1. How many are 11 times 72? 84? 36? 27? 46 36?

2. How many are 12 times 64? 38? 56? 29? 44? 82?

3. How many are 13 times 29? 36? 48? 53? 64? 73?

4. How many are 14 times 33? 86? 98? 77? 68? 28?

5. How many are 15 times 46? 38? 96? 74? 28? 33?

6. How many are 16 times 27 54? 32? 91? 77? 66?

7. How many are 17 times 86? 42? 68? 34? 22? 53?

8. How many are 18 times 43? 36? 26? 68? 95? 58?

9. How many are 19 times 36? 58? 88? 74?

27? 68?

DIVISION.

LESSON XXIII.

BLACKBOARD EXERCISES.

1. 2) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

1

2. 3) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

3. 4) 1 2 3 4

6 7 8 9 10 11 12 13 14 15

N. B. Complete the exercises by using each of the nine digits as a divisor.

NOTES FOR THE TEACHER.-1. The above and following blackboard exercises are to be studied and recited in the same way as the similar exercises in addition, subtraction, and multiplication.

2. The remainders should be given, thus (Ex. 2.): No times and 1 over; no times and 2 over; once; one and one over; one and 2 over; &c. It is very important that these exercises should be LEARNED SO THOROUGHLY that the quotients and remainders can be recited with the utmost promptness.

PROBLEMS.

1. What is meant by 1 half? ANS.-One of the two equal parts into which a unit or a number of units is divided.

2. How many in 1 half of 6 stars? Of 18 stars?

Of 20 stars?

3. How many in 1 half of 12 oranges? Of 16 apples? Of 24 pears?

4. How many in one half of 32 pounds? Of 14 gallons? Of 26 inches?

5. What is meant by 1 third? ANS.-One of the three equal parts into which a unit or number of units are divided.

6. What is meant by 1 fourth? By 1 sixth? By 1 ninth?

7. What is meant by 1 eleventh? teenth ?

By 1 fif

8. How many in 1 third of 12 stars? In 1 fourth of 12 stars?

9. How many in 1 third of 6 stars ? Of 9 stars? Of 12 stars?

10. What is meant by 1 fifth? By 1 seventh? By 1 ninth?

11. How many in 1 seventh of 14? Of 21? Of 28 ?

12. How many in 1 eighth of 16? Of 24? Of 96?

13. How many in 1 eighth of 24? Of 36? Of 88?

14. How many in 1 nmth of 27? Of 72? Of 108?

15. How many in 1 eleventh of 99? Of 88? Of 121?

PROBLEM.-If 15- apples are equally divided among 3 boys, how many apples will each boy receive?

ARITH. FORM.*-If three boys have 15 apples, one boy will have one third of 15 apples, which is 5 apples.

NOTE.-Let the pupil be taught that one third of a thing or number is the same as the quotient when the thing or number is divided by 3; hence, for brevity, we say, one third of a thing or of a number," instead of a "thing or a number divided by three."

66

16. If 9 peaches cost 27 cents, what is the cost of 1?

17. If 8 lead-pencils cost 24 cents, how much is that apiece?

18. I pay 32 dollars for 8 cords of wood; how much is that per cord?

* The following formula is preferred by some :

FORM.-One boy will have one third as many apples as three boys; 3 boys have 15 apples, therefore one boy will have one third of 15 apples, which is 5 apples.

19. A man earned $36 in 9 days; how much is that per day?

20. 8 gold chains cost $64; what is the cost of each?

21. 5 barrels of apples are worth $35; what is the value of 1 barrel?

22. In 7 hours a man rode 84 miles; how far was that an hour?

23. 9 pounds of sugar cost 81 cents; how much is that a pound?

24. In 9 rows of trees there are 72 trees; how many trees in each row?

25. A man traveled 72 miles in 6 hours; how far did he travel in one hour?

26. 8 bins of equal size contain 72 bushels of wheat; how many bushels does each contain ?

27. If 81 cents be paid for 9 dozen eggs, what will be the cost of 1 dozen ?

28. 11 tons of hay are worth $77; what is the value of one ton?

29. 12 men can perform a certain piece of work in 48 days; what part of it can 1 man perform?

30. If 7 men can eat a cheese in 7 days, what part of it can 1 man eat in the same time?

31. One man can perform a piece of work in 48 days; how long will it take 12 men to do it?

32. One man can do a piece of work in 56 days? how long will it take 8 men?

33. One man can build a barn in 63 days; how long will it take 9 men to do it?