20. If 90 nuts are distributed among some boys, each one receiving 9, how many boys are allowed to share?

21. At 10 cents per yard, how much calico can be purchased for 80 cents? how much for 100 cents?

22. 32 are how many times 2? 4? 8? 16?

23. 36 are how many times 2? 3? 4? 6? 9? 12? 18?

24. 48 are how many times 2? 3? 4? 6? 8? 12? 16?

25. 60 are how many times 2? 3? 4? 5? 6? 10 ? 12? 15?

26. 64 are how many times 2? 4? 8? 16? 27. 168 are how many

244 are how many?

246 are how many?

28. How many times 8 in 72? In 72 how many times 9? 80 10 are how many? How many times 8 in 80 ?

29.

How many times 12 in 84? how many times 7 in 84 ?

30. 12 divided by what number gives the quotient 6? 4? 3? 2?

31. 39 divided by what number gives the quotient 3? 13?

32. What numbers, multiplied together, will produce 12? 16? 15? 18? 24? 27? 36? 42? 48? 49?

33. How many times 3 tens in 12 tens? in 18 tens? in 24 tens? in 27 tens?

34. How many times 30 in 120? in 180? in 240? in 270 ?

35. How many times 6 tens in 36 tens? in 48 tens? in 54 tens? in 72 tens?

36. How many times 60 in 360? in 480? in 540? in 720 ?

37. What is Division ?

38. What is the number to be divided called?

39. What is the number we divide by called?

40. What is the result of the operation called? 41. What is the number called that remains undivided, after the division is performed?

SECTION XIII.

IN the previous section questions were proposed in which the divisor was exactly contained in the dividend. In the present section the dividend will not exactly contain the divisor, and the remainder is given as a part of the answer: thus, 73 gives 2 for the quotient, and 1 for the remainder.

1. How many times 3, and what remainder, in 11 ? 2. In a piece of cloth containing 15 yards, how many pieces, of 4 yards each, may be obtained, and how many yards will there be remaining?

3. How many times 4, and what remainder, in 17? in 23? in 27 ? in 33? in 37 ? in 45?

4. How many miles can you ride in a stage-coach for 27 cents, if you pay 5 cents for every mile, and how many cents will you have remaining?

5. How many times 5, and what remainder, in 18? in 21? in 29? in 33? in 42? in 47? in 53 ?

6. A gardener wishes to place 49 trees in rows of 6 trees each; how many rows will there be, and how many trees will he have remaining?

7. How many times 6, and what remainder, in 17? in 21? in 26? in 33? in 45? in 49? in 62? in 73 ? 8. If you have 53 shillings, to how many men can you give 7 shillings each, and what number of shillings will you have remaining?

9. How many times 7, and what remainder, in 13? in 19? in 25 ? in 31? in 38? in 43? in 50? in 58? in 69? in 76 ?

10. I have 47 pounds of tea in a chest; how many packages of 8 pounds can I put up, and how many pounds will remain in the chest?

11. How many times 8, and what remainder, in 17? in 23? in 36? in 42? in 50? in 59? in 65? in 76? in 90 ?

12. How many tons of coal, at 9 dollars a ton, can be bought for 85 dollars, and how many dollars will remain?

13. How many times 9, and what remainder, in 17? in 25? in 29? in 39? in 48? in 59? in 64? in 75? in 82? in 94?

14. John has 43 cents; to how many poor women can he give 10 cents each, and how many cents will he have left?

15. How many times 10, and what remainder, in 24? in 36? in 48? in 55? in 64? in 73? in 89? in 97 ?

16. A grocer has 92 gallons of oil to draw off into casks that will hold 11 gallons each; how many casks can he fill, and how many gallons will he have remaining?

17. How many times 11, and what remainder, in 25? in 37? in 45? in 59? in 64? in 78? in 89? in 96?

18. A gardener has 65 peaches which he wishes to send to market in baskets that will contain 12 peaches each; how many full baskets can he send, and how many peaches will he have remaining?

19. In a gross there are 12 dozen; how many gross

in 105 dozen?

20. How many times 12, and what remainder, in 21? in 37? in 49? in 56? in 63? in 82? in 95? in 109? in 126?

21. How many yards of calico, at 13 cents a yard, can be purchased for 76 cents, and what number of cents will there be remaining?

MULTIPLICATION COMBINED WITH DIVISION.

SECTION XIV.

= 4

OBS. The sign of equality,=, is read are, or are equal to ; as 2 and 2 = 4 is read, 2 and 2 are 4, and 8 X 510 = is read, 8 times 5 divided by 10 are equal to 4.

=

1. FROM the product of 6 times 4, how can 3 be subtracted?

many times

2. How many times are S contained in 4 times 6? 3. Bought oranges at 4 cents each, and paid 4 tencent pieces for them; what number of oranges did I buy?

4. Sold 6 pounds of pilot-bread at 5 cents a pound; how many 3 cent pieces are required to pay for it? 5. 10 times 3 are how many times 5?

6. 6 times 6 are how many times 3?

7. A man purchased 10 chaldrons Sidney coal for 6 dollars a chaldron; how many 5 dollar gold pieces are required in payment?

8. How many times are 8 contained in 10 times 4? in 2 times 12? in 2 times 16?

9. A farmer exchanged 3 pounds of butter, worth G6 cents, for cocoa worth 6 cents a pound; how much cocoa did he receive?

10. How many times are 7 contained in 2 times 14? in 3 times 14? in 6 times 14?

11. Loaf-sugar, at 10 cents per pound, is given in exchange for 5 pounds of Java coffee, at 11 cents per pound, and 5 dozen of eggs, at 9 cents per dozen; how many pounds of sugar are given?

12. 5 times 8 are how many times 10?

13. Twelve inches make one foot; how many feet are there in 24 inches? in 3 times 16 inches? in 6 times 10 inches?

14. How many times 2 feet in 72 inches?

15. Bought 6 cords of wood at 7 dollars a cord; how many sheep, at 3 dollars a head, will be equal in value to the wood?

16. 6 times 7 are how many times 6? 3? 4? 5? 11? 14?

17. Four farthings make one penny; how many pence in 6 times 6 farthings?

18. 10 times 7 are how many times 11? 8? 10? 12? 6?

19. How many barrels of flour, at 6 dollars a barrel, are equal in value to 6 bags of coffee, at 12 dollars a bag?

20. 6 times 12 are how many times 6? 7? 8? 9? 10?

21. A tailor bought 11 yards of broadcloth, at 6 dollars a yard, and gave in payment vests worth 5 dollars apiece; how many vests did he give, and what number of dollars remained unpaid?

22. 11 times 6 are how many times 5? 8? 9? 11? 12?

23. A milkman bought 12 pounds of brown sugar, at 7 cents a pound, and paid for it with milk, at 6 cents a quart; how many quarts of milk did it require?

24. 12 times 7 are how many times 6? 8? 9? 10? 11? 12?

25. How many are 8 × 12 ÷ 4 ? 42, therefore 8 X 12 ÷ 4 Or 12 ÷ 4

= 24.

SOLUTION. S 2 X 12 = 24.

3, therefore 8 × 12 ÷ 4 8 times 3 After becoming familiar with this process, the pupil will be able to give the answer at sight.

26. How many are 12 × 7÷ 14? SOLUTION. 14 is equal to 2 times 7; therefore, 12 multiplied by 7 divided by 14, is the same as 12 divided by 2, which is 6.

27. How many are 8 X 14'16? 8 × 14 ÷ 4? 8 X 147? 8 X 14 ÷ 28?