8. How many slates, at 8 cents a piece, can you buy for 40 cents ? 9. Four quarts make one gallon : how many gallons are there in 48 quarts ? 10. At 7 dollars a ton, how many tons of coal can be bought for 63 dollars ? DIVISION TABLE. , once 2 in 3 in 4 in 5 in 6 in 7 in 8 in 9 in 2, once 3, once 4, once 5, once 6, once 7, once 8, once 9,0 4, 26, 2 8, 2 10, 212, 214, 216, 2 18, 2 6, 3 9, 3 12, 3 15, 3 18, 321, 3 3 24, 3 27, 8, 4 12, 416, 4 20, 4 24, 4 28, 4 4 32, 4 36, 10, 5 15, 5 20, 5 25, 5 30, 5 35, 5 10, 5 45, 12, 6 18, 6 24, 6 30, 636, 6 42, 6 48, 6 54, 14, 721, 728, 7 35, 742, 7 49, 7 56, 7 63, 16,8 24, 8 32, 8 40, 8 48, 8 56, 8 64, 8 72, 8 18, 9 27, 9 36, 9 45, 9154, 963, 972, 9 81, 11. How many pair of boots, at 2 dollars a pair, can be bought for 24 dollars ? for 22 ? 20 ? 18? 16 ? 14 ? 12 ? 10 ? 12. How many barrels of cider, at 3 dollars a barrel, can you buy for 36 dollars ? for 30 ? 27 ? 24 ? 21 ? 18 ? 15 ? 12 ? 13. How many quarts of milk, at 4 cents a quart, can you buy for 48 cents ? for 44 ? 40 ? 36 ? 32 ? 28 ? 24 ? 20 ? 16? 14. At 5 cents an ounce, how many ounces of wafers can you buy for 60 cents ? for 55 ? 50 ? 45 ? 40 ? 35 ? 30 ? 25 ? 15. At 6 shillings a pair, how many pair of gloves can be bought for 60 shillings ? for 54 ? 48 ? 42 ? 36 ? 30 ? 24 ? 18? 16. How many pounds of butter, at 7 cents a pound, can be purchased for 63 cents ? 56 ? 49 ? 42 ? 35 ? 28 ? 21 ? 14 ? 17. How many cloaks will 72 yards of cloth make, allowing 8 yards to a cloak ? how inany 64 ? 56 ? 48 ? 40 ? 32 ? 24 ? 18. How many cows, at 9 dollars apiece, can be can bought for 81 dollars ? for 72 ? 63 ? 54 ? 45? 36 ? 27? 18? 9? 19. How many times is 4 contained in 36 ? 48 ? 40 ? 20. How many times is 8 contained in 40 ? 56 ? 48 ? 64 ? 72 ? 21. In 25, how many tiines 4, and how many over ? Ans. 6 times and 1 over. 22. In 34, how many times 5, and how many over? In 43 ? 45 ? 37 ? 28 ? 39 ? 23. In 23, how many times 3, and how many over? How many times 4? 2? 10 ? 6? 24. In 24, how many times 7, and how many over ? 6 ? 5? 9 ? 12 ? 2 ? 25. In 36, how many times 6 ? 7? 3? 8 ? 12 ? 5 ? 9? 26. In 32, how many times 6 ? 4? 3 ? 16? 27. How many hats, at 6 dollars apiece, can be bought for 60 dollars ? 28. How many tons of hay, at 9 dollars per ton, you buy for 81 dollars ? 29. If you travel 7 miles an hour, how long will it take to travel 70 miles ? 30. If you pay 10 cents apiece for slates, how many can you buy for 95 cents, and how many cents over ? 31. George bought 12 oranges which he wishes to divide equally between his 2 brothers : how many can he give to each ? Suggestion. Since there are 12 oranges to be divided equally between 2 boys, each boy must receive 1 orange as often as 2 oranges are contained in 12 oranges; that is, each must receive as many oranges as 2 is contained times in 12. But 2 is contained in 12, 6 times; for 6 times 2 make 12. Ans. They received 6 oranges apiece. 32. Henry has 15 apples, which he wishes to divide equally among 3 of his companions : how many can he give to each? 33. A gentleman sent 20 peaches to be divided equally among 4 boys : how many did each boy receive ? 34. A dairy woman having 30 pounds of butter, wish es to pack it in 5 boxes, so that each box shall have an equal number of pounds : how many pounds must she put in each box? 35. I have 21 acres of land, which I wish to fence into 7 equal lots : how many acres must I put into each lot? 36. A boy having 28 marbles, wished to distribute them into 4 equal piles : how many must he put in a pile ? 37. I have 40 peach-trees, which I wish to set out in 5 equal rows : how many must I set in a row ? 38. There were 45 scholars in a certain school, and the teacher divided them into 5 equal classes : how many did he put in a class ? 39. If 50 dollars were divided equally among 10 men, how many dollars would each man receive ? 40. A company of 8 boys buying a boat for 32 dollars, agreed to share the expense equally : how much must each one pay? 41. In a certain orchard there are 54 apple-trees, and 6 trees in each row: how many rows are there in the orchard ? 42. If 63 quills are divided equally among 7 pupils, how many will each receive ? 43. If you divide 36 into 4 equal parts, how many will there be in a part ? 44. If you divide 56 into 8 equal parts, how many will each part contain ? 45. If you divide 48 into 6 equal parts, how many will each part contain ? 46. A gentleman distributed 40 dollars equally among 8 beggars : how many dollars did he give to each? 47. A company of 6 boys found a pocket-book, and on returning it to its owner, he handed them 60 dollars to be shared equally among them: what was each one's share ? 48. A merchant received 72 dollars for 6 coats of equal value: how much was that apiece ? 49. A man paid 81 cents for the use of a horse and buggy to ride 9 miles : how much was that a mile ? 50. If you divide 90 dollars into 10 equal parts, how many dollars will there be in each part ? 1 Obs. The object in each of the last twenty questions, is to divide a given number into several equal parts, and ascertain the value of these parts; but the method of solving them is precisely the sume as that of the preceding ones. 64. The process by which the foregoing examples are solved, is called Division. It consists in finding how many times one given number contains another. The number to be divided is called the dividend. The number obtained by division, or the answer to the question, is called the quotient. It shows how many times the dividend contains the divisor. Obs. The term quotient is derived from the Latin word quoties, which signifies how often, or how many times. Hence, it may be said, 65. Division is finding a quotient, which multiplied into the divisor, will produce the dividend. 66. The number which is sometimes left after division, is called the remainder. Thus in the twenty-first example, when we say 4 is contained in 25, 6 times and 1 over, 4 is the divisor, 25 the dividend, 6 the quotient, and 1 the remainder. Obs. 1. The remainder is always less than the divisor ; for if it were equal to, or greater than the divisor, the divisor could be contained once more in the dividend. 2. The remainder is also of the same denomination as the divi. dend; for it is a part of it. 67. Division is denoted in two ways : Quest.–64. What is the operation called by which the above examples have been solved? In what does it consist? How many numbers are given? What is the number to be divided called? The number hy which we divide ? What is the number ohtained, called? What does the quotient show? 65. What then may division be said to be ? 66. What is the number called which is sometimes left after division? When we say 4 is in 25, 6 times and 1 over, what is the 4 called? The 25 ? The 6? The 1 ? When we say 6 is in 45, 7 times and 3 over, which is the divisor? The dividend? The quotient ? The remainder. Obs. Is the remainder greater or less than the divisor? Why? Of what denom. ination is it? Why? 67. How many ways is division denoted ? First, by a horizontal line between two dots - , called the sign of division, which shows that the number preceding it is to be divided by the number after it. Thus the expression 24-6, signifies that 24 is to be divided by 6. Second, division is often expressed by placing the divisor under the dividend with a short line between 'hem. Thus the expression 35, shows that 35 is to be divided by 7, and is equivalent to 35-7. Obs. 1. It will be perceived that division is similar in principle to subtraction, and may be performed by it. For instance, to find how many times 3 is contained in 12, as in the first example, subtract 3 (the divisor) continually from 12 (the dividend) until the latter is exhausted; then counting these repeated subtractions, we shall have the true quotient. Thus 3 from 12 leaves 9; 3 from 9 leaves 6; 3 from 6 leaves 3; 3 froin 3 leaves 0. Now by counting, we find that 3 can be taken from 12, 4 times ; or that 3 is contained in 12, 4 times. Hence, Division is sometimes defined to be a short way of performing repeated subtractions of the same number. Obs. 2. It will also be observed that division is the reverse of multiplication. Multiplication is the repeated addition of the same number; division is the repeated subtraction of the same number. The product of the one answers to the dividend of the other; but the latter is always given, while the former is required. 3. When the dividend denotes things of one denomination only, the operation is called Simple Division. EXERCISES FOR THE SLATE. Ex. 1. How many barrels of cider, at 2 dollars a barrel, can you buy for 648 dollars ? Suggestion. Since 2 dollars will buy 1 barrel, 648 dollars will buy as many barrels as 2 is contained tiines in 648. Quest.- What is the first? What does this sign show? What is the second way of denoting division? Ohs. To what rule is division simiJar in principle ? How is division sometimes defined? Of what is die vision ihe reverse ? How does this appear? When the dividend denotes things of one denomination only, what is the operation called ? |