DIVISION TABLE. 1 in 1 1 time 5 in 5 1 time 9 in 9 1 time 1 in 2 2 times 5 in 10' 2 times 9 in 18 2 times 1 in 3 3 times | 5 in 15 3 times 9 in 27 3 times 1 in 4 4 times 5 in 20 4 times 9 in 36 4 times 1 in 55 times 5 in 25 5 times 9 in 45 5 times 1 in 6 6 times 5 in 30. 6 times 9 in 54 6 times . 1 in 77 times 5 in 35 7 times 9 in 63 7 times 1 in 8 8 times' | 5 in 40 8 times 9 in.72 8 times 1 in 9 9 times 5 in 45 9 times 9 in 81 9 times 2 in 2 1 time 6 in 6 1 time 10 in 10 1 time 2 in 4 2 times 6 in 12 2 times 10 in 20 2 times 2 in 6 3 times 6 in 18 3 times 10 in 30 3 times 2 in 8 4 times 6 in 24 4 times 10 in 40 4 times 2 in 10 5 times 6 in 30 5 times 10 in 50 5 times 2 in 12 6 times 6 in 36 6 times 10 in. 60 6 times 2 in 14 7 times 6 in 42 7 times 10 in 70 7 times 2 in 16 8 times | 6 in 48 8 times 10 in 80 8 times 2 in 18 9 times 6 in 54 9 times 10 in 90 9 times 3 in 3 1 time 7 in 7 1 time 11 in 11 1 time 3 in 6 2 times 7 in 14 2 times 11 in 22 2 times 3 in 9 3 times 7 in 21 3 times 11 in 33 3 times 3 in 12 4 times 7 in 28 4 times 11 in 44 4 times 3 in 15 5 times 7 in 35 5 times 11 in 55 5 times 3 in 18 6 times 7 in 42 6 times 11 in 66 6 times 3 in 21 7 times 7. in 49 times | 11 in 77 7 times 3 in 24 8 times 7 in 56 8 times 11 in 88 8 times 3 in 27 9 times 7 in 63 9 times 11 in 99 9 times 4 in 4 l time 8 in 8 l time 12 in 12 1 time 4 in 8 2 times 8 in 16 2 times 12 in 24 2 times 4 in 12 3 times 8. in 24 3 times 12 in 36 3 times 4 in 16-4 times 8 in 32 4 times 12 in 48 4 times 4 in 20 5 times 8 in 40. 5 times 12 in 60 5 times 4 in 24 6 times 8 in 48 6 times 12 in 72 6 times 4 in 28 7 times 8 in 56 ,7 times 12 in 84 7 times 4 in 32 8 times 8 in 64 8 times 12 in 96 8 times 4 in 36 9 times 8 in 72 9 times 12 in 108 9 times 34. There are three numbers in every division, and sometimes four: 1st, the dividend ; 2d, the divisor; 3d, the quotient; and 4th, the remainder. QUESTIONS. 1. If 12 apples be equally divided among 4 boys, how many will each ḥave? How many tinies is 4 contained in 12 ? 2. If 24 peaches be equally divided among 6 boys, how many will each have? How many times is 6 contained in 24 ? 3. A man has 32 miles to walk, and can travel 4 miles an hour, how many hours will it take him ? 4. A farmer receives 28 dollars for 7 sheep: how much is that apiece? 5. How many lead pencils could you buy for 42 cents, if they cost 6 cents apiece? 6. How many oranges could you buy for 72 cents, if they cost 6 cents apiece ? 7. A trader wishes to pack 64 hats in boxes, and can put but 8 hats in a box: how many boxes does he want ? 8. If a man could build 7 rods of fence in a day, how long will it take him to build 77 rods? 9. If a man pays 56 dollars for seven yards of cloth, how much is that a yard ? 10. Twelve men receive 108 dollars for doing a piece of work, how much does each one receive ? 11. A merchant has 144 dollars with which he is going to buy cloth at 12 dollars a yard: how many yards can he purchase ? 12. James is to learn forty-two verses of Scripture in a week: how much must he learn each day? 13. How many times is 4 contained in 50, and how a many over ? 14. A man has 96 pounds of butter, and wishes to put 12 pounds in a box: how many boxes does he want? 15. Janies goes to school for 12 weeks, and receives 132 credit marks: how many does he get each week ? 34. How many numbers are there in every division? Name thom 16. Four men bought a pair of oxen for one hundred dollars, and sold them again for eighty-four dollars : how much did each one lose? 17. How many times is 8 contained in 100, and how many over? 18. How many times is 11 contained in 60, and how many over? 19. How many times is 9 contained in 86, and how many over ? 20. How many times is 7 contained in 79, and how many over ? 21. How many times is 5 contained in 59, and how many over ? 22. A mother wishes to distribute 30 apples among 8 children: how many will each have, and how many will be left ? 23. How many times 4 in 23, and how many over ? In 27 ? In 40 ? In 46 ?. In 35 ? In 39 ? 24. How many times is 6 contained in 70, and how many over ? In 65 ? In 61 ? 25. How many times 7 in 43, and how many over? 26. How many times 9 in 50, and how many over ? In 54 how many times ? In 80 how many times, and what over? In 86 ? In 94 ? 27. How many times 8 in 57, and how many over ? In 65 ? In 87 ? In 100 ? 28. How many times 11 in 54, and how many over? In 67 ? In 85 ? In 97 ? In 62 ? In 59 ? 29. How many times 12 in 100, and how many over? In 120 ? In 87 ? In 77 ? In 66 ? In 130 ? 30. James bought 9. tops for 72 cents: what did he pay apiece? 12 in 90, how many times, and how many 31. A man paid thirty-six dollars for twelve sheep, and fifteen dollars apiece for two cows: how much more did he pay apiece for the cows than the sheep? 32. A drover has eight calves for which he paid forty dollars, and nine sheep for which he paid twenty-seven dollars : how much more did he pay apiece for the calves than for the sheep? over ? EXAMPLES ILLUSTRATING PRINCIPLES. OPERATION. Diviser. Tele Dividend. OPERATION. 35. Let it be required to divide 86 by 2. Place the divisor on the left of the dividend, draw a curved line between them, and a straight line under the dividend. Now, there are 8 tens and 6 units to be divided by 2. We say, 2 in 8, 4 2)86 times, which being 4 tens we write the 43 quotient. 4 under the tens. We then say, 2 in 6, 3 times, which are three units, and must be written under the 6. The quotient, therefore, is 4 tens and 3 units, or 43. 1. Let it be required to divide 729 by 3. In this example there are 7 hundreds, 2 tens, and 9 units, all to be 3)729 divided by 3. Now we say, 3 in 7, 243 2 times and 1 over. Set down the 2, which are hundreds, under the 7. But of the 7 hundreds there is 1 hundred or 10 tens not yet divided." We put the 10 tens with the 2 tens, making 12 tens, and then say, 3 in 12, 4 times, and write the 4 in the quotient, in the tens' place; then say, 3 in 9, 3 times. tient, therefore, is 243. 2. Let it be required to divide 729 by 9. In this example, we say, 9 in 7 we cannot, but 9 in 72, 8 times, which are 9)729 8 tens: then, 9 in 9, 1 time. The 81 quotient is therefore 81. The quo OPERATION. 35. When you divide 8 tons by 2, is the quotient tens or units ? When 6 units are divided by 2, what is the quotient? Ex. 1. When the 7 hundreds are divided by 3, of what denomination is the quotient? To how many tens is the undivided hundred equal ? When the 12 tens are divided by 3, what is the quotient ? When the 9 units are divided by 3, what is the quotient? 3. Let it be required to divide 36548 by 5. The 36 thousands being divided OPERATION. by 5 gives 7 thousands for the first 5)36548 figure of the quotient. We then 7309–3 romain. divide the 15 hundreds, giving a quotient figure of 3; then 4 tens, giving 0; and then 48 units, giving 9 and a remainder 3. The division of the 3 must be expressed by writing 5 under the 3, thus, : The true quotient, therefore, is 7309; which is read, seven thousand three hundred and nine, and three divided by five. Therefore, When there is a remainder after division, it must be written after the quotient, and the divisor placed under it. 3 CASE I. 36. Short Division, or when the divisor does not exceed 12. RULE. 1. Set down the divisor on the left of the dividend, draw a curved line between them, and a straight line under the dividend. II. Begin with the left-hand figure of the dividend and divide each figure, in succession, by the divisor, when such division is possible, and write each quotient figure directly under the figure divided. III. When any figure of the dividend is not divisible by the divisor, write 0 for the quotient figure, and consider the remainder as tens, to which add the next figure of the dividend, regarded as units, and divide this sum for the next figure of the quotient. Ex. 3. When there is a remainder after division, what do you do with it? If there be a remainder after division, how must it be written? 36. What is short division? How do you set down the numbers to be divided? How do you divido ? Repeat the rule. |