Note. It is well for scholars to read the tables in class, the same as reading lessons, by which means they will learn them in a few hours. The most of the Arithmetic may be read occa sionally. How many oranges could you buy for 24 cents at 6 cents an orange? If you ride 4 miles an hour, how many hours would it take you to ride 36 miles? With 72 cents, how many knives could you buy at 12 cents a-piece? How many times 9 in 81? how many times 11 in 80, and how many over? How many times 12 in 84? how many times 12 in 136, and how many over? QUESTIONS AND EXAMPLES. Divisor 3)976432 dividend. Explanation.-Begin and say 3 is in 9 3 times, which Quotient 325477-1 over, or rem. set down; then 3 is in 7 Proof X3+1. 976432 twice and 1 over; this 1 is now supposed to be placed at the left of the next figure 6, which would be 16; then say 3 is in 16 5 times and 1 over; then 3 in 14 4 times and 2 over; now this 2 is supposed to be placed at the left of the next figure 3, which will make it 23; then 3 is in 23 7 times and 2 over; this 2 placed at the left of the next figure 2 is 22; then 3 is in 22 7 times and 1 over, a remainder which must be placed at the right. Then multiply the quotient by the divisor, and add in the 1, for the proof. Note.-If the divisor is not contained in the next figure of the dividend, write a cipher in the quotient, and join this figure in the dividend, to the figure next to it, as so many tens. 37. A farmer sold 540 bushels of grain to 9 men; how much did each man receive for his share? Ans. 60 bush. Ans. 64D. Ans. 733. much is that 38. Divide 320D. equally among 5 persons. 39. How many times is 9 contained in 6597 ? 40. If a man spend 424D. in 8 months, how per month? 41. If 9 persons sell property to the amount of 20763D., how much will each man receive for his share? 42. Divide 378567 by 2; by 3: 2)378567 Ans. 315472-1 remainder. Ans. 53D. Ans. 2307D. 3)378567 REVIEW. What is Division? How many parts are there in Division! Which is the Dividend? Which is the Divisor? Which is the Quotient? Which is the Remainder? When the Divisor does not exceed 12, what is the rule? What is this called? How do you prove Division? Having the Dividend and Quotient given, how is the Divisor found? If you have the Divisor and Quotient given, how can you find the Dividend? Recite the Table. Note to Teachers.-It is expected that in every case the pupil will commit to memory the tables and rules, before he shall attempt the solution of the questions. It is evidently erroneous for a scholar to attempt to work by, or follow, a given mathematical rule, unless he has learned it and understands its import, merely from a given example, which I regret to say is too frequently the case; consequently, the scholar never has a correct knowledge of the science of numbers. The questions, or interrogatories, given in the Review, can be used by the teacher at the beginning of the rule, or as they are given, or, which would be still better, at the beginning and close of the solution of the questions in the rule. LONG DIVISION. LONG DIVISION is generally used when the divisor is more than 12. RULE. 1. Write down the dividend, and draw curved lines at the right and left sides of the dividend, thus: )90(, and place the divisor at the left hand, as in Short Division. 2. See how often the divisor is contained in the least number of figures into which it can be divided, and set that number at the right hand of the dividend, which is the multiplier. 3. Multiply the divisor by this figure in the quotient, and place the result under the figures in the left of the dividend, into which you are dividing. 4. Then subtract the result from the number directly over it, and set down the remainder, which must always be less than the divisor. 5. Bring down the next figure of the dividend, and place it at the right of the remainder; if this number is less than the divisor, place a cipher in the quotient, and bring down another figure; which forms another dividend, into which divide as before, and so continue until all the figures are brought down and divided. Note.-If there be ciphers at the right of the dividend and divisor, you can omit an equal number of each, by placing a périod at the left, thus: 1.00)10.00(10 answer. EXAMPLES AND QUESTIONS. Dividend. Explanation. You can not Divisor 7)54306(7758 quotient. say 7 in 5, because 5 is less 49 53 49 40 35 56 56 O remainder. than 7; but say 7 in 54 7 times, then subtract 35 from 40, and 5 remain; then bring down the next figure 6 at the right of the 5, which will make 56; then 7 is in 56, 8 times 7 is 56, and O remainder. Ans. 832, 92 rem. 37. How many times is 176 contained in 146524? 38. How many times is 250 contained in 925500? Ans. 3702. Ans. 646. Ans. 1747, 41 rem. 41. The crew of a ship consisting of 150 men, are entitled to 24750D. prize money; what is the share of each man? Ans. 165D. 42. What number must be multiplied by 150 to produce 24750? Ans. 165. 43. A garrison of 2441 men have received 9764 pounds of flour; how much is the share of each man? Ans. 4 pounds. 44. A gentleman bequeathed his estate, which was estimated at 247655D., to his 4 sons and only daughter; how much did each receive? Ans. 49531D 45. What is the quotient of 678976500 divided by 6789 ? 46. What is the quotient of 10000000 divided by 99? 47. Divide 500D. equally among 10 men; 40 men; 100 men; 150 men. |