dividend, and find how often 4 is contained in 17, this is 4 times with a remainder ; or, since the denomination of the 17 is thousands, the number of times is 4 thousands, and the remainder 1 thousand; place the 4 under the thousands' figure in the dividend, and change the 1 thousand into 10 hundreds, and add the 5 hundreds in the dividend; we now have 15 hundreds, and since 4 is contained in 15 three times, with a remainder 3, therefore 4 is contained in 15 hundreds three hundred times, with a remainder 3 hundred; place 3 in the hundreds' place, and change the remainder into 30 tens ; next adding the 8 tens in the dividend, we get 38 tens, and 4 is contained in this number 9 tens times and 2 tens over; put 9 in the tens' place; lastly, changing the remainder into 20 units, and, adding the 4 units, we get 24 units, and 4 is contained in 24 six times without remainder; we therefore put 6 in the units' place. Hence the following rule for dividing by numbers which do not exceed 12: Place the divisor in a curve to the left of the dividend, and draw a line. Find how often the divisor is contained in the first figure, or, if necessary, the number formed by the first two or more figures of the dividend, and place this figure for the first figure of the quotient; bring the remainder (if any) to the next lower denomination by multiplying by 10, and add the next figure in the dividend, or, which is the same thing, imagine the remainder to be placed before the next figure in the dividend, and find how many times the quotient is contained in the number thus formed; set down the number of times for the second figure of the quotient, and proceed as before with the remainder. Proof-Division may be proved by multiplying the divisor and quotient together, and adding the remainder, if any, to the product. If the result be equal to the dividend, the work is correct. For example, 17 divided by 5 gives a quotient 3 and remainder 2; and if we multiply 5 and 3 together, and add the remainder 2 to the product, we get the dividend 17. F. (2) (5) (1) 375975 by 2. 537409 by 3. (3) 654793 by 4. (4) 728397 by 5. 637549 by 6. (6) 275493 by 7. (7) 437956 by 8. G. 4395876 by 4. (2)3968759 by 4. (a) 6379587 by 5. 3954769 by 5. (5) 4376985 by 6. 2539476 by 7. f (6) (12) 587637 by 11. 375479 by 12. (13) 643758 by 12. SECTION II. When the divisor is the exact product of two numbers, neither of which exceeds 12, the dividend may be divided by one of the numbers and then the result by the other number. If there are remainders to each division, the whole remainder may be found by multiplying the last remainder by the first divisor and adding to the product the first remainder. We will illustrate this method by dividing 347 marbles equally amongst 27 boys, or, which is the same thing, amongst three classes, each consisting of 9. boys..: Instead of giving each boy his share of the marbles we will divide them into three equal lots, and give one lot to the monitor of each class to distribute equally amongst his class fellows. 3) 347 Dividing 347 by 3, we get 115, with a remainder 2. We will therefore 115.2 give each monitor 115 marbles to divide equally amongst the 9 boys of his class, and request him to bring any marbles that may be left after such division to put with our own remainder. 9 ) 115 12...7 Each monitor dividing 115 by 9 would get a quotient 12, and remainder 7. He would therefore give every boy in his class 12 marbles, and bring us the 7 marbles left. Now there are three classes, in each of which 7 marbles are left, therefore we shall have 3 times 7, or 21 marbles to put with the 2 marbles left at first, and this gives 23 for the whole remainder. The working is arranged in practice as follows :— First dividing by 3 we get a quotient 115, and remainder 2. 23 Next dividing 115 by 9 we get 12...7 S à quotient 12, and remainder 7. 3 ) 347 9). 115 ... 21 We then say 3 times 7 is 21 and 2 are 23. (5) 397 by 15. H.(1) 583 by 25. (*) 296 by 35. (2) 701 by 16. (6) 397 by 28. (10) 839 by 49. (11) 637 by 50. (12) 953 by 56. When the divisor is 10, 100, 1000, &c., the division is effected by cutting off from the right of the dividend as many figures as there are noughts in the divisor. Example.-Divide 583 by 100. Here 583 is 5 hundreds and 83, therefore the number of hundreds is 5 and the remainder 83. Divide 43798 by 1000. Since 43798 is 43 thousands and 798; therefore the number of thousands is 43, and the remainder 798. Write down the quotients and the remainders (if any) in the following examples. When the divisor consists of a number not greater than 12 followed by noughts, cut off the |