SECTION V. Division of any two numbers whatever. Here the dividend is 98 thousands 7 hundreds 3 tens 5 units; now 31 is contained in 98 three times with remainder 5, and therefore in 98 thousand 3 thousand times with remainder 5 thousand or 50 hundred, adding the 7 hundred in the dividend, we get 57 hundred; now 31 is contained in 57 once with remainder 26, and therefore it is contained in 57 hundred 1 hundred times with remainder 26 hundred or 260 tens; adding the 3 tens in the dividend we get 263 tens, and since 31 is contained in 263 eight times, with remainder 15, therefore it is contained in 263 tens 8 tens times with remainder 15 tens or 150 units, lastly adding the 5 units in the dividend we get 155 units and 31 is contained in this number 5 units times without remainder. Hence the quotient is 3 thousands hundred 8 tens 5 units, or 3185. The above process may be expressed thus :— 31)98 th. 7 hn. 3 tns. 5 uts.(3 th. 1 hn. 8 tens. 5 uts. 93 th. 5 th. 7 hn. 26 hn. 3 tns. 15 tns. 5 uts. or 155 uts. 155 uts. In practice the denominations of the figures are omitted and the division is generally performed as follows: 31)98735(3185 93 57 31 263 248 155 155 Write the divisor to the left of the dividend, and the figures of the quotient as they arise to the right, and draw lines to separate the divisor and quotient from the dividend. Since the divisor is not contained in the first figure of the dividend, we take the number 98 formed by the first two figures; now 31 is contained in 98 three times, therefore we put 3 for the first figure of the quotient and multiply the divisor by this quotient figure; 3 times 31 is 93, which subtracted from 98 leaves 5; to this remainder we bring down 7, the next figure of the dividend, this makes 57, and 31 is contained in it once with a remainder; put 1 for the second figure of the quotient, and subtract 31 from 57, this leaves 26; to this remainder bring down 3 the next figure in the dividend, this makes 263, and 31 is contained in it 8 times with a remainder; put 8 for the third figure of the quotient, 8 times 31 is 248, and this subtracted from 263 leaves 15; lastly bring down 5 from the dividend, this makes 155, and 31 is contained in it 5 times; 5 times 31 is 155; subtracting, there is no remainder. Hence the quotient is 3185 as before. Divide 244126597 by 46000. Cut off three noughts in the divisor and three figures in the dividend and divide 244126 by 46; the quotient is 5307 and the remainder 4; bring 46,000)244126,597(5307 down the figures cut 230 141 138 326 322 4597 off in the dividend and we get 4597 for the complete remainder. When the work is expressed in full, as in the above examples, the operation is called Long Division; but when the multiplication and subtraction are performed mentally the quotient only being set down, the operation is called Short Division. Examples.-Divide— 341 by 31. (5) 1395 by 31.6958 by 71. (6) 3233 by 61. (10) 6097 by 91. 4544 by 71. 4758 by 61. M.(1) (2) (3) 861 by 41. 1173 by 51. (7) (1) 1394 by 41. (8) (3) 14924 by 41. (9) 76360 by 92. (10) 50499 by 93. (8) 19584 by 34. (0) 6131985 by 865. (9) (10) 1. Express in words 15, 38, 70, 63; and in figures fourteen, twenty-three, fifty, eighty-seven. 2. Add together 5, 4, 3, 8; and find the sum of 14, 9, 23, 7, 28. 3. Find the difference between 257 and 538. B. 1. Express in figures nineteen, thirty-seven, eighty-four; and in words 20, 48, 69, 96. 2. Find the sum of 8, 3, 7, 9; and of 23, 16, 9, 15, 37. 3. Find the difference between 6408 and 2943. 4. Multiply 5769 by 8, and 3674 by 10. 5. Divide 3975 by 5, and 14373 by 9. C. 1. Express in Roman numerals 7, 9, 12, 19, 23; and in Arabic figures XI., XXIV., XXXV. 2. Find the sum of 15, 18, 7, 24, 35; and of 473, 64, 542, 64, 287. 3. Subtract 3547 from 6489. 4. Multiply 4376 by 9, and 375 by 13. 5. Divide 14368 by 8, and 6603 by 31. D. 1. In the number 3745 what is the value of the figure 7? 2. Write the numeration table as far as thousands. 3. Add together 38, 47, 23, 189,.76; and 473, 86, 58, 379, 247. 4. Find the difference between 2738 and 3507; and between 12374 and 6859. 5. Multiply 3479 by 23; and 5367 by 304. 6. Divide 23456 by 23; and 34567 by 42. E. 1. Write the following numbers in figures-one hundred and ten, one hundred and one, three hundred and eleven, four hundred and fifty-six, five hundred and eight. 2. What is the sum of ninety-eight, two hundred and fifty-seven, three hundred and twenty-four, seven hundred and sixty-nine, and thirty-seven? |