1. Divide 2. Divide 3. Divide 4. Divide 5. Divide EXERCISES. 3. 4. 486235490 by 2. 527430828 by 7. 11. Divide thirty-five millions; two hundred and seventy-nine thousand, eight hundred and six, the dividend, by twelve the divisor. When the divisor has two component parts that do not exceed 12. Rule, there are usually two Quotient.. 127718897+2=23 rem. remainders; thus, in the ex ample, 5 is the first remainder, and 2 the last. In order to find the whole remainder, the Rule is-Multiply the last remainder with the first divisor, and to the product add the first remainder. Hence 2, the last remainder, multiplied with 9, the first divisor=18, and 5, the first remainder, added to this, make 23,-the whole remainder. EXERCISES. 12. Divide 2351869274 by 18. Quotient 130659404+ 2. 13. Divide 3197612805 by 32. Quotient 99925400+ 5. 14. Divide 7514086329 by 48. Quotient 156543465+ 9. 15. Divide 9068427513 by 66. Quotient 137400416+57. 16. Divide 3175381602 by 81. Quotient 39202242 17. Divide 6730815724 by 96. Quotient 70112663+76. 5463791248 by 121. Quotient 45155299+69. 18. Divide 19. Divide fifty-seven millions; two hundred and nineteen thousand, and eighty, the dividend, by one hundred and forty-four, the divisor. Quotient 397354+104. This example proves the example in Multiplication, see page 8. When the divisor has two or more figures, and the foregoing Rules cannot be used, as in the following Examples. Divisor. Dividend. Quotient. 37) 912763 (24669 74 172 148 247 222 256 222 343 333 Remainder 10 Proof. 37 37 in 91 twice, put 2 in the quotient; multiply the divisor by this figure; twice 7 are 14, carry 1; twice 3 and 1 are 7; put 74 under 91, and subtract 4 from 11, 7 remain, carry 1; 1 and 7 are 8, from 9, 1; the remainder is 17.* Bring down the next figure, 2. 37 in 172 are 4; put 4 in the quotient; 4 times 37=148; subtract 148 from 172, the remainder is 24.* Bring down 7. 37 in 247 are 6; put 6 in the quotient; 6 times 37 are 222; subtract 222 from 247, the remainder is 25.* Bring down 6. 37 in 256 are 6. 6 times 37 are 222; subtract 222 from 256, the remainder is 34.* Lastly bring down 3. 37 in 343 are 9; 9 times 37=333; subtract 333 from 343, the remainder is 10.* The quotient is 24669, and 10 remaining. *The remainder must always be less than the divisor. Should it be greater, remove the last figure put in the quotient, and place a greater instead. Quotient 1544960+92125 remainder. 30. Divide thirty-one thousand, seven hundred and three millions; four hundred and sixty-five thousand, two hundred and seventy-nine, -by five thousand, three hundred and ninety-eight. 31. Divide five hundred and thirteen thousand, two hundred and nine millions; one hundred and eighty-four thousand, six hundred and fifty-three, by ninety-seven thousand and sixty-two. When there are ciphers at the end of the divisor, as in the following 32. Divide 33. Divide EXERCISES. 8370469 by 700 3694578269 by 38000 34. Divide 12704589647 by 135000 Quotient 94108+9647 rem. There is a contracted way of performing Long Division (called the Italian method,) which differs only from the common method by omitting the several products. Example. Divisor. Dividend. Quotient. 437) 2875961 (6581 2539 3546 501 64 Remainder. 437 in 2875, 6; 6 times 7 are 42, 42 from 45, 3 remain, carry 4. It is to be observed that 4 is supposed to stand before 5, that 42 may be subtracted and whatever figure is supposed to be so placed, is always carried to the next. 6 times 3 and 4 carried are 22; 22 from 27, 5 remain, carry 2: 6 times 4 and 2 are 26; 26 from 28, 2 remain. Bring down 9. 437 in 2539, 5: 5 times 7 are 35; 35 from 39, 4 remain, carry 3; 5 times 3 and 3 are 18; 18 from 23, 5 remain, carry 2: 5 times 4 are 20, and 2 are 22; 22 from 25, 3 remain. Bring down 6; 437 in 3546, 8: 8 times 7 are 56; 56 from 56, 0 and carry 5: 8 times 3 and 5 are 29; 29 from 34, 5 remain, carry 3: 8 times 4 and 3 are 35; 35 from 35, 0. LastlyBring down 1; 437 in 501, once; 7 from 11, 4 remain, carry 1; 1 and 3 are 4; 4 from 10, 6 remain, carry 1; 1 and 4 are 5; 5 from 5, 0. The quotient is 6581, and 64 remaining. Another Example. Divisor. Dividend. Quotient. 7285) 540729863 (74225 Proof. Multiplicand 74225 The foregoing exercises, from No. 20 to the end, may be worked by the contracted method. |