KEY TO CARD No. 23. ance of 1 and say 8 times-set 8 in the quotient and multiply 99 by 8. Place the product under 867-subtract-the remainder is 75-bring down the next figure 2 from the dividend to the right side of 75 makes 752. Third. How many times 99 in 752? seek how many times 9 in 75-it is contained 8 times; but allow 1 and say 7 times. Multiply 99 by 7-place the product under 752-subtract-the remainder is 59-bring down the next and last figure 4 from the dividend to the right side of 59---this makes 594. Fourth. How many times 99 in 594? seek how many times 9 in 59--6 times 9 are 54-set 6 in the quotient and multiply 99 by 6.-Place the product under 594-subtract-the remainder is nothing-place three periods under 594. The quotient or answer is 9876. LESSON 7. See Card 24, for proof. Divide 34615 by 182. 182)31615(190|| 182 1641 1638 ...35 First. How many times 182 in 346? seek how many times 18 in 34-one-set 1 in the quotient-multiply 182 by 1-place the product under 346-subtract-the remainder is 164. Bring the next figure 1 from the dividend to the right side of 164, makes 1641. Second. How many times 182 in 1641? look at the Table under 18, and see how many times 18 in 164-the last number under 18 is the place to begin to count upwards-the first number less than 164 is the guide to guess by, that is, 162-opposite 162 stands 9 times-then place 9 in the quotients KEY TO CARD No. 23. Multiply the divisor 182 by 9-place the product under 1641-subtract-the remainder is 3-bring down 5, the last figure in the dividend to the right side of 3 makes 35. Third. How many times 182 in 35-no times-set 0 in the quo tient-call this 35 a remainder, a number undivided. The quotient or answer is 19035.* LESSON 8. See Card 24, for proof. Divide 64329 by 194. 194)64329(331 582 .612 .309 194 115 First. How many times 194 in 643? To make a guess, say how many times 19 in 64? Look at the Table-begin at the last number under 19 and count upwards till you come to a number less than 64, say 57-opposite this stands 3-set 3 in the quotient and multiply the divisor 194 by 3. Place the product under 643-subtract-the remainder is 61-bring down the next figure 2 from the dividend to the right side of 61. makes 612. Second. How many times 194 in 612? To make a guess, seek how many times 19 in 61-look at the Table-begin at the last number under 19, count up till you find a number less than 61-say 57 as before; opposite 57 stands 3-set 3 in the quotient. Multiply the divisor 194 by 3-place the product under 612-subtract—the remainder is 30-bring down the next figure 9 from the dividend to the right side of 30, makes 309. If the dividend had been dollars, this remainder 35 should be reduced to cents and divided by 182.-If the dividend had been pounds Avoirdupois, the pounds must have been reduced to ounces, &c. then divided by 182. KEY TO CARD No. 23. Third. How many times 194 in 309? To make a guess, say how many times 19 in 30-We readily know but one-set 1 in the quotient, and set once 194 under 309-subtractthe remainder is 115. The quotient or answer is 3311. LESSON 9. See Card 24, for proof. Divide 684,927 by 4300. DIRECTIONS. Cut off the two ciphers from the divisor and divide by 43. Cut off as many figures from the right of the dividend, viz. 27. Your dividend will then be 6849 to be divided by 43. EXAMPLE. 4300)6849|27(159 43 254 215 .399 1227 The 27 cut off is a part of the remainder and must be placed on the right of 12, makes a remainder of 1227. First. How many times 43 in 68?-We know by reflecting a moment that it can be contained only once. Set 1 in the quotient and place once 43 or one time 43 under 68-subtract -the remainder is 25-bring down the next figure 4 from the dividend, makes 254. Second. How many times 43 in 254?-To make a guess, seek how many times 4 in 25-though it is contained 6 times, allow 1 and say 5 times-set 5 in the quotient. Multiply 43 by 5-place the product under 254-subtract-the remainder is 39-bring down the next figure 9 from the dividend to the right side of 39, makes 399. KEY TO CARD No. 24. Third. How many times 43 in 399?-To make a guess, seek how many times 4 in 39-we know that 9 times 4 are contained in 36 and can venture to place 9 in the quotient. Multiply 43 by 9-place the product under 399-subtract-the remainder is 12; and to this remainder must be annexed 27, the two figures cut off the dividend-this number 27 being annexed, will make a remainder of 1227. The quotient or answer is 159137. 4300 LESSON 10. Divide 1,288,241 by 5600. DIRECTIONS. Cut off the two ciphers in the divisor, and as many figures in the dividend, then divide by 56. 5600)12882|41(230|| 112 .168 168 .....241 EXAMPLE. First. How many times 56 in 128?-to make a guess, seek how many times 5 in 12we know it will be twice. Set 2 in the quotient and multiply 56 by 2-place the product under 128-subtract—the remainder is 16-bring down the next figure 8 from the dividend to the right side of 16, makes 168. Second. How many times 56 in 168?-Say how many times 5 in 16-we easily perceive it is contained 3 times-set 3 in the quotient. Multiply 56 by 3-set the product under 168-subtractnothing remains-bring down the 2. Third. 2 How many times 56 in 2?-we cannot have 56 in 2, therefore set 0 in the quotient. Now the 2 is a part of the remainder-bring the 41, which was cut off the dividend, to the right side of 2, and it makes a remainder of 241.--The quotient or answer is 230 2 KEY TO CARD No. 24. LESSON 11. Divide 8,123,187 by 346. 346)8123187(23477|| 692 1203 1038 .1651 .2678 2422 .2567 2422 Rem. .145 First. How many times 346 in 812-seek how many times 3 in 8-say twiceset 2 in the quotient and multiply 346 by 2. Place the product under 812-subtract--the remainder is 120-bring down the next figure 3 from the dividend to the right side of 120, makes 1203. Second. How many times 346 in 1203-seek how many times 3 in 12-though it is 4 times, allow one and say 3 times. Set 3 in the quotient and multiply 346 by 3-place the product under 1203-subtract-the remainder is 165bring down the next figure 1 from the dividend to the right side of 165, makes 1651, Third. How many times 346 in 1651 ?-Seek how many times 3 in 16-it is 5 times-but allow one and say 4 times. Set 4 in the quotient and multiply $46 by 4-place the product under 1651-subtract-the remainder is 267-bring down the next figure 8 from the dividend, makes 2678. Fourth. How many times 346 in 2678-Seek how many times 3 in 26-though 3 times, yet allow one and say 7 times. Set 7 in the quotient and multiply 346 by 7-place the product under 2678-subtract-the remainder is 256bring down the next and last figure 7 from the dividend, makes 2567. |