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. ...35 LESSON 7. See Card 24, for proof. Divide 34615 by 182. 182)31615(1901 First. 182 How many times 182 in 346? seek how many times 18 in 34–one set 1 in the 1641 1638 quotient—multiply 182 by 1-place the product under 346-subtract-the re mainder 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 quotient: 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. quotient-call this 35 a remainder, a number undivided. The quotient or answer is 190,00* LESSON 8. See Card 24, for proof. Divide 64329 by 194. 194)64329(331 || First. 582 How many times 194 in 643 ? To make .612 a guess, say how many times 19 in 64 ? 582 Look at the Table—begin at the last number under 19 and count upwards till .309 you come to a number less than 64, say 194 57-opposite this stands 3-set 3 in the 115 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 6). 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 331 11 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 43|00)6819|27(159 The 27 cut off is a part of the re43 mainder and must be placed on the 254 right of 12, makes a remainder of 1227. 215 First. How many times 43 in 68 ?_We .399 know by reflecting a moment that it 387 can be contained only once. . 1227 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 nunber 27 being annexed, will make a remainder of 1227. The quotient or answer is 159377 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. EXAMPLE. 56100)12882|41(2301 First. 112 How many times 56 in 128?-to make .168 a guess, seek how many times 5 in 12168 we know it will be twice. Set 2 in the quotient and multiply .241 ||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. 2 Multiply 56 by 3-set the product under 168-subtractnothing remains-bring down the 2. Third. 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 230-240p. KEY TO CARD No. 24. . LESSON 11. Divide 8,123,187 by 346. 346)8123187(23477 First. 692 How many times 346 in 812—seek 1203 how many times 3 in 8—say twice1038 set 2 in the quotient and multiply 346 by 2. .1651 Place the product under 812_sub1384 tract--the remainder is120--bring down .2678 the next figure 3 from the dividend to Second. How times 346 in 1203—seek how many times 3 in 12—though it is 4 Rem. .145 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 165— bring 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 946 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 8 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 256– bring down the next and last figure 7 from the dividend, makes 2567. |