KEY TO CARD No. 24. many times 3 ...456 Fifth How many times 346 in 2567 ? seek how in 25—8 times but allow one and say 7 times. Set 7 in the quotient and multiply 346 by 7-place the product under 2567—subtract—the remainder is 145. The quotient or answer is 23477446. LESSON 12 Divide 123,456,789 by 123. 123)123456789(1003713 First. 123 How many times 123 in 123?we readily say one-set 1 in the quotient. 369 Multiply 123 by 1-the product .877 is 123—place this product under 861 the number 123 in the dividend subtract—there remains 0—bring . 168 123 down the next figure 4 from the dividend. .459 Second. 369 How many times 123 in 4?.90 not one ; set 0 in the quotientbring down the next figure 5; it makes 45. Third. How many times 123 in 45 ?—not one; set 0 in the quotient-bring down the next figure 6; it makes 456. Fourth. How many times 123 in 456 ? 3 times-set 3 in the quotient—Multiply the divisor 123 by 3--place the product under 456—subtract—the remainder is . 87—bring down the next figure 7; it makes 877. Fifth. How many times 123 in 877 ? To make a guess, say 12 in 87—7 times-place 7 in the quotient.-Multiply the di KEY TO CARD No. 24. visor 123 by 7–place the product under 877—subtractthe remainder is 16-bring down the next figure 8; it makes 168. Sirth, How many times 123 in 168 ? one-set 1 in the quotient. Multiply and subtract—the remainder is 45—bring down 9 the last figure in the dividend; it makes 459. Seventh. How many times 123 in 459 ? seek how many times 12 in 45—3 times--set 3 in the quotient.—Multiply the divisor 123 by 3-place the product under 459—-subtractthe remainder is 90. The quotient or answer is 1,003,713,99 which number, in words, will read thus, One million three thousand seven hundred and thirteen, and ninety, one hundred and twenty-threes. Note.—The three following questions may be wrought by Short Division, if you cut off the cipher in the divisor, and the right hand figure in the dividend. Although this mode of cutting off ciphers, will sometimes expedite business; yet it is not advisable except when the calculator understands his problem, and is master of the subject then under consideration. LESSON 13. In 78,433 shillings, how many pounds ? 20)78433 Here cut off the 0 in the diAnswer, 3921£. 13s. visor 20, and the right hand 3 in the dividend, then divide 7843 by 2. How many times 2 in 7? 3 times and 1 over; set 3 under the 7. One over carry to the left side of 8 makes 18– 2 in 1849 times; set 9 under 8---2 in 4---twice; set 2 under the 4. Then 2 in 3-once and 1 over-set 1 under the 3 and carry the 1 over to the left side of the 3 cut off, which will make 13 shillings for a remainder. This gives a quotient number, Three thousand nine hun KEY TO CARD No. 24. dred and twenty-one pounds thirteen shillings, for an answer, or thus, 392113. LESSON 14. If 40 rods make 1 furlong, I wish to know how many furlongs are in 98643 rods ? 410)986413 Answer, 2466 fur. 3 rods. How many times 4 in 9 ? twice, and 1 over; set down 2 under 9 and carry 1 to the left side of 8 makes 18—How many times 4 in 18? 4 times and 2 over; set 4 under 8 and carry 2 to 6 makes 26—How many times 4 in 26 ? 6 times and 2 over; set 6 under 6 and carry 2 to 4 makes 24—How many times 4 in 24? 6 times; set 6 under 4. The quotient is 2466, and the figure cut off the dividend, is of a furlong, or 3 rods remaining. LESSON 15. Sixty seconds make 1 minute. How many minutes in 39645 seconds ? 6|0)396415 Answer, 660 m. 45 sec. How many times 6 in 39?-6 times and 3 over—6 in 36? 6 times--6 in 4? 0, but 4 remains to be placed on the left side of the 5 cut off---this makes 45 seconds for a remainder, or of a minute. The Quotient is 660 and 45 the Remainder. Note-When the Remainder is less than the Divisor, it is a sign that the work is correct; but if the Remainder happen greater than the Divisor, the work is wrong. Let us prove a few Lessons in Long Division, by Multiplication. RULE. Multiply the Divisor and Quotient together, the Product will be like unto the Dividend. If there be a Remainder, add it to the Product. KEY TO CARD No. 24. For examples take the six following Lessons on Card No. 23, and right hand page of Card 24. Proof, 9 7 7 7 24 Proof, 34 6 1 5 In this Lesson 7th, take the Divisor for a Multiplicand, because the Quotient 190 has a cipher at the right; which cipher may be omitted in Multiplication, and only annexed in the place of units. LESSON 8.---Page 157. LESSON 9.---Page 158. The Divisor is, 194 The Quotient is, 15 9 331 The Divisor, 4300 194 4 7700 5 8 2 6 3 6 5 8 2 Remainder, 1 2 2 7 Remainder, 115 Proof, 6 4 3 2 9 Proof, 6 8 4 9 27 The ciphers are to be omitted in Multiplication, and added in the place of units and tens. END OF PART SIXTH. INTRODUCTION TO ARITHMETIC, PART VII. CONTAINING, COMPOUND DIVISION, ARITHMETICAL CHARACTERS, AND DECIMALS. COMPOUND DIVISION. KEY TO CARD No. 25. LESSON 1. Divide £784 16s. 4d. between 4 men. £. s. d. Pounds. 4)784 16 4 Four in 7-1 and 3 over--4 in 38-9 and 196 4 1 over-4 in 24-6 times. Shillings. Four in 16--4 times. Pence. Four in 4-1. Quotient in words, One hundred and ninety-six pounds four shillings and one penny. This is each man's part. LESSON 2. Divide £ 1454 19s. between 8 men. £. d. Pounds. 8)1454 19 00 How many times 8 in 1d 1 and 6 181 17 4 2ll over-How many times 8 in 65 ? 8 and 1 over-How many times 8 in 14 ? 1 and 6 over to carry to the shillings. s. |