easier than to subtract from 40 the number 5 eight times to find an answer. What are the names of the terms in Division? The number we divide by, is called DIVISOR; that which we divide, DIVIDEND; the result, or answer, QuoTIENT; and if any thing be left undivided, it is a REMAIN DER. Classes may lecture in this manner on some day appoin ted, and the most expert may be entitled to precedence as in spelling. END OF PART FOURTH, INTRODUCTION TO ARITHMETIC. PART V. CONTAINING LONG DIVISION. LONG DIVISION. KEY TO CARD No. 23. LESSON 1. In 79,392 ounces Avoirdupois, how many pounds, allowing 16 ounces to each pound? 16)79392(4962 64 153 144 ..99 96 .32 32 NOTE.-16 is the Divisor. 79392 is the Dividend. 4962 is the Quotient. When any number of figures remain in the place of the two periods under 32, such number will be called the Remainder. Let the Division Table, Card No. 22, be suspended before the class. The overseer will direct the class to prepare their lesson on the slates, as it is represented on card No. 23. Then say, how many times 16 in 79 ́? Look at the table under 16-Begin at the last number opposite 16, that is, 144; count upwards till you find a number less than 79, say 64-opposite 64 you will· find 4 times-Then say, I can have 4 times 16 in 79; set 4 in the quotient. 79. Now multiply 16 by 4, and place the product under L* Four time 6 are 24-4 and carry 2-4 times 1 is 4 and 2 are 6-thus we have 64 standing under 79. Subtract this number 64 from 79-the remainder is 15. Bring down the next figure in the dividend, that is, 3, and place it on the right hand side of 15, which will make 153. Now say, how many times 16 in 153? Look at the last number in the table under 16, which is 144, opposite that stands 9 times-as 144 is less than 153. I find that 16 will be contained 9 times in 153; set 9 in the quotient. Multiply the divisor 16 by 9, and set the product under 153. Nine times 6 are 54-4 and carry 5—9 times 1 are 9 and 5 are 14. Thus we have the number 144 under 153. Subtract this number 144 from 153. The remainder is 9. Bring down the next figure from the dividend, that is, 9, which will make 99. How many times 16 in 99? Begin at the lowermost number under 16 in the table, say, 144, and look upwards till you find a number less than 99, let it be 96-opposite 96 stands 6 times. Set 6 in the quotient, and multiply 16 by 6. Six times 6 are 36-6 and carry 3-6 times 1 are 6 and 3 are 9. Thus we have 96 standing under 99. Subtract 96 from 99-the remainder is 3. Bring down the next and last figure in the divi dend, viz. 2, which makes 32. How many times 16 in 32? The Table tells you twice 16 is 32. Place 2 in the quotient, and multiply 16 by 2. Twice 6 are 12-2 and carry 1-Twice 1 are 2 and 1 are 3. Thus we have 32 standing under 32. Subtract 32 from 32 and 0 remains-place 2 periods under 32, as you see on the Card. The figures in our quotient amount to 4962, which is the answer to the question. How many times 16 in 79392? Ans. 4962 times. If 16 ounces make 1 pound, then 32 ounces will make 2 pounds; because we can have twice 16 in 32. Forty-eight ounces make 3 pounds; because we can have 3 times 16 in 48. Sixty-four ounces make 4 pounds; because we can have 4 times 16 in 64. Eighty ounces make 5 pounds; because we can have 5 times 16 in 80. And 79392 ounces make 4962 pounds; because we can have 4962 times 16 in 79392. Let the class write these observations several times on their slates. They will thereby obtain an idea of a part, and by degrees understand the whole. As the spears of grass and herbs, imperceptibly make their daily growth; so our knowledge increases by small portions, till we become masters of many valuable arts. KEY TO CARD No. 23. If 48297 cents are to be divided between 17 boys, how many may each one have? 17)48297(2841 34 142 136 ..69 68 17 17 First. I say how many times 17 in 48 ? twice; set 2 in the quotient, and multiply the divisor by 2-the product is 34, which place under 48; then subtract 34 from 48, and there remain 14-bring down the next figure from the dividend, viz. 2, and place it on the right hand side of 14, which makes 142. Second. How many times 17 in 142? by the Table I find 8 times; set 8 in the quotient, and multiply 17 by 8-place the product under 142-subtract, and 6 remain. Now bring down the next figure 9 from the dividend, and place it on the right of 6, makes 69. Third. How many times 17 in 69? 4 times; set 4 in the quotient, and multiply the divisor 17 by 4-place the product under 69-subtract it from 69 and there remains 1-to the right of this 1, bring down 7, the last figure in the dividend, makes 17. Fourth. I say 17 in 17-once-set one in the quotient, and say once 7 is 7-once 1 is 1 makes 17 to place under 17-subtract, and O remains-place your periods under 17, and the lesson is done. Answer, 2841 cents for each boy, or, $28.41. KEY TO CARD No. 23. LESSON 3. In 98688 hours how many days? Twenty-four hours make one day. NOTE. 24)98688(4112|| 96 .26 24 .28 24 .48 First. See how many times 24 are in 96. In order to guess at the number of times, find how many times the first figure in the quotient is contained in the first figure of the dividend, that is, how many times 2 in 9? 4 times -therefore set 4 in the quotient, and multiply the divisor 24 by 4. Place the product under 98-subtract-the remainder will be 2-bring down the next figure of the dividend, ||6, to the right side of the 2, makes 26. Second.. How many times 24 in 26? once- -set 1 in the quo. tient, and multiply the divisor 24 by 1-once 4 is 4 |