KEY TO CARD No. 21. Fourth. Eight times 8 are 64---4 and carry 6---8 times 7 are 56 and 6 are 62---2 and carry 6---8 times 6 are 48 and 6 are 54---4 and carry 5---8 times 5 are 40, and 5 are 45. Add the intermediate Products. Total Product in words, Forty-nine million seven hundred and sixty seven thousand six hundred and seventy. LESSON 7.1 Multiplicand, 9 8 7 0 0 Multiply by 4, by 5, and by 6, Multiplier, 6 5 4 0 paying no regard to the ciphers. First. 3948 Four times 7 are 28–8 and 4 9 3 5 5 9 2 2 carry 2–4 times 8 are 32 and 2 are 34–4 and carry 3-4 Product, 6 4 5,4 9 8,00 0|| times 9 are 36 and 3 are 39. Second. Five times 7 are 35-5 and carry 3—5 times 8 are 40 and 3 are 433 and carry 4-5 times 9 are 45 and 4 are 49. Third. Six times 7 are 422 and carry 4-6 times 8 are 48 and 4 are 52—2 and carry 5–6 times 9 are 54 and 5 are 59. Add the intermediate Products. We have now a total Product of 645498-annex the three ciphers, that is, place them on the right hand of these figures and they will make the answer required, viz: 645,498,000. Product in words, Six hundred and forty-five million four hundred and ninety-eight thousand. KEY TO CARD No. 21. LESSON 8. Multiplicand, 4 0 7 80 Multiply by the two figures, Multiplier, 1 600 add the intermediate products, then count the ciphers and an2 4 4 6 8 4 0 7 8 nex them to the total product. First. Product, 6 5,2 4 8,0 0 0 Six times 8 are 48–8 and carry 4-6 times 7 are 42 and 4 are 46–6 and carry 46 times 0 is O but 4 is 4-6 times 4 are 24. Second. Total Product in words, Sixty-five million two hundred and forty-eight thousand. LESSON 9. 99900 Multiply by the 7. 700 Seven times 9 are 63—3 and carry 69,9 3 0,0 006–7 times 9 are 63 and 6 are 69-9 and carry 6–7 times 9 are 63 and 6 are 69. Bring down the ciphers—They make Sixty-nine million nine hundred and thirty thousand. LECTURING, Notation is the recording or noting any number of objects or things : ia Arithmetic it signifies the writing down any number of figures, as, 1 2 3 4. What is meant by NUMERATION? The act of numbering after figures are noted or written; for instance, read the figures, 1, 2, 3, and 4, thus, One thousand two hundred and thirty-four. What is ADDITION ? more 6, more 7, equal 21. Or, 3 added to 5, added to 6, added to 7, equal 21 for a RESULT or SuM TOTAL. What do we understand by the word SUBTRACTION ? Subtraction is the lessening of any quantity, as, the number 15 taken from 20, leaves 5 for a REMAINDER. What is the arithmetical name of the upper number in Subtraction? Call it MAJOR or MINUEND: the middle number we will call MINOR or SUBTRAHËND, and the lowermost number, REMAINDER. Note 1.-It may be well to call these numbers Minuend and Subtrahend. Note 2.-This Rule partakes of the nature of Division, as for example: subtract 4 from 24, five times, the remainder will be 4, the same as the quotient of 24 when divided by 6: that is, 24 less 4, equals 20; 20 less 4, equals 16; 16 less 4, equals 12; 12 less 4, equals 8; 8 less 4, equals 4. Or, how many times 6 in 24? 4 times. What is MULTIPLICATION ? Multiplication is the increasing of numbers with rapidity, instead of a tedious and slow way of operating by Addition, thus, 5 times 8 are 40; instead of 8 and 8 are 16, and 8 are 24, and 8 are 32, and 8 are 40. By what name shall we call the terms in this Rule ? The Number to be multiplied is called, MULTIPLICAND; the number we multiply by, MULTIPLIER ; and the lowermost number, PRODUCT. The Multiplicand and Multiplier are also called Factors; and may be termed, upper and lower Factor. Note. When the lower Factor consists of several figures, there will be more products than one, and they may be called Intervening or Intermediate Products. How shall we define Division ? Division is a concise way of working Subtraction, or of apportioning a larger number into smaller and equal parts; as, 41 dollars divided between 5 men, will give each man 8, and 1 over for a Remainder. This mode is 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 REMAINDER. Classes may lecture in this manner on some day appointed, and the most expert may be entitled to precedence as in spelling. LESSON 1. In 79,392 ounces Avoirdupois, how many pounds, allowing 16 ounces to each pound? 16)79392(4962 NOTE. -16 is the Divisor. 64 79392 is the Dividend. 4962 is the Quotient. When any number of figures remain in the place of the two periods under 32, ..99 such number will be called the Remainder. 96 Let the Division Table, Card No. 22, 32 -be suspended before the class. 32 The monitor will direct the class to prepåre their lesson on the plates, as it is re presented on Card No. 23. Then say, how many times 16 in 79 ? Look at the Table under 16„Beğin 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. Now multiply 16 by 4, and place the product under 79. Four times 6 are 24–4 and carry 2—4 times 1 is 4 and 2 are 6-thus we have 64 standing under 79. KEY TO CARD No. 23. 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 bý 9, and set the product under 153. Nine times 6 are 54–4 and carry 5–9 times 1 is 9 and 5 are 14. Thus we have the number 144 under 153. 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 thg Table, say 144, and look upwards-tit. you find a number-less than 99, let it be 96-opposite 96 stands 6 timeş. Set 6 in the quatient; and multiply 16 by 6. Six times 6 are 3646 and carry 3-6 times 1 19.6 ähd 3 are 9. Thus we have 96 standing under 99. Bring down the next-and last figure in the dividend, viż2, which makes 32. How many times 16 in 32 ? , 2. Twice 6 are 122 and carry 1-Twice 1 is 2.and I is 3. Thus we have 32 standing under: 32. Subtract 32 from 32 and 0 remains--place two periods under 32, as you see on the Card. |