Begin with the 4 the first figure on the right of the Multiplier. Four times 2 are 8; set 8 exactly under the 4-4 times 3 are 12; set 2 on the left side of 8 and carry 1 -4 times 4 are 16 and one I carried makes 17; set down 7 and carry 1—4 times 6 are 24 and one I carried makes 25; set down 5 and carry 2-4 times 4 are 16 and 2 are 18; set down 18. Second. Twice 2 are 4-set 4 under the 2-Twice 3 are 6; set six under the 7-Twice 4 are 8; set 8 under the 5-Twice 6 are 12; set 2 under the 8 above and carry 1-Twice 4 are 8 and one I carried makes 9; set 9 under the 1. Third. Five times 2 are 10; set 0 under the 6-5 times 3 are 15 and one I had to carry make 16-set 6 under the 8 and carry 1-5 times 4 are 20 and one I carried makes 21; set 1 under the 2 and carry 2-5 times 6 are 30 and 2 I carried are 32; set 2 under the 9 and carry 3-5 times 4 are 20 and 3 I carried are 23; set 23 on the left side of the whole. Add these three products as in addition of whole numbers. Eight is 8-4 and 2 are 6-6 and 7 are 13; 3 and carry 1-1 to 6 makes 7 and 8 are 15 and 5 are 20 -0 and carry 2-2 to 1 is 3 and 2 are 5 and 8 are 13 -3 and carry 1-1 to 2 makes 3 and 9 are 12 and 1 is 13-3 and carry 1-1 to 3 makes 4-2 make 2. Product in words, Twenty-four million three hundred and thirty thousand three hundred and sixtyeight. Now let each one become expert in reading figures -Let the Numeration Table hang in view. Product 4 4, 8 3 3, 5 3 6 Second. Three times 8 are 24 -4 and carry 2- -3 times 4 are 12 and 2 are 14-4 and carry 1-3 times 2 are 6 and 1 is 7-3 times 1 are 3-3 times 6 are 18. Third. Seven times 8 are 56-6 and carry 5-7 times 4 are 28 and 5 are 33-3 and carry 3-7 times 2 are 14 and 3 are 17-7 and carry 1-7 times 1 is 7 and 1 are 8 -7 times 6 are 42. Add these intermediate Products. Total product in words, Forty-four million eight hundred and thirty-three thousand five hundred and thirty-six. KEY TO CARD No. 20. LESSON 3. Multiplicand, 1 6 7 3 9 Multiplier, First. 287 Seven times 9 are 63-3 and carry 6-7 times 3 are 1 17 17 321 and 6 are 27-7 and 1 3 3 9 1 2 334 78 carry 2-7 times 7 are 49 and 2 are 51-1 and carry 5-7 times 6-are 42 and 5 Product 4, 8.0 4,0 9 3 are 47-7 and carry 4-7 times 1 is 7 and 4 are 11. Second. Eight times 9 are 72-2 and carry 7-8 times 3 are 24 and 7 are 31-1 and carry 3-8 times 7 are 56 and 3 are 59-9 and carry 5-8 times 6 are 48 and 5 are 53-3 and carry 5-8 times 1 is 8 and 5are 13. Third. Twice 9 are 18-8 and carry 1-Twice 3 are 6 and 1 is 7-7 and carry nothing-Twice 7 are 14-4 and carry 1-Twice 6 are 12 and 1 is 13-3 and carry one-Twice 1 is 2 and 1 is 3. Add the intermediate Products. Total Product in words, Four million eight hundred and four thousand and ninety-three. NOTE:-For our better understanding the nature of multiplication, we will analyze a sum and multiply the component parts by any mutiplier we choose, and see if the product will be equal to that produced by the usual mode of multiplying. + Multiplicand, 4 5 6 | First compo 6 or units nent part Multiplier 24 1 8 2 4 Third 400 hundreds. Proof of Product, 1 0 9 4 4 A analysis 4 5 6 2d. component part 5 0 By these operations we 2d. Product, 1 2 0 0 keeping units, tens, hun perceive the necessity of dreds, &c. in their proper places. For, units multi 3d component part 4 0 0|plied by 24 produce a cer 3d 'Product, tain sum; tens another sum 960 Ogreater than that of units, land hundreds another, still greater, and in a ten fold proportion of the distance they stand from units. From this we see the reason why the intermediate products incline obliquely to the left. KEY TO CARD No. 20: 4 5 6 7 1 8 2 6 8 22835 27402 LESSON 4: First. Four times 7 are 28-8 and carry 2-4 times 6 are 24 and 2 are 26-6 and carry 2-4 times 5 äre 20 and 2 are 22-2 and carry 2-4 times 4 are 16 and 2 are 18. Second. Twice 7 are 14—4 and carry 2 9,7 9 5,1 0 8-twice 6 are 12 and 1 is 13-3 and carry 1-twice 5 are 10 and 1 is 11-1 and carry one-twice 4 are 8 and 1 is 9. Third. Five times 7 are 35- -5 and carry 3-5 times 6 are 30 and 3 are 33-3 and carry 3-5 times 5 are 25 and 3 are 28-8 and carry 2-5 times 4 are 20 and 2 are 22. Fourth. Six times 7 are 42-2 and carry 4-6 times 6 are 36 and 4 are 40-0 and carry 4-6 times 5 are 30 and 4 are 34-4 and carry 3-6 times 4 are 24 and 3 are 27. Add the intermediate Products. Total product in words, Twenty-nine million seven hundred and ninety-five thousand one hundred and eight. KEY TO CARD No. 21., Multiplicand, LESSON 5. 4 87 6||First figure of the Mul6 5 4 3 1950 4 tiplier. Three times 6 are 18 1 4 6 2 8-8 and carry 1-3 times 7 are 21 and 1 is 22 -2 and carry 2-3 times 8 are 24 and 2 are 26-6 and carry 2 24380 29256 Product, 3 1,9 0 3,6 6 8-3 times 4 are 12 and Second. 2 are 14. Four times 6 are 24-4 and carry 2-4 times 7 åre 28 and 2 are 30-0 and carry 3-4 times 8 are 32 and 3 are 35-5 and carry 3-4 times 4 are 16 and 3 are 19. Third. Five times 6 are 30-0 and carry 3-5 times 7 are 35 and 3 are 38-8 and carry 3-5 times 8 are 40 and 3 are 43-3 and carry 4-5 times 4 are 20 and 4 are 24. Fourth. Six times 6 are 36-6 and carry 3-6 times 7 are 42 and 3 are 45-5 and carry 4-6 times 8 are 48 and 4 are 52-2 and carry 5-6 times 4 are 24 and 5 are 29. Add the intermediate products. Total product in words, Thirty-one million nine hundred and three thousand six hundred and sixtyeight. |
