J. Find the difference between 1. Sixty-five and thirteen. 10. Seventy-three and nineteen. K. 1. Four hundred and thirty-eight and two hundred and sixty-four. 2. Two hundred and fifty-eight and five hundred and sixty-three. 3. Ninety-eight and three hundred and seventyone. 4. Seven hundred and forty-three and two hundred and sixty-seven. 5. Five hundred and six and two hundred and ninety-eight. 6. Seventy-six and eight hundred and sixty-four. 7. Three hundred and two and two hundred and ninety-five. 8. Eight hundred and sixty-seven and nine hundred and fifty. 9. Ninety-four and six hundred. 10. Three hundred and twenty-four and two hundred and sixty-four. L. 1. Three thousand one hundred and six and two thousand nine hundred and seven. I 2. Three thousand and ninety-eight and four thousand and five. 3. Nine hundred and seventy-eight and three thousand and forty. 4. Four thousand and nine and six thousand. 5. Twenty-nine thousand and ninety-five and fifty thousand and forty. 6. Thirty-six thousand and four and five thousand nine hundred and eight. 7. Nine hundred and nine and eleven thousand and sixty. 8. One hundred and nine and ten thousand one hundred and one. 9. Thirty thousand one hundred and four and six hundred and eighteen. 10. Nine hundred and one and eleven thousand. ) CHAPTER IV. MULTIPLICATION.SECTION I. IF John has 4 pockets and 7 marbles in each pocket, we may find how many marbles he has altogether by addition, thus : 7 7 7 7 28 Hence John has 28 marbles altogether; that is, 7 repeated 4 times, or as it is commonly expressed, 4 times 7 is 28. In the same way we may find that 4 times 9 is 36 ; 7 times 8...56; 8 times 9...72, and so on. But if we were required to find 79 times 574, the addition would be very long, for it would be necessary to set down 574 seventy-nine times, and add them together; or, in other words, to work an addition sum of seventy-nine lines. Now this operation can be greatly simplified by a method called multiplication, which is an easy way of finding the sum of a number repeated several times. The number to be repeated is called the multiplicand; the number of times it is to be repeated the multiplier, and the result is called the product. Thus, if we repeat 8 seven times, or, which is the same thing, multiply 8 by 7, 8 is the multiplicand, 7 the multiplier, and the result 56 is the product. Sometimes the multiplicand and multiplier are called factors; thus, 4 9, 66, and 3 12 are called factors of 36, because 4 times 9, 6 times 6, or 3 times 12 is 36. We will now show how to multiply by a number not greater than 12, but it is necessary in the first place to learn by heart all the products obtained by multiplying the first 12 numbers by each of themselves. All these products may be found in the Multiplication Table. Examples.-Multiply 4769 by 3. may find the result by addition, thus : 4769 and 9 9 are 18 and 9 are 27 ; set down 7 4769 and carry 2 ; 6 and 6 are 12 and 6 are 4769 18 and 2 carried are 20; set down o and 14307 carry 2, and so on. But in multiplication we only place the multiplier 3 under the units' figure of the multiplicand, and 4769 instead of adding as above, we say 3 times 9 is 27 ; set down 7 and carry 2; 3 times 3 6 is 18 and 2 carried are 20; set down o 14307 and carry 2 ; 3 times 7 is 21 and 2...23 ; 3 and carry 2 ; 3 times 4 is 12 and 2... 14. Multiply 538 by 12. 538 Placing the units and tens of the multiplier under those of the multiplicand, we say twelve times 8 is 96; 6 and carry 9; twelve 6456 times 3 is 36 and 9 are 45 ; 5 and carry 4; twelve times 5 is 69 and 4 are 64. I 2 |