PART I SAVING TIME BY CHAPTER I SAVING TIME BY SHORT-CUTS The Panama Canal is a world-famous short-cut. The ocean distance from New York to San Francisco around South America is 13,135 miles. The short-cut through the Panama Canal saves 7873 miles of this distance. How many miles is it from New York to San Francisco by way of the Canal? The cost of the Panama Canal was four hundred million dollars, yet it is a paying investment. The modern world considers short processes worth while. Economy of time always pays. That is why this Second Course in the New Mathematics begins with work in short-cuts. These methods are applied to the solution of everyday problems, while last year's study of the coöperation of arithmetic, algebra, and geometry is continued. Finally, in Part II, all this work is reviewed in connection with the business world. Speeding Up. In the Woodrow Wilson Junior High School Robert Weller got the answers to most of the problems more quickly than the rest of the class. When the others wondered about this, Robert told them that his father, who was an expert accountant, taught him a lot of short processes to save time and labor. Some of these short-cuts we shall take up now. Short-Cut I. To Multiply or Divide by 10, 100, 1000, and so on. If we are asked to multiply a number like 723 by 100, we may add two zeros, thus: 723 × 100 72,300. This is the same as writing 723 in the form 723.00 and moving the decimal point two places to the right. Similarly, 16.823 x 100 = 1682.3. = Likewise if we are to divide 186.17 by 100, we may do so by moving the decimal point two places to the left. Thus 186.17 100 1.8617. If we have to divide a number like 2.86 by 100, we must supply a zero in order to locate the decimal point. 2.86 100 = .0286. = From this we get the following Rule. (1) To multiply by 10, 100, 1000, and so on, we move the decimal point of the multiplicand as many places to the right as there are zeros in the multiplier, supplying zeros if necessary. (2) To divide by 10, 100, 1000, and so on, move the decimal point of the dividend as many places to the left as there are zeros in the divisor, supplying zeros when necessary. Note. Moving the decimal point one place to the right or three places to the left is sometimes called "Pointing off one place to the right, or pointing off three places to the left." Remember that multiplying by (.1), ro (.01), rooo (.001), is the same as dividing by 10, 100, or 1000. Testing Short-Cut I with Paper-and-Pencil 1. Multiply 1532 by 10; by 100; by 1000; by 10,000. 2. Divide 806.721 by 10; by 100; by 1000; by 1,000,000. 3. Multiply 5.678 by 100 and add the product to the result of 4567.9 divided by 1000. 4. Add 576.84 and 46.075 and divide the result by 1000. 5. Multiply each of the following by 1000: .00075; .0056; 56.894. 6. How many centimeters in 675.3 meters? How many millimeters? (See the table on page 357 of the Appendix.) 7. How many kilograms in 946,372 grams? |