Fractions TableDate: 06/20/98 at 06:15:55 From: Betsy Mikula Subject: Fractions Could you please help me locate a math table that illustrates fractions to the 16th's? Many thanks. Date: 06/20/98 at 14:58:07 From: Doctor Gary Subject: Re: Fractions I can do better than that, by helping you make one of your own. First, you need to appreciate that a fraction is just a shorthand way of writing that the numerator (top of the fraction) is being divided by the denominator (bottom of the fraction). If you can do long division, you can create a table of decimal equivalents for any denominator you like. Even better, you can save yourself a lot of work by recognizing that many fractions that may look different (for example, three-fourths and twelve-sixteenths) are actually the same. Once you've calculated that 3/4 is .75, you know that 6/8, 9/12 and 12/16 are also equal to .75. It really doesn't take more than the knowledge of the following two decimal equivalents to create a table of all the decimal equivalents of any fraction with a denominator of 2, 3, 4, 5, 6, 8, 9, 10, 12, 15 or 16: _ one ninth = .1 (an endless string of ones) one tenth = .1 Here's how we can use just these two decimal equaivalents, and our knowledge of fractions, to calculate the value of 7/12: Since 1/2 is the same as 5/10, 1/2 is 5 times .1 or .5. 6/12 is the same as 1/2, so 6/12 is also equal to .5 7/12 is the sum of 6/12 and 1/12, so we can calculate 1/12 as follows: 1/12 is half of 1/6. 1/6 is half of 1/3. 1/3 is three times 1/9, so 1/3 is equal to an endless string of threes to the right of the decimal point. 1/6 is half of that, which is a decimal point followed by a one and an endless string of sixes. 1/12 is half of 1/6, which is a decimal point followed by a zero, an eight and an endless string of threes. If we add 6/12 to 1/12, we get: _ _ .5 + .083 = .583 = 7/12 You could also calculate a decimal equivalent for 11/12 by recognizing that it is 12/12 minus 1/12. 12/12 is 1. 1 minus 1/2 is: _ _ 1 - .083 = .916 = 11/12 As you create your table, you'll come to appreciate the shortcuts of calculating decimal equivalents by recognizing a fraction as the sum of various other fractions. One day, you may even be able to calculate 43 and one-third percent of 360 in your head, by recognizing that 43 and one-third percent is the sum of 1/10 and 1/3. When your table is done, make sure to check your work. Here's one way you can test to make sure a decimal equaivalent is correct: If .875 really is 7/8, then .875 times 8 and divided by 7 should be 1. Is it? Creating your own table is not only more fun than looking at one someone else made up, but is also more likely to help you learn in a way that will stay with you forever. Enjoy. -Doctor Gary, The Math Forum http://mathforum.org/dr.math/ |
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