Ordering Fractions by Changing Them to Decimals
Date: 12/11/2008 at 21:45:42 From: Julie Subject: placing fractions in order 3/10, 1/2, 7/8, 4/5, 1/6, 3/4, 9/10, 1/3, 3/5, 3/8, 1/4, 1/10 Can you help me put these in order? Please! I just really don't understand fractions. I know 1/4, 1/2 etc... but when there is another number other than 1 on top, I get confused.
Date: 12/11/2008 at 23:27:37 From: Doctor Wilko Subject: Re: placing fractions in order Hi Julie, Thanks for writing to Ask Dr. Math! There are many different ways to teach or explain this. I'll try one way which may be different from what your daughter was taught, but it may help you understand better. 1. Common Denominators Before I get to your exact problem, I think it'll still be insightful to talk a little about fractions and common denominators. The denominator is the number on the bottom of the fraction. If the denominators of a bunch of fractions are the same, the problem is easier to handle. For instance, in your fractions above you have 3/10, 9/10, and 1/10. These have the same denominator, which makes them easier to compare directly. One way to think about fractions is in terms of a pie. The denominator tells you the total pieces of pie and the numerator (top number) is, say, how many pieces of pie you are going to eat out of the total. So, for 3/10, this is like saying there are 10 pieces of pie and you are going to have 3 of them. So, it should make sense if we rank these in order of smallest to largest, then the rank is 1/10, 3/10, and 9/10, because eating 1 out of 10 pieces of pie is a lot less than eating 9 out of 10 pieces of pie. You could summarize this and say: if you compare fractions with the same denominators (bottom numbers), then the fraction with the smallest numerator (top number) is the smallest fraction and the fraction with the largest numerator is the largest fraction. Again, this method is nice if you have fractions with the same denominator. In fact you can take fractions with different denominators and do some math to get them to all have common denominators and then still use this method. For what you're doing, I think there is a more concrete way to understand how to order the fractions from smallest to largest. Let's look at that now. 2. Change Fractions to Decimals What I explained above is nice if all your fractions have the same denominator, but unfortunately that's not the case with your problem. You have 12 fractions all having different combinations of numerators and denominators. One nice thing with fractions is that any fraction can be converted to an equivalent decimal by dividing the numerator by the denominator. For instance, take the fraction 1/10. In your calculator press 1, divided by, 10. 1/10 = 0.10 The part I like about this is to think of the decimals as money! So 1/10 (of a dollar) = 0.10 (this is a dime; 10 cents). Using our example from above, 1/10 = 0.10 3/10 = 0.30 9/10 = 0.90 10 cents is less than 30 cents, which is less than 90 cents. This rank order also confirms our answer from above. Now if we convert the 12 fractions from above into decimals and think of the decimals as money, we should have a more intuitive feel for ordering them. 1/10 = 0.10 (10 cents; smallest) 1/6 ~ 0.167 1/4 = 0.25 3/10 = 0.30 1/3 ~ 0.333 3/8 = 0.375 1/2 = 0.50 3/5 = 0.60 3/4 = 0.75 4/5 = 0.80 7/8 = 0.875 9/10 = 0.90 (90 cents; largest) Does this help? Please write back if you need anything else. :-) Also, I'd encourage you to search our archives for additional information on fractions or for any future problems you may have--our archives are a great resource! - Doctor Wilko, The Math Forum http://mathforum.org/dr.math/
Date: 12/12/2008 at 04:46:21 From: Julie Subject: Thank you (placing fractions in order) Thank you from the bottom of my heart for the help I so desperately needed. What a great explanation, I understood exactly what you meant! I just really appreciate that there are people out there like you!
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