Converting Mixed Numbers to/from Improper FractionsDate: 10/28/2001 at 15:37:01 From: Jo Subject: Improper fractions I have to change mixed numbers like 1 3/4 into improper fractions, and write fractions like 7/5 in simplest form by changing them to a mixed numbers. I don't know how to do this. Date: 10/29/2001 at 11:56:41 From: Doctor Ian Subject: Re: Improper fractions Hi Jo, You can represent a proper fraction with a picture like this, +---+---+ |###| | +---+---+ 3/4 |###|###| +---+---+ right? Well, you can represent a unitary fraction with a similar picture: +---+---+ |###|###| +---+---+ 4/4 = 1 |###|###| +---+---+ So if you have something like 2 3/4, you can represent it this way: +---+---+ +---+---+ +---+---+ |###|###| |###|###| |###| | +---+---+ +---+---+ +---+---+ |###|###| |###|###| |###|###| +---+---+ +---+---+ +---+---+ and now you can just count the #'s: +---+---+ +---+---+ +---+---+ |###|###| |###|###| |###| | +---+---+ +---+---+ +---+---+ = 11/4 |###|###| |###|###| |###|###| +---+---+ +---+---+ +---+---+ Of course, it's a hassle to draw pictures, so you can do the same thing with numbers: 4 3/5 = 4 + 3/5 = 1 + 1 + 1 + 1 + 3/5 = 5/5 + 5/5 + 5/5 + 5/5 + 3/5 = (5 + 5 + 5 + 5 + 3)/5 = (4*5 + 3)/5 This last line looks almost like a formula, doesn't it? It's just the same numbers arranged in a different way. I'll bet that if you were to work enough examples like this, you could probably convince yourself that you can convert any mixed fraction into an improper fraction this way: A + B/C = (A*C + B)/C Of course, if you just try to remember the formula without understanding (from practice) why it works, you might get it mixed up. So you want to be careful not to try to 'memorize' the formula. Now, what about going the other way? Well, again using pictures, suppose we have a fraction like 25/6. We can start breaking 25 items into groups of 6: ##### ##### ##### ##### ##### ### ##### ### ### ##### = ##### + ### = ### + ### + ### = ... ##### #### ##### \__________/ \________________/ 25 19 + 6 13 + 2(6) Eventually, you end up with ### ### ### ### # + ### + ### + ### + ### \__________________________/ 1 + 4(6) Do you see how this corresponds to the picture that you would draw for the fraction 4 1/6? Again, you can do this with numbers instead of pictures, which speeds things up: 25/6 = 19/6 + 1 = 13/6 + 2 = 7/6 + 3 = 1/6 + 4 And eventually it would occur to you to notice that if you divide 25 by 6, you get 4 remainder 1, which is to say, ___ 6 ) 25 = 4 remainder 1 = 4 + 1/6 But again, if you just try to remember this 'method', you're likely to get mixed up under pressure (for example, when you're taking a test). The safest thing to do is to work it out the long way until you find yourself jumping ahead to the answer because you know what it's going to turn out to be. Does this help? Write back if you'd like to talk about this some more, or if you have any other questions. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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