Adding FractionsDate: 01/06/2003 at 16:03:17 From: Sharon Subject: Adding fractions My problem is 3/4 + 1/6. I have figured out how to get the same denominators, but in the example 3/4 + 1/6 the denominator is 12 but it says to build up my numerator, so then it is written 9/12 + 2/12 = 11/12. I don't understand how they get 9 and 2 for numerators. Date: 01/06/2003 at 17:34:52 From: Doctor Ian Subject: Re: Adding fractions Hi Sharon, Suppose you have a piece of cake, and you cut it into 4 pieces and give one piece away. You now have 3/4 of the cake, right? +-----------+ | | | 1/4 | | | +-----------+-----------+ 1/4 + 1/4 + 1/4 = 3/4 | | | | 1/4 | 1/4 | | | | +-----------+-----------+ Now, suppose you cut each of these pieces into three smaller pieces: +-----------+ | . . | | . . | | . . | +-----------+-----------+ | . . | . . | | . . | . . | | . . | . . | +-----------+-----------+ How big is each of these pieces? Well, if we'd cut the cake into pieces of this size to begin with, ............+-----------+ . . . | . . | . . . | . . | . . . | . . | +-----------+-----------+ | . . | . . | | . . | . . | | . . | . . | +-----------+-----------+ we'd have had 12 pieces. (Count them to make sure.) So each of these smaller pieces is 1/12 of the original cake, and when we have 3/4 of the cake, that's the same as having 9/12 of the cake: +-----------+ +-----------+ | . . | | | | 1 . 2 . 3 | | 1 | | . . | | | +-----------+-----------+ = +-----------+-----------+ | . . | . . | | | | | 4 . 5 . 6 | 7 . 8 . 9 | | 2 | 3 | | . . | . . | | | | +-----------+-----------+ +-----------+-----------+ 9/12 3/4 Does that make sense? Now, how do we get from 3/4 to 9/12 without drawing a picture? Well, remember, we divided something into 4 pieces, and kept three of them. If we divided it into 3 times as many pieces, we'd keep three times as many of those, right? So keep 3 pieces keep 3*3 pieces --------------- must be the same as ----------------- out of 4 pieces out of 3*4 pieces Does _that_ make sense? The way we write it in symbols is 3 3 * 3 9 - = ----- = -- 4 3 * 4 12 Does this answer your question? If so, you should be able to 'build up' 1/6 in the same way that we 'built up' 3/4: 1 ? * 1 ? - = ----- = -- 6 ? * 6 12 If not, write back and let me know where I lost you. I hope this helps! - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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