Fractions of a CupDate: 04/15/2003 at 22:30:06 From: Kirstie Subject: Reducing many cups to one cup If you made 1 cup of mix, how much water and how much concentrate would you need? MIX W 3 cups concentrate 4 cups cold water I can't figure out how to reduce many cups to 1 cup. I thought it was 1/4 cup water and 1/3 cup concentrate, but I don't think that's right. Date: 04/16/2003 at 14:16:04 From: Doctor Ian Subject: Re: Reducing many cups to one cup Hi Kirstie, One way you can check your answer is this: The quantities would have to add up to 1 cup. Do you see why? Let's try that: 1/4 + 1/3 = 3/12 + 4/12 = 7/12 which is less than a cup. So we need to find a different answer. Let's say you make all 7 cups of the mix. Then you have 7 cups of mix, which contains 3 cups of concentrate, and 4 cups of water. +-------------+ | | <-- concentrate +-------------+ | | <-- concentrate +-------------+ | | <-- concentrate +-------------+ | | <-- water +-------------+ | | <-- water +-------------+ | | <-- water +-------------+ | | <-- water +-------------+ Now to get 1 cup, you're going to divide the mix into 7 equal parts: +-------------+ |c|c|c|c|c|c|c| Each 'c' is 1/7 of a cup |c|c|c|c|c|c|c| |c|c|c|c|c|c|c| +-------------+ |w|w|w|w|w|w|w| Each 'w' is 1/7 of a cup |w|w|w|w|w|w|w| |w|w|w|w|w|w|w| |w|w|w|w|w|w|w| +-------------+ And keep one of them: +-+ |c| |c| |c| +-+ |w| |w| |w| |w| +-+ So how much of each (concentrate or water) do you have? Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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