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### Fractions of a Cup

```Date: 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/
```
Associated Topics:
Elementary Fractions
Elementary Word Problems

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