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### X is What Part of Y?

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Date: 11/01/2001 at 04:52:15
From: Leanne Lee
Subject: (no subject)

Dear Dr. Math,

Set 1:
2/5 is what part of 4/5?

Set 2:
What part of 2/3 is 4/5?

Set 3:
What part is 4/5 of 3?

Set 4:
2/3 is what part of 2?

I don't know how to work it out because sometimes they use the words
"what part is, what part of" put in front of the sentence, middle, or
at the end of the sentence. It is very confusing to me. Would you

Thank you very much.
```

```
Date: 11/01/2001 at 11:27:42
From: Doctor Ian
Subject: Re: (no subject)

Hi Leanne,

This makes more sense if you think about evenly divisible integers.

When you're asked, 'X is what part of Y?' you find the answer by
dividing X by Y. For example,

2 is what part of 4?

The answer is obviously 1/2; and 2/4 = 1/2. The sense is reversed when
you're asked, 'What part of X is Y?' Then you find the answer by
dividing Y by X.  For example,

What part of 4 is 2?

Again, the answer is obviously 1/2; and 2/4 = 1/2.

The only wrinkle here is that you're dealing with fractions. Remember
that to divide by a fraction, you invert and multiply:

2
----- = 2 * (4/3)
3/4

and you should be okay.

By the way, this is a useful strategy in other situtations. Teachers
often make up problems with messy numbers, which can startle you into
forgetting things you actually know. For example, if I ask you, "At
26.3 miles per hour, how many hours does it take to go 193.7 miles?"
you might end up guessing.

But if you change the numbers to something like "At 60 miles per hour,
how many hours does it take to go 30 miles? How about 120 miles?" then
you can see what the answers _must_ be (half an hour and two hours),
of values.

Does this help?

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Fractions

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