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### Eliminating Fractions in Division

```Date: 11/20/2003 at 18:58:29
From: Duckie
Subject: Dividing a whole number and a fraction

The question is:

Make an equivalent division problem for 5 divided by 1/3 by
multiplying both the dividend and divisor by three. Then find the
quotient.

I keep reading it over and over but I just don't understand what
```

```
Date: 11/21/2003 at 01:29:03
From: Doctor Ian
Subject: Re: Dividing a whole number and a fraction

Hi Duckie,

Let's look at something simpler.  Suppose we have something like

12 divided by 4 = ?

or

___
4 ) 12 = ?

Note that we can write it as a fraction, too:

12
-- = ?
4

These are all just ways of writing the same thing.  Now, what's
interesting about the fraction form is that we can see that if we
multiply the numerator and denominator by the same thing, we change
the _appearance_ of the fraction without changing the _value_:

12   5   60
-- * - = --
4   5   20

Does that make sense?  Well, it means we could do the same thing in
the other forms, too:

___          _______
4 ) 12 = (4*5) ) (12*5)

___
= 20 ) 60

Now, this is useful when we've got a fraction, because we can multiply
both numbers by the denominator of the fraction, e.g.,

____          __________
5 ) 2/9 = (5*9) ) (2/9 * 9)

__
= 45 ) 2

Does this make sense?

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

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