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### Multiplying by the Reciprocal to Divide Two Fractions

```Date: 05/08/2008 at 21:38:10
From: Amanda
Subject: dividing fractions

I can not figure out how you divide fractions, like 2/9 by 7/45.

I do not get reciprocals and how you change it from dividing to
multiplying.

```

```
Date: 05/09/2008 at 09:23:11
From: Doctor Ian
Subject: Re: dividing fractions

Hi Amanda,

The "rule" is that you invert the bottom fraction and multiply by it
instead.  Here's an explanation of why that works:

Multiplying and Dividing Fractions
http://mathforum.org/library/drmath/view/58080.html

A shorter explanation is that you can just use equivalent fractions to
get the result.  That is, if we have a fraction like

2
-
9

we can multiply it by n/n, where n is any number but zero; and we get
a fraction with the same value, e.g.,

2   5   10
- * - = --          2/9 and 10/45 have the same value
9   5   45

Does that look familiar?  If so, consider that we can start with this,

2
-
9
----
7
--
45

and multiply both the top and bottom by 45/7, i.e., the reciprocal of
the bottom fraction:

2   45
- * --
9    7
----------
7   45
-- * --
45    7

Now, what's the bottom going to equal?  It has to be 1, right?  So the
whole thing is equal to

2   45
- * --
9    7
----------

1

or just

2   45
- * --
9    7

Which is to say, it's equal to the numerator times the reciprocal of
the denominator.

Does that make sense?

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/

```

```
Date: 05/09/2008 at 21:22:57
From: Amanda
Subject: Thank you (dividing fractions)

THANK YOU.....I hope my grade goes up I do understand it NOW.....THANK
YOU SOOOOOOO MUCH.
```
Associated Topics:
Elementary Division
Elementary Fractions

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