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### Multiplying a Fraction by a Variable

```Date: 08/17/2006 at 20:36:29
From: Erin
Subject: How do I find what s equals

1
How do I find the product of ---a ?
3

```

```
Date: 08/19/2006 at 11:43:58
From: Doctor Ian
Subject: Re: How do I find what s equals

Hi Erin,

1
-(6)
3

This is just

1/3 of 6

which we can find this way:

1      1   6   1*6
-(6) = - * - = ---
3      3   1    3

Does that make sense?  I know that we could reduce the 1*6 to just 6,
and reduce the 6/3 to 2, but let's NOT do that for a moment.

Now, suppose we're in the same situation, but the 6 is smudged, so we
can't see what it is.  But we know it's _some_ number, and since it's
a number, we can treat it the same we we treated 6.

Let's use "s" to represent the smudged number--it's just a marker
that we're using to keep track of it, so later if someone tells us
what it was, we can replace the marker with the value.

1      1   s   1*s
- s  = - * - = ---
3      3   1    3

What if we had 2/5 of some smudged number?

2      2   s   2*s
- s  = - * - = ---
5      5   1    5

Or 23% of some number?  The notation 23% just means 23/100, so we'd have

23       23   s   23*s
--- s  = --- * - = ----
100      100   1    100

the value of the variable is supposed to be.

Does that make sense?

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

```

```
Date: 08/19/2006 at 14:32:41
From: Erin
Subject: Thank you (How do I find what s equals)

Hi thank you sooooo much it seems really easy now.  Now when I turn in
my homework to my math teacher all the answers will be right since
now I know how to deal with those kind of fractions.  Once again thank
you!!  I know where to go now if I ever need help in the future again.
```
Associated Topics:
Middle School Algebra
Middle School Fractions

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