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### Adding Fractions That Have Variables

```Date: 03/24/2002 at 13:39:33
From: Sal Anicito

9a        2
----  +  ----
10        5

I have the answer in the back of the book but I don't know how to
solve it. The answer is showing:

9a + 4
--------
10
```

```
Date: 03/24/2002 at 13:45:11
From: Doctor Ian
Subject: Re: Adding fractions with variables

Hi Sal,

Let's back up a step. Would you be able to handle this without the
variable?  That is, how would you add

9   2
-- + - = ?
10   5

Don't just tell me the answer. Show me the steps that you would
follow.

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

```
Date: 03/24/2002 at 23:18:26
From: Sal Anicito

I would first find the LCD, which would be 10. Then say 5 into 10 is
2 and 2 x 2 = 4, which would give me 4/10. Then 10 into 10 is 1 and
1 x 9 is 9, which would give me 9/10. Then add 9 + 4, which is 13, so
I would get 13/10 for an answer. Is that right?
```

```
Date: 03/25/2002 at 07:09:14
From: Doctor Ian
Subject: Re: Adding fractions with variables

Hi Sal,

That's exactly right.

9   2    9   2   2    9    4   13
-- + - = -- + - * - = -- + -- = --
10   5   10   5   2   10   10   10

The thing is, it works the same way even if you have a variable in
there:

9a   2    9a   2   2    9a    4   9a + 4
--- + - = --- + - * - = --- + -- = ------
10   5    10   5   2    10   10      10

The only difference is that you don't know what the value of a happens
to be. To see why this works, choose a value for a, but don't do the
multiplication yet:

9*2    2    9*2    2   2    9*2     4   9*2 + 4
----- + - = ----- + - * - = ----- + -- = --------
10     5      10   5   2     10    10      10

A variable is just a number whose value you don't yet know; and a
variable expression (like '9a') is just an operation that you're
putting off until later.

Does this help?

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

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