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### Converting Negative Mixed Numbers to Improper Fractions

```Date: 10/25/2006 at 00:22:58
From: Brenda
Subject: Negative Mixed Numbers

During the process of converting a negative mixed number into an
improper fraction, I noticed that we do not pay any attention to the
rules of adding negative and positive numbers.

For example: -4 1/7 = -4 X 7 + 1 = -28 + 1 = -29/7, not -27/7

Why is this so?  The rules of adding integers don't seem to apply.
Shouldn't the final answer be -27/7?

```

```
Date: 10/25/2006 at 00:38:54
From: Doctor Ian
Subject: Re: Negative Mixed Numbers

Hi Brenda,

The rules apply just fine, once you realize that the mixed number

a b/c

is an abbreviation for

(a + b/c)

So

-4 1/7

means

-(4 + 1/7)

= -(28/7 + 1/7)

= -(29/7)

= -29/7

It's exactly the same thing that happens with decimals, because
decimals ARE mixed numbers:

-3.29

= -3 29/100

= -(3 + 29/100)

Does that make sense?  Let me know if you need more help.

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Place Value
Middle School Negative Numbers

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