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/