I'm comfortable with fractions like − 3 8 being the same as 3 − 8 (though I'd think the latter anachronistic and would in any case probably prefer to write either of those two as − 3 8 ), and of course I'm comfortable with improper fractions like − 8 3 being the mixed number − 2 2 3 However, if I'm trying to teach a computer how to handle negative vulgar fractions, I should also consider the remaining cases, so how should I interpret:1. 2 − 2 3 2. 2 2 − 3 3. 2 − 2 − 3 4. − 2 − 2 3 5. − 2 2 − 3 6. − 2 − 2 − 3 I'm considering the logical approach, by inference from 2 2 3 and − 2 2 3 so I'd get:1. 1 1 3 2. 1 1 3 3. 1 2 3 4. − 1 1 3 5. − 1 1 3 6. − 2 2 3

Question

I&#039;m comfortable with fractions like             −      3        8   being the same as       3          −      8       (though I&#039;d think the latter anachronistic and would in any case probably prefer to write either of those two as    −      3    8   ), and of course I&#039;m comfortable with improper fractions like             −      8        3   being the mixed number   −  2      2    3   However, if I&#039;m trying to teach a computer how to handle negative vulgar fractions, I should also consider the remaining cases, so how should I interpret:1.  2            −      2        3  2.  2      2          −      3      3.  2            −      2              −      3      4.  −  2            −      2        3  5.  −  2      2          −      3      6.  −  2            −      2              −      3      I&#039;m considering the logical approach, by inference from   2      2    3   and   −  2      2    3   so I&#039;d get:1.  1      1    3  2.  1      1    3  3.  1      2    3  4.  −  1      1    3  5.  −  1      1    3  6.  −  2      2    3

Myla Pierce · Accepted Answer

Recall that when   a  ,  b  ,  c  ∈      Z    a            b      c        =  a  +            b      c      If       b    c    &amp;lt;  0, then       |          b      c        |   is subtracted from   a.So, for example  −  2            −      2        3    =  −  2  −      2    3    =  −      (    2    +          2      3        )  whereas  −  2            −      2              −      3        =  −  2  +      2    3    =  −      (    1    +          1      3        )

polivijuye · Accepted Answer

Section 3.8 of Charles McKeague&#039;s Pre-Algebra: A Text/Workbook has the key information, with worked examples.  3      2    3    −  1      1    6  is implicitly bracketed as      (    3          2      3        )    −      (    1          1      6        )  so the answer in this example is  2      1    2  Applying that the the examples in the original question is then straightforward, and the proposed interpretations are correct.Edit: Answers at Primary/Elementary Pedagogy: What is the rationale for the absent &#039;+&#039; in mixed fractions? also indicate the reason why we write a mixed number as   1      1    2   and not as   1  +      1    2

I'm comfortable with fractions like − 3 </mrow>

Answered question

Answer & Explanation

New Questions in Pre-Algebra