# Thread: How to change a proper, negative fraction to an improper fraction

1. ## How to change a proper, negative fraction to an improper fraction

How would you write -1 13/56 as an improper fraction? If it wasn't negative, the answer would be 69/56. Since it is negative, is the answer -69/56? OR is the answer -43/56, which a colleague says; his reasoning being, to find the numerator: -1 x 56 = - 56; then add 13 to get -43. So his answer is -43/56. Which is correct?

2. ## Re: How to change a proper, negative fraction to an improper fraction

-43/56 is greater than -1, but the mixed number is actually less than -1, therefore your colleague's answer is not correct; -69/56 is the answer. I always used to solve these by ignoring the negative sign, solving as if the mixed number was positive, then tacking the negative sign back onto the improper fraction.

3. ## Re: How to change a proper, negative fraction to an improper fraction

Hello, jacklogan!

$\text{How would you write }\text{-}1\tfrac{13}{56}\text{ as an improper fraction?}$
$\text{If it wasn't negative, the answer would be }\tfrac{69}{56}.$
$\text{Since it is negative, is the answer }\text{-}\tfrac{69}{56}\,?$
$\text{Or is the answer }\text{-}\tfrac{43}{56}\text{ which a colleague claims.}$

I hope he doesn't apply that to Real Life.

Suppose he had $5.75 and he spent$2.25.
. . How much would he have left?

How would he get that awful answer?
. . Like this . . .

. . $\begin{array}{c}\5.75\, = \,5\tfrac{3}{4}\text{ dollars} \\ \\[-3mm] \2.25 \,=\,2\tfrac{1}{4}\text{ dollars} \end{array}$

$\begin{array}{ccccccccc}\5.75 - 2.25 &=& 5\frac{3}{4} - 2\frac{1}{4} \\ \\[-3mm] & = & 5 + \frac{3}{4} - 2 \;{\color{red}+\;\frac{1}{4}} \\ \\[-3mm] &=& (5-2) + (\frac{3}{4} + \frac{1}{4}) \\ \\[-3mm] &=& 3 + \frac{4}{4}\\ \\[-3mm] &=& \4 \end{array}$

Ask him to consider this . . .

What is $\text{-}1\tfrac{1}{4}$ ?

He believes it means: . $\text{-}1 \:{\color{red}+\: \tfrac{1}{4}} \:=\:\text{-}\tfrac{3}{4}$

If that is true, why didn't they write $\text{-}\tfrac{3}{4}$ in the first place?

4. ## Re: How to change a proper, negative fraction to an improper fraction

Originally Posted by jacklogan
How would you write -1 13/56 as an improper fraction? If it wasn't negative, the answer would be 69/56. Since it is negative, is the answer -69/56? OR is the answer -43/56, which a colleague says; his reasoning being, to find the numerator: -1 x 56 = - 56; then add 13 to get -43. So his answer is -43/56. Which is correct?
This whole thread is result of just out-of-date group of people.
The truth is there is absolutely no reason to use so-called improper fractions.

Given the wide use of calculators and computer algebra systems in which improper fractions have no place, what good are they? Let's drop their use!