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?

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.

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

Hello, jacklogan!

Quote:

$\displaystyle \text{How would you write }\text{-}1\tfrac{13}{56}\text{ as an improper fraction?}$

$\displaystyle \text{If it wasn't negative, the answer would be }\tfrac{69}{56}.$

$\displaystyle \text{Since it is negative, is the answer }\text{-}\tfrac{69}{56}\,?$

$\displaystyle \text{Or is the answer }\text{-}\tfrac{43}{56}\text{ which a colleague claims.}$

Your colleague is *dangerously* wrong.

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?

*His* answer would be $4.00.

How would he get that awful answer?

. . Like this . . .

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

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

Ask him to consider this . . .

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

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

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

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

Quote:

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!