Negative Signs and Fractions

Negative signs bother many students, particularly when they are followed by fractions. In such situations, it is important to remember that the vinculum (the horizontal line between numerator and denominator) serves as a grouping symbol – like parentheses would. I recommend that students always put a numerator with more than one term in parentheses before bringing a leading negative sign into the numerator.

The answer shown below is wrong.  Try working your way through the problem backwards, from the answer up. As you find each mistake, try to identify the thinking behind it… what perspective led to the mistake? What should have been done instead?

\dfrac{2-w}{3}-\dfrac{2w-5}{2}

=\dfrac{2-w}{3}\cdot\dfrac{2}{2}-\dfrac{2w-5}{2}

=\dfrac{2(2-w)}{6}+\dfrac{-2w-5}{6}

=\dfrac{4-w-2w-5}{6}

=\dfrac{-1-3w}{6}

.

..

Hint 1: the correct answer to the original problem is: \dfrac{-8w+19}{6}

Hint 2: several mistakes have been made in the work above – they are not all sign or distribution errors

Published by

Whit Ford

Math teacher, substitute teacher, and tutor (along with other avocations)

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