Question

Emily thinks that -11/6 - (-2/3) is -5/2. Identify the error ghat emily made. Then correct Emily’s error and find the correct value.

Answer 1

$\bf \stackrel{\textit{she subtracted }\frac{2}{3}\textit{ instead of adding it}}{-\cfrac{11}{6}-\left(\cfrac{2}{3} \right)\impliedby \stackrel{LCD}{6}\implies \cfrac{-(1)11~~-~~(2)2}{6}}\implies \cfrac{-11~~-~~4}{6} \\\\\\ \cfrac{-15}{6}\implies \stackrel{simplified}{-\cfrac{5}{2}}\impliedby \textit{that's correct, assuming is }\frac{2}{3}~~but~is~~-\frac{2}{3}\\\\ -------------------------------$

$\bf \stackrel{\textit{recall that minus times minus is plus}}{-\cfrac{11}{6}-\left(-\cfrac{2}{3} \right)\implies -\cfrac{11}{6}+\cfrac{2}{3}}\implies \cfrac{-(1)11+(2)2}{6} \\\\\\ \cfrac{-11+4}{6}\implies -\cfrac{7}{6}\quad \checkmark$