Question

Which fraction is greater than -2/3 and less than -1/2?? Please help!! Thank you!!

Answer 1

first of all let's recall that on the negative side of the number line, the closer to 0, the greater, so -1 is much greater than -1,000,000.

well, let's simply try to convert both fractions to the same denominator by multiplying top and bottom by 1 or namely the same value, hmmm let's multiply -2/3 by 2/2 = 1, and -1/2 by 3/3 = 1

`-\cfrac{2}{3}\cdot \cfrac{2}{2}\implies -\cfrac{4}{6}\hspace{5em}-\cfrac{1}{2}\cdot \cfrac{3}{3}\implies -\cfrac{3}{6}`

well, rats, no much wiggling room there, well, let's simply multiply them again by 1, in this case hmmmm 2/2 for both

`-\cfrac{4}{6}\cdot \cfrac{2}{2}\implies \boxed{-\cfrac{8}{12}}\hspace{5em}-\cfrac{3}{6}\cdot \cfrac{2}{2}\implies \boxed{-\cfrac{6}{12}} \\\\\\ \underset{-\cfrac{2}{3}}{\boxed{-\cfrac{8}{12}}}\hspace{5em} < \qquad -\cfrac{7}{12}\qquad < \hspace{5em} \underset{-\cfrac{1}{2}}{\boxed{-\cfrac{6}{12}}}`