Question

Which is greater, the sum of $\frac{-7}{12}$ and $\frac{2}{5}$ of the sum of $\frac{-3}{8}$ and $\frac{-11}{-12}$, and by how much?

Answer 1

Let $x=\frac{-7}{12}+\frac{2}{5}=\frac{-35+24}{60}=\frac{-11}{60};y=\frac{-3}{8}-\frac{11}{-12}=\frac{-3}{8}+\frac{11}{12}$

$=\frac{-36+88}{96}=\frac{52}{96}=\frac{13}{24}$

As $y>0,x<0\Rightarrow y$ is greater by

$y-x=\frac{13}{24}+\frac{11}{60}=\frac{1}{6}(\frac{13}{4}+\frac{11}{10})=\frac{130+44}{40\times 6}=\frac{174}{40\times 6}=\frac{29}{40}$.