Question

Which fraction out of 5/8 and 7/11 is closest to 2/3?

Answer 1

Well... hell, let's just convert them all with the same denominator then

hmmm let's see, we have the denominators of 8,11 and 3

so... we'll multiply the 5/8 times (11*3) or 33
and then we'll multiply 7/11 times (8*3) or 24
and then we'll multiply 2/3 times (8 * 11)

notice, we're simply using the other's denominator's product, to multiply the fractions... anyhow... let's check

$\bf \cfrac{5}{8}\cdot \cfrac{3\cdot 11}{3\cdot 11}\implies \cfrac{165}{264} \\\\\\ \cfrac{7}{11}\cdot \cfrac{8\cdot 3}{8\cdot 3}\implies \cfrac{168}{264} \\\\\\ \cfrac{2}{3}\cdot \cfrac{8\cdot 11}{8\cdot 11}\implies \cfrac{176}{264}\\\\ -------------------------------\\\\ \textit{now, which of }\cfrac{165}{264}\textit{ and }\cfrac{168}{264}\textit{ is closest to }\cfrac{176}{264}\quad ?$