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$({2\fraction{5}{8}}) / ({1\fraction{3}{4}}) $
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\frac{\left(2\times 8+5\right)\times 4}{8\left(1\times 4+3\right)}
Divide \frac{2\times 8+5}{8} by \frac{1\times 4+3}{4} by multiplying \frac{2\times 8+5}{8} by the reciprocal of \frac{1\times 4+3}{4}.
\frac{5+2\times 8}{2\left(3+4\right)}
Cancel out 4 in both numerator and denominator.
\frac{5+16}{2\left(3+4\right)}
Multiply 2 and 8 to get 16.
\frac{21}{2\left(3+4\right)}
Add 5 and 16 to get 21.
\frac{21}{2\times 7}
Add 3 and 4 to get 7.
\frac{21}{14}
Multiply 2 and 7 to get 14.
\frac{3}{2}
Reduce the fraction \frac{21}{14} to lowest terms by extracting and canceling out 7.