To simplify the expression
\[ \frac{7 \times 8 + 20 \times 4.5}{16 \times 0.5} \]
we will first calculate the values in the numerator and denominator separately.
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Calculate the numerator: \[ 7 \times 8 = 56 \] \[ 20 \times 4.5 = 90 \] Adding these together: \[ 56 + 90 = 146 \]
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Calculate the denominator: \[ 16 \times 0.5 = 8 \]
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Now, we can substitute these computed values back into the fraction: \[ \frac{146}{8} \]
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Finally, simplify the fraction: When we divide 146 by 8, we perform the division: \[ 146 \div 8 = 18.25 \]
Thus, the simplified value of the expression is
\[ \boxed{18.25} \]