Question

10\frac{5}{16} - \left(5\frac{1}{4} + 2\frac{9}{16}\
ight)

Explanation:

Step1: Convert to improper fractions

$10\frac{5}{16}=\frac{10\times16+5}{16}=\frac{165}{16}$, $5\frac{1}{4}=\frac{5\times4+1}{4}=\frac{21}{4}$, $2\frac{9}{16}=\frac{2\times16+9}{16}=\frac{41}{16}$

Step2: Unify denominators

$\frac{21}{4}=\frac{21\times4}{4\times4}=\frac{84}{16}$

Step3: Calculate sum inside parentheses

$\frac{84}{16}+\frac{41}{16}=\frac{84+41}{16}=\frac{125}{16}$

Step4: Subtract the two fractions

$\frac{165}{16}-\frac{125}{16}=\frac{165-125}{16}=\frac{40}{16}$

Step5: Simplify the result

$\frac{40}{16}=\frac{5}{2}=2\frac{1}{2}$

Answer:

$2\frac{1}{2}$ (or $\frac{5}{2}$)