Answer
$1\frac{1}{16}.$
Work Step by Step
By unifying the denominators, we have
$$
\frac{3}{8}+\frac{1}{4}+\frac{7}{16}=\frac{6}{16}+\frac{4}{16}+\frac{7}{16}\\
=\frac{6+4+7}{16}=\frac{17}{16}=1\frac{1}{16}.
$$
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