#### Answer

Estimated answer = 31
Exact answer = $30\frac{5}{14}$

#### Work Step by Step

$14\frac{6}{7}$ + $15\frac{1}{2}$
Estimation:
$14\frac{6}{7}\approx 15$
$15\frac{1}{2} \approx 16$
Therefore
$14\frac{6}{7}$ + $15\frac{1}{2}$ $\approx$ 15 + 16 = 31
Exact Calculation:
$14\frac{6}{7}$ + $15\frac{1}{2}$
= $14\frac{6\times2}{7\times2}$ + $15\frac{1\times7}{2\times7}$
(14 is the least common denominator)
= $14\frac{12}{14}$ + $15\frac{7}{14}$
= $14$ + $15$ + $\frac{12}{14}$ + $\frac{7}{14}$
(Adding whole part separately and fractional part separately)
= $29$ + $\frac{12 + 7}{14}$
= $29$ + $\frac{19}{14}$
= $29$ + $\frac{14 + 5}{14}$
= $29$ + $\frac{14}{14} + \frac{5}{14} $
= 29 + 1 + $\frac{5}{14}$
= $30\frac{5}{14}$
The estimate was 31, so the exact answer of $30\frac{5}{14}$
is reasonable.