Answer
Estimated answer = 38
Exact answer = $38\frac{5}{28}$
Work Step by Step
$22\frac{3}{4}$ + $15\frac{3}{7}$
Estimation:
$22\frac{3}{4}\approx 23$
$15\frac{3}{7} \approx 15$
Therefore
$22\frac{3}{4}$ + $15\frac{3}{7}$ $\approx$ 23 + 15 = 38
Exact Calculation:
$22\frac{3}{4}$ + $15\frac{3}{7}$
= $22\frac{3\times7}{4\times7}$ + $15\frac{3\times4}{7\times 4}$
(28 is the least common denominator)
= $22\frac{21}{28}$ + $15\frac{12}{28}$
= $22$ + $15$ + $\frac{21}{28}$ + $\frac{12}{28}$
(Adding whole parts separately and fractional parts separately)
= $37$ + $\frac{21 + 12}{28}$
= $37$ + $\frac{33}{28}$
= $37$ + $\frac{28 + 5}{28}$
= $37$ + $\frac{28}{28} + \frac{5}{28} $
= 37 + 1 + $\frac{5}{28}$
= $38\frac{5}{28}$
The estimate was 38, so the exact answer of $38\frac{5}{28}$
is reasonable.
