Answer
Estimated answer = 8
Exact answer = $7\frac{11}{12}$
Work Step by Step
$19\frac{2}{3}$ - $11\frac{3}{4}$
Estimation:
$19\frac{2}{3} \approx 20$
$11\frac{3}{4} \approx 12$
Therefore
$19\frac{2}{3}$ - $11\frac{3}{4}$ $\approx$ 20 - 12 = 8
Exact Calculation:
$19\frac{2}{3}$ - $11\frac{3}{4}$
= $19\frac{2\times4}{3\times4}$ - $11\frac{3\times3}{4\times3}$
(12 is the least common denominator)
= $19\frac{8}{12}$ - $11\frac{9}{12}$
= ($19$ - $11$) + ($\frac{8}{12}$ - $\frac{9}{12}$)
(Solving whole parts separately and fractional parts separately)
= $8$ + $\frac{8 - 9}{12}$
= $8$ + $\frac{-1}{12}$
= $7 + 1$ - $\frac{1}{12}$
= $7$ + $\frac{12}{12}$ - $\frac{1}{12}$
= $7$ + $\frac{12 - 1}{12}$
= $7$ + $\frac{11}{12}$
= $7\frac{11}{12}$
The estimate was 8, so the exact answer of
$7\frac{11}{12}$ is reasonable.
