Answer
Estimated answer = 13
Exact answer = $12\frac{19}{20}$
Work Step by Step
$18\frac{3}{4}$ - $5\frac{4}{5}$
Estimation:
$18\frac{3}{4} \approx 19$
$5\frac{4}{5} \approx 6$
Therefore
$18\frac{3}{4}$ - $5\frac{4}{5}$ $\approx$ 19 - 6 = 13
Exact Calculation:
$18\frac{3}{4}$ - $5\frac{4}{5}$
= $18\frac{3\times5}{4\times5}$ - $5\frac{4\times4}{5\times4}$
(20 is the least common denominator)
= $18\frac{15}{20}$ - $5\frac{16}{20}$
= $18$ + $\frac{15}{20}$ - ($5$ + $\frac{16}{20})$
= $18$ + $\frac{15}{20}$ - $5$ - $\frac{16}{20}$
= ($18$ - $5$) + ($\frac{15}{20}$ - $\frac{16}{20}$)
(Solving whole parts separately and fractional parts separately)
= $13$ + $\frac{15 - 16}{20}$
= $13$ + $\frac{-1}{20}$
= $12 + 1$ - $\frac{1}{20}$
= $12$ + $\frac{20}{20}$ - $\frac{1}{20}$
= $12$ + $\frac{20 - 1}{20}$
= $12$ + $\frac{19}{20}$
= $12\frac{19}{20}$
The estimate was 13, so the exact answer of
$12\frac{19}{20}$ is reasonable.
