Answer
Estimated answer = 11
Exact answer = $10\frac{23}{24}$
Work Step by Step
$14\frac{5}{8}$ - $3\frac{2}{3}$
Estimation:
$14\frac{5}{8} \approx 15$
$3\frac{2}{3} \approx 4$
Therefore
$14\frac{5}{8}$ - $3\frac{2}{3}$ $\approx$ 15 - 4 = 11
Exact Calculation:
$14\frac{5}{8}$ - $3\frac{2}{3}$
= $14\frac{5\times3}{8\times3}$ - $3\frac{2\times8}{3\times8}$
(24 is the least common denominator)
= $14\frac{15}{24}$ - $3\frac{16}{24}$
= $14$ + $\frac{15}{24}$ - ($3$ + $\frac{16}{24})$
= $14$ + $\frac{15}{24}$ - $3$ - $\frac{16}{24}$
= ($14$ - $3$) + ($\frac{15}{24}$ - $\frac{16}{24}$)
(Solving whole parts separately and fractional parts separately)
= $11$ + $\frac{15 - 16}{24}$
= $11$ + $\frac{-1}{24}$
= $10 + 1$ - $\frac{1}{24}$
= $10$ + $\frac{24}{24}$ - $\frac{1}{24}$
= $10$ + $\frac{24 - 1}{24}$
= $10$ + $\frac{23}{24}$
= $10\frac{23}{24}$
The estimate was 11, so the exact answer of
$10\frac{23}{24}$ is reasonable.
