Question
Simplify:$8\frac{5}{6}-3\frac{3}{8}+2\frac{7}{12}$
✓
Answer
We have:$8\frac{5}{6}-3\frac{3}{8}+2\frac{7}{12}$
$=\frac{53}{6}-\frac{27}{8}+\frac{31}{12}$
$\begin{array}{c|c}2&6,8,12\\\hline2&3,4,6\ \\\hline3&3,2,3\ \\\hline2&1,2,1\ \\\hline&1,1,1\ \end{array}$
$L.C.M.$ of $6, 8$ and $12 = (2 \times 2 \times 2 \times 3) = 24$
$=\frac{(212-81+62)}{24}$
$\Big(\frac{24}{6}=4,4\times53=212\Big)$
$\Big(\frac{24}{8}=23,3\times7=81\Big)$ and
$\Big(\frac{24}{12}=2,2\times31=62\Big)$$=\frac{(274-81)}{24}$
$=\frac{193}{24}$
$=8\frac{1}{24}$
$=\frac{53}{6}-\frac{27}{8}+\frac{31}{12}$
$\begin{array}{c|c}2&6,8,12\\\hline2&3,4,6\ \\\hline3&3,2,3\ \\\hline2&1,2,1\ \\\hline&1,1,1\ \end{array}$
$L.C.M.$ of $6, 8$ and $12 = (2 \times 2 \times 2 \times 3) = 24$
$=\frac{(212-81+62)}{24}$
$\Big(\frac{24}{6}=4,4\times53=212\Big)$
$\Big(\frac{24}{8}=23,3\times7=81\Big)$ and
$\Big(\frac{24}{12}=2,2\times31=62\Big)$$=\frac{(274-81)}{24}$
$=\frac{193}{24}$
$=8\frac{1}{24}$
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