Question

Simplify.$1\frac{7}{12}+8\frac{5}{9}-4\frac{5}{6}-2\frac{1}{18}$

Answer 1

Simplify the terms $1\frac{7}{12}+8\frac{5}{9}-4\frac{5}{6}-2\frac{1}{18}$

$1\frac{7}{12}+8\frac{5}{9}-4\frac{5}{6}-2\frac{1}{18}=\frac{1\times 12+7}{12}+\frac{8\times 9+5}{9}-\frac{2\times 18+1}{18}$

$\mathrm{}$$$\begin{gathered} =\frac{12+7}{12}+\frac{72+5}{9}-\frac{24+5}{6}-\frac{36+1}{18} \\ =\frac{19}{12}+\frac{77}{9}-\frac{29}{6}-\frac{37}{18} \\ =\frac{19\times 6}{12\times 6}+\frac{77\times 8}{9\times 8}-\frac{29\times 12}{6\times 12}-\frac{37\times 4}{18\times 4} \\ =\frac{114}{72}+\frac{616}{72}-\frac{348}{72}-\frac{148}{72} \\ =\frac{114+616-348-148}{72} \\ =\frac{730-496}{72} \\ =\frac{234}{72} \\ =\frac{13}{4} \\ =3\frac{1}{4} \end{gathered}$$

$\therefore$$1\frac{7}{12}+8\frac{5}{9}-4\frac{5}{6}-2\frac{1}{18}=3\frac{1}{4}$