Question

Simplify:

\[9\frac{3}{4} \div \left[ 2\frac{1}{6} + \left\{ 4\frac{1}{3} - \left( 1\frac{1}{2} + 1\frac{3}{4} \right) \right\} \right]\]

Answer 1

The given expression

\[= 9\frac{3}{4} \div \left[ 2\frac{1}{6} + \left\{ 4\frac{1}{3} - \left( 1\frac{1}{2} + 1\frac{3}{4} \right) \right\} \right] \]
\[ = \frac{39}{4} \div \left[ \frac{13}{6} + \left\{ \frac{13}{3} - \left( \frac{3}{2} + \frac{7}{4} \right) \right\} \right] \]
\[ = \frac{39}{4} \div \left[ \frac{13}{6} + \left\{ \frac{13}{3} - \left( \frac{6 + 7}{4} \right) \right\} \right] \]
\[ = \frac{39}{4} \div \left[ \frac{13}{6} + \left\{ \frac{13}{3} - \frac{13}{4} \right\} \right] \left(\text{ Removing parentheses }\right)\]
\[ = \frac{39}{4} \div \left[ \frac{13}{6} + \left\{ \frac{52 - 39}{12} \right\} \right] \]
\[ = \frac{39}{4} \div \left[ \frac{13}{6} + \frac{13}{12} \right] \left(\text{ Removing braces }\right)\]
\[ = \frac{39}{4} \div \left[ \frac{26 + 13}{12} \right] \]
\[ = \frac{39}{4} \div \frac{39}{12} (\text{Removing square brackets})\]
\[ = \frac{39}{4} \times \frac{12}{39} = 3 (\text{Removing }' \div ')\]