Evaluating the Expression using BODMAS

The given expression is:

\(3 \div 18 \text{ of } 3 \times 6 - 22 \times 6 \div 18 - 3 \div 2 + 10 - 3 \div 9 \text{ of } 3 \times 9\)

Apply BODMAS. 'Of' is evaluated before division/multiplication.

• \(18 \text{ of } 3 = 54\)
• \(9 \text{ of } 3 = 27\)

Expression becomes:

\(3 \div 54 \times 6 - 22 \times 6 \div 18 - 3 \div 2 + 10 - 3 \div 27 \times 9\)

Evaluate division and multiplication from left to right:

• \(3 \div 54 \times 6 = \frac{1}{18} \times 6 = \frac{1}{3}\)
• \(22 \times 6 \div 18 = 132 \div 18 = \frac{22}{3}\)
• \(3 \div 2 = \frac{3}{2}\)
• \(3 \div 27 \times 9 = \frac{1}{9} \times 9 = 1\)

Expression reduces to:

\(\frac{1}{3} - \frac{22}{3} - \frac{3}{2} + 10 - 1\)

Now perform addition/subtraction from left to right:

• \(\frac{1}{3} - \frac{22}{3} = \frac{-21}{3} = -7\)
• \(-7 - \frac{3}{2} = \frac{-17}{2}\)
• \(\frac{-17}{2} + 10 = \frac{3}{2}\)
• \(\frac{3}{2} - 1 = \frac{1}{2}\)

Hence the value of the expression is \(\frac{1}{2}\).