The value of 3 ÷ 18 of 3 × 6 - 22 × 6 ÷ 18 - 3 ÷ 2 + 10 - 3 ÷ 9 of 3 × 9 is
1/2
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 \(\frac{1}{2}\).
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