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Difficulty: Very hardSimplification and BODMAS Rule
What is the numerical value of the following mathematical expression evaluated using the BODMAS rule?
12.5% of 480−[334÷{1.25+12 of (3.6−1.8−0.7‾)}]×81512.5\% \text{ of } 480 - \left[ 3 \frac{3}{4} \div \left\{ 1.25 + \frac{1}{2} \text{ of } \left( 3.6 - \overline{1.8 - 0.7} \right) \right\} \right] \times \frac{8}{15}

Answer: 59.2

Answer

The evaluated numerical value of the expression is 59.2.
Following strict BODMAS hierarchy—evaluating the vinculum (1.1), parentheses (2.5), 'of' operation (1.25), curly brackets (2.5), square bracket division (1.5), multiplication (0.8), percentage term (60), and final subtraction—gives 60 - 0.8 = 59.2.

Step-by-Step Solution

1
Evaluate the expression under the vinculum bar.
1.8 - 0.7 = 1.1
The vinculum has the highest priority and acts as an implicit innermost bracket.
2
Evaluate the terms inside the round brackets (parentheses).
3.6 - 1.1 = 2.5
Round brackets must be resolved after the vinculum.
3
Evaluate the 'of' operation inside the curly brackets.
(1/2) * 2.5 = 1.25
'Of' precedes addition and multiplication in the standard BODMAS order.
4
Complete the addition within the curly brackets.
1.25 + 1.25 = 2.5 = 5/2
Brackets must be fully simplified from inside out.
5
Perform division inside the square brackets.
(15/4) / (5/2) = (15/4) * (2/5) = 3/2 = 1.5
Square brackets are evaluated after inner curly brackets.
6
Multiply the square bracket result by 8/15.
1.5 * (8/15) = (3/2) * (8/15) = 4/5 = 0.8
Multiplication takes precedence over final subtraction.
7
Calculate the initial percentage 'of' term.
12.5% of 480 = 0.125 * 480 = 60
'Of' operation on percentage takes precedence before subtraction.
8
Subtract the bracketed product from the initial term.
60 - 0.8 = 59.2
Subtraction is performed last according to BODMAS.

Key Concept

BODMAS Order of Operations with Vinculum and Nested Brackets
Estimated Time:2m 0s
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Topics

Simplification and BODMAS Rule

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