Simplify Mathematical Expression Using BODMAS Order

Let's simplify the given mathematical expression by following the order of operations, commonly known as BODMAS or PEMDAS.

• Brackets (or Parentheses)
• Orders (or Exponents, roots, etc.)
• Division and Multiplication (from left to right)
• Addition and Subtraction (from left to right)

The expression given is: \(18 \div 3 \text{ of } 2 \times 5 + 72 \div 18 \text{ of } 2 \times 3 - 4 \div 8 \times 2\)

The term "of" indicates multiplication and is typically performed after Brackets and Orders, but before standard Division and Multiplication.

Step-by-Step Calculation of the Expression

Step 1: Evaluate 'of' operations

First, we calculate the parts involving 'of':

• \(3 \text{ of } 2 = 3 \times 2 = 6\)
• \(18 \text{ of } 2 = 18 \times 2 = 36\)

Substitute these values back into the expression:

\(18 \div 6 \times 5 + 72 \div 36 \times 3 - 4 \div 8 \times 2\)

Step 2: Evaluate Division and Multiplication from left to right

Next, we perform all division and multiplication operations from left to right.

For the first part (\(18 \div 6 \times 5\)):

• \(18 \div 6 = 3\)
• \(3 \times 5 = 15\)

For the second part (\(72 \div 36 \times 3\)):

• \(72 \div 36 = 2\)
• \(2 \times 3 = 6\)

For the third part (\(4 \div 8 \times 2\)):

• \(4 \div 8 = \frac{4}{8} = \frac{1}{2}\)
• \(\frac{1}{2} \times 2 = 1\)

Now substitute these results back into the expression:

\(15 + 6 - 1\)

Step 3: Evaluate Addition and Subtraction from left to right

Finally, perform the addition and subtraction operations from left to right.

• \(15 + 6 = 21\)
• \(21 - 1 = 20\)

Final Answer

The simplified value of the expression is 20.

Revision Table: Breakdown of Expression Simplification

Additional Information on 'of' in BODMAS

The term "of" is often used in mathematical expressions and typically implies multiplication, especially in contexts like fractions or percentages of a quantity (e.g., "half of 10", "10% of 200"). When "of" appears alongside division or multiplication symbols in a single expression without brackets separating them, the convention is to evaluate the "of" operation before the standard division and multiplication from left to right.

This priority helps maintain consistency in simplifying expressions. Always remember to handle operations within brackets first, then powers/roots, then 'of', followed by division and multiplication (left to right), and finally addition and subtraction (left to right).