Evaluating Mathematical Expressions Using Order of Operations

To find the value of the given expression, we need to follow the order of operations. The standard rule for the order of operations is often remembered by the acronyms BODMAS or PEMDAS.

• BODMAS: Brackets, Orders (powers and square roots), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
• PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Let's break down the expression: \(1800 \div 20 \times \{(12 - 6) + (24 - 12)\}\)

Applying the Order of Operations (BODMAS/PEMDAS)

Step 1: Solve the operations inside the innermost parentheses/brackets.

The innermost brackets are \((12 - 6)\) and \((24 - 12)\).

• Calculate \(12 - 6\):

  \(12 - 6 = 6\)

• Calculate \(24 - 12\):

  \(24 - 12 = 12\)

Now substitute these values back into the expression:

\(1800 \div 20 \times \{6 + 12\}\)

Step 2: Solve the operations inside the curly braces.

The expression inside the curly braces is \(\{6 + 12\}\).

• Calculate \(6 + 12\):

  \(6 + 12 = 18\)

Substitute this value back into the expression:

\(1800 \div 20 \times 18\)

Step 3: Perform Division and Multiplication from left to right.

Now we have division and multiplication. We perform them in the order they appear from left to right.

• Perform the division first: \(1800 \div 20\):

  \(1800 \div 20 = 90\)

The expression becomes:

\(90 \times 18\)

• Perform the multiplication: \(90 \times 18\):

  \(90 \times 18\)

  We can calculate this as \(9 \times 18 \times 10\).

  \(9 \times 18 = 162\)

  \(162 \times 10 = 1620\)

So, the value of the expression is \(1620\).

Summary of steps:

The final value of the expression \(1800 \div 20 \times \{(12 - 6) + (24 - 12)\}\) is \(1620\).

Revision Table: Order of Operations

Understanding the hierarchy of mathematical operations is crucial for correctly solving expressions.

Additional Information on Evaluating Expressions

When evaluating complex mathematical expressions, always remember to follow the order of operations consistently. Making a mistake in the order can lead to a completely different and incorrect answer. This rule ensures that everyone gets the same result when evaluating the same expression.

For example, in the expression \(1800 \div 20 \times 18\), if we performed multiplication before division (incorrectly), we would get:

• \(20 \times 18 = 360\)
• \(1800 \div 360 = 5\)

This result (5) is different from the correct result (1620), highlighting the importance of the left-to-right rule for operations at the same level (multiplication and division, or addition and subtraction).