Solving Mathematical Expressions with BODMAS

To solve the given expression, we need to follow the order of operations, commonly known as BODMAS or PEMDAS.

The expression is: \(5.6 - \{2 + 0.6 \text{ of } (2.1 - 2.6 \times 1.12)\}\)

Remember, 'of' means multiplication.

The BODMAS rule dictates the sequence of operations:

• Brackets first (parentheses, curly braces, square brackets)
• Orders (powers and square roots)
• Division and Multiplication (from left to right)
• Addition and Subtraction (from left to right)

Step-by-Step Calculation of the Expression

Let's break down the calculation according to the BODMAS rule.

Step 1: Calculate the innermost bracket

We first evaluate the expression inside the parentheses: \((2.1 - 2.6 \times 1.12)\).

Inside this bracket, we must perform multiplication before subtraction.

Calculate \(2.6 \times 1.12\):

\(2.6 \times 1.12 = 2.912\)

Now, perform the subtraction inside the bracket:

\(2.1 - 2.912\)

\(2.1 - 2.912 = -0.812\)

So the expression becomes: \(5.6 - \{2 + 0.6 \text{ of } (-0.812)\}\)

Or: \(5.6 - \{2 + 0.6 \times (-0.812)\}\)

Step 2: Calculate inside the curly braces

Next, we evaluate the expression inside the curly braces: \(\{2 + 0.6 \times (-0.812)\}\).

Inside the braces, we must perform multiplication before addition.

Calculate \(0.6 \times (-0.812)\):

\(0.6 \times (-0.812) = -0.4872\)

Now, perform the addition inside the braces:

\(2 + (-0.4872)\)

\(2 + (-0.4872) = 2 - 0.4872 = 1.5128\)

So the expression simplifies to: \(5.6 - \{1.5128\}\)

Step 3: Perform the final subtraction

Finally, we perform the subtraction outside the curly braces.

\(5.6 - 1.5128\)

\(5.6 - 1.5128 = 4.0872\)

Final Result of the Expression

The calculated value of the expression \(5.6 - \{2 + 0.6 \text{ of } (2.1 - 2.6 \times 1.12)\}\) is \(4.0872\).

Revision Table: Order of Operations

Additional Information: Decimals and Negative Numbers

When solving expressions involving decimals and negative numbers, it's crucial to pay close attention to the signs and decimal places.

• Multiplying a positive number by a negative number results in a negative number.
• Subtracting a larger number from a smaller number results in a negative number (e.g., \(2.1 - 2.912 = -0.812\)).
• Adding a negative number is the same as subtracting its positive counterpart (e.g., \(2 + (-0.4872) = 2 - 0.4872\)).
• Ensure correct alignment of decimal points during addition and subtraction.
• Count the total number of decimal places in the numbers being multiplied to determine the position of the decimal point in the product.