Evaluating the Mathematical Expression Using BODMAS

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

• B/P: Brackets (Parentheses)
• O/E: Orders (Exponents, roots)
• D/M: Division and Multiplication (from left to right)
• A/S: Addition and Subtraction (from left to right)

The given expression is: \(3 - (- 6)\{- 2 - 9 - 3\} \div 7\{1 + (- 2)(- 1)\}\)

Step-by-Step Evaluation of the Expression

Step 1: Evaluate expressions inside the curly braces {}

First curly brace: \(\{- 2 - 9 - 3\}\)

• \( -2 - 9 = -11 \)
• \( -11 - 3 = -14 \)

So, \(\{- 2 - 9 - 3\} = -14\).

Second curly brace: \(\{1 + (- 2)(- 1)\}\)

• Perform the multiplication inside: \( (-2)(-1) = 2 \)
• Perform the addition: \( 1 + 2 = 3 \)

So, \(\{1 + (- 2)(- 1)\} = 3\).

Substituting these values back into the expression, we get:

\(3 - (- 6)\{-14\} \div 7\{3\}\)

This can be written as:

\(3 - [(- 6) \times (-14)] \div [7 \times 3]\)

Step 2: Evaluate the multiplications that form the terms for division

Left multiplication: \( (- 6) \times (-14) \)

• \( (-6) \times (-14) = 84 \) (Product of two negative numbers is positive)

Right multiplication: \( 7 \times 3 \)

• \( 7 \times 3 = 21 \)

Substituting these values back into the expression, we get:

\(3 - 84 \div 21\)

Step 3: Perform the division

According to BODMAS, division is performed before subtraction.

\( 84 \div 21 = 4 \)

Substituting this value back into the expression, we get:

\(3 - 4\)

Step 4: Perform the subtraction

\( 3 - 4 = -1 \)

Final Value of the Expression

The value of the given expression \(3 - (- 6)\{- 2 - 9 - 3\} \div 7\{1 + (- 2)(- 1)\}\) is \( -1 \).

Revision Table: Key Concepts

Additional Information: Understanding Order of Operations

The order of operations is crucial for consistently evaluating mathematical expressions. Without a standard order, the same expression could yield different results depending on which operation is performed first. The BODMAS/PEMDAS rule ensures that everyone arrives at the same correct answer.

Remember to work from left to right when you encounter operations at the same level, such as division and multiplication, or addition and subtraction.

Negative numbers play a significant role in this expression. Pay close attention to the rules for arithmetic with negative numbers, especially when multiplying or dividing.