Solving Mathematical Expressions: Order of Operations

To solve the given expression, we need to follow the correct order of operations. A commonly used acronym for the order of operations is BODMAS or PEMDAS.

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

Step-by-Step Solution for -4 - (-7 - 12 ÷ 4)

The expression we need to evaluate is: $$-4 - (-7 - 12 \div 4)$$

Step 1: Solve the expression inside the brackets

First, we focus on the part inside the parentheses: $$(-7 - 12 \div 4)$$

Inside the brackets, we have subtraction and division. According to the order of operations (BODMAS/PEMDAS), division comes before subtraction.

Perform the division: $$12 \div 4 = 3$$

Now substitute this value back into the expression inside the brackets:

$$-7 - 3$$

Perform the subtraction inside the brackets:

$$-7 - 3 = -10$$

So, the expression inside the brackets simplifies to $$-10$$.

Step 2: Substitute the result back into the original expression

Now the original expression becomes:

$$-4 - (-10)$$

Step 3: Simplify the expression with the negative sign

Subtracting a negative number is the same as adding the corresponding positive number. So, $$- (-10)$$ is equivalent to $$+ 10$$.

The expression is now:

$$-4 + 10$$

Step 4: Perform the final addition

Finally, perform the addition:

$$-4 + 10 = 6$$

Thus, the value of the expression $$-4 - (-7 - 12 \div 4)$$ is $$6$$.

Summary of Calculation Steps

The final answer is 6.

Revision Table: Key Mathematical Concepts

Additional Information: Understanding Integer Operations

Working with negative numbers is a fundamental part of algebra. It's important to be comfortable with addition, subtraction, multiplication, and division of integers.

• When adding two numbers with the same sign, you add their absolute values and keep the sign. E.g., $$-5 + (-3) = -8$$.
• When adding two numbers with different signs, you subtract the smaller absolute value from the larger absolute value and use the sign of the number with the larger absolute value. E.g., $$-10 + 7 = -3$$.
• Subtracting a number is the same as adding its opposite. E.g., $$5 - 7 = 5 + (-7) = -2$$.
• Multiplying or dividing two numbers with the same sign results in a positive number. E.g., $$-4 \times -5 = 20$$.
• Multiplying or dividing two numbers with different signs results in a negative number. E.g., $$-4 \times 5 = -20$$.

Practicing these basic rules helps in solving more complex expressions and equations.