Evaluate the given expression: (-4) + (-12) ÷ (-6)
-2
Evaluate Negative Integer Arithmetic Expression
This solution provides a step-by-step guide to evaluate the mathematical expression \( (-4) + (-12) \div (-6) \). We will apply the standard order of operations, commonly known as PEMDAS or BODMAS, to ensure the calculation is performed correctly.
Understanding Order of Operations (PEMDAS/BODMAS)
The order of operations dictates the sequence in which mathematical operations should be performed to get a unique and correct result. The acronym PEMDAS stands for:
- Parentheses (or Brackets)
- Exponents (or Orders)
- Multiplication and Division (performed from left to right)
- Addition and Subtraction (performed from left to right)
In our expression \( (-4) + (-12) \div (-6) \), we have addition and division. According to PEMDAS/BODMAS, division takes precedence over addition.
Step 1: Perform Division
First, we address the division part: \( (-12) \div (-6) \).
Recall that dividing a negative number by another negative number results in a positive number.
Calculation: \( \frac{-12}{-6} = 2 \).
After performing the division, the expression simplifies to \( (-4) + 2 \).
Step 2: Perform Addition
Now, we perform the addition: \( (-4) + 2 \).
When adding a positive number to a negative number, we can think of it as moving along the number line. Starting at \( -4 \), we move \( 2 \) units to the right (in the positive direction).
Calculation: \( -4 + 2 = -2 \).
Conclusion: Evaluate Expression Result
By following the order of operations, we have successfully evaluated the expression. The result of \( (-4) + (-12) \div (-6) \) is \( -2 \).
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