Decoding the Order of Operations: What is $8 – 8 times 8 + 8$?
Internet math puzzles love to trick us. On the surface, a string of simple numbers and basic operations looks harmless, but throw them together without parentheses, and social media comment sections instantly erupt into chaos.
Let’s break down the viral expression $8 – 8 times 8 + 8$ step-by-step using PEMDAS to find the definitive answer.
Understanding PEMDAS
Before tackling the problem, let’s review the rulebook. PEMDAS (often remembered as Please Excuse My Dear Aunt Sally) tells us the exact order in which mathematical operations must be evaluated:
- Parentheses (innermost first)
- Exponents (powers and square roots)
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
A common mistake people make is thinking Addition always comes before Subtraction because the ‘A’ comes before ‘S’ in PEMDAS. In reality, multiplication and division share the same priority (evaluated left-to-right), and addition and subtraction also share the same priority (evaluated left-to-right).
Step-by-Step Breakdown
Let’s look at our expression:
$$8 – 8 times 8 + 8$$
Step 1: Handle Multiplication and Division
Scanning the expression from left to right for multiplication or division, we find $8 times 8$.
- $8 times 8 = 64$
Now, substitute that result back into the expression:
$$8 – 64 + 8$$
Step 2: Handle Addition and Subtraction (Left to Right)
Now we are left with only subtraction and addition. Remember the golden rule: evaluate these from left to right, not addition first!
First, perform the subtraction on the left:
- $8 – 64 = -56$
Next, take that result and perform the final addition:
- $-56 + 8 = -48$
The Final Verdict
By strictly following the order of operations, the expression $8 – 8 times 8 + 8$ simplifies step-by-step to:
- $8 – mathbf{64} + 8$
- $mathbf{-56} + 8$
- $-48$
The correct answer is $-48$. Next time you see a tricky math puzzle online, you’ll know exactly how to conquer it!
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