The Trap of the Order of Operations: Solving $8 – 8 times 8 + 8$

Every so often, a deceptively simple arithmetic expression pops up on social media, sparking thousands of heated comments, divided opinions, and passionate debates. At first glance, $8 – 8 times 8 + 8$ looks like a harmless second-grade math problem. Yet, it frequently trips up adults and students alike.

So, what is the exact answer, and why do so many people get it wrong? Let’s break it down step by step.

The Verdict Up Front

Before diving into the rules, let’s put the controversy to rest. The correct answer to $8 – 8 times 8 + 8$ is $-48$.

If you arrived at zero or another number, don’t worry—you aren’t alone! Let’s examine how the rules of mathematics lead us directly to $-48$.

The Rulebook: PEMDAS and BODMAS

To evaluate any mathematical expression containing multiple operations, we cannot simply read from left to right like a book. Instead, we rely on a universally accepted standard: the Order of Operations, commonly remembered by acronyms like PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction).

When we apply these rules to our expression, a strict hierarchy emerges:

• Step 1: Multiplication and Division (Left to Right)
  Before we can add or subtract, we must handle multiplication. In our expression, the core multiplication is $8 times 8$.
  $$8 times 8 = 64$$

• Step 2: Substitute Back Into the Equation
  Now that we have evaluated the multiplication, our original expression transforms:
  $$8 – 64 + 8$$

• Step 3: Addition and Subtraction (Left to Right)
  A common misconception is that addition always comes before subtraction because the ‘A’ comes before the ‘S’ in PEMDAS. In reality, addition and subtraction share the exact same priority level and must be evaluated strictly from left to right.

  • First, calculate $8 – 64$:
    $$8 – 64 = -56$$
  • Next, add $8$ to that result:
    $$-56 + 8 = -48$$

Why Do People Get It Wrong?

It is natural to wonder how a simple string of eights can cause so much confusion. The errors typically stem from two common traps:

Trap 1: Reading Left to Right Blindly

If you ignore the order of operations and calculate straight across:

1. $8 – 8 = 0$
2. $0 times 8 = 0$
3. $0 + 8 = 8$

This yields an intuitive but completely incorrect answer of $8$. Multiplication must always take precedence over adjacent addition and subtraction.

Trap 2: The Addition-Before-Subtraction Myth

Some people correctly spot the multiplication ($8 times 8 = 64$), leaving $8 – 64 + 8$. However, if they mistakenly add $64 + 8$ first (treating addition as superior to subtraction), they get $8 – 72 = -64$. Remembering that addition and subtraction are equals evaluated left to right prevents this pitfall.

Conclusion

Mathematics is built on precision and universally agreed-upon conventions. Without the order of operations, mathematical communication would break down, and equations would yield different answers depending on who was reading them.

The expression $8 – 8 times 8 + 8$ serves as a wonderful reminder of why these rules exist—and why a quick double-check using PEMDAS is always a good idea!