The error doesn’t stem from a lack of logic, but from forgetting the order of operations (the well-known rule known as PEMDAS or BODMAS ). Our brains naturally tend to read from left to right, which leads to two very common pitfalls:
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The trap of reading directly (from left to right):
Some first calculate $2 – 2 = 0$ , then multiply by $3$ ( $0 \times 3 = 0$ ), and finally add $3$ . They thus find 3 .
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The trap of poorly implemented PEMDAS:
Others remember that addition comes before subtraction in the word PEMDAS and do $3 + 3 = 6$ at the end, getting $2 – 6 = -4$ or other erroneous variations like $2 – (6 + 3) = -7$ .
MathematicsThe step-by-step solution: The absolute rule
Multiplication takes precedence over addition and subtraction. Furthermore, addition and subtraction have the same priority and are performed simply from left to right.
Here is the exact sequence of events:
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Priority to multiplication:
$$2 \times 3 = 6$$The expression then becomes: $2 – 6 + 3$
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From left to right:
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We begin with the subtraction: 2 – 6 = -4
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We finish with the addition: -4 + 3 = -1
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The final, indisputable answer
The correct result is -1 !
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