Order Of Ops: 6-1x0+2÷2=7: Debunking the Myth

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Discussion Overview

The discussion revolves around the evaluation of the mathematical expression 6 - 1 × 0 + 2 ÷ 2, specifically addressing the application of the order of operations (PEMDAS) and the resulting answer, which some participants claim is 7 while others suggest it could be 5.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant initially calculates the expression to be 5 using PEMDAS but is told the answer is 7.
  • Another participant explains the order of operations, stating that multiplication and division should be performed from left to right before addition and subtraction.
  • There is a clarification that addition and subtraction are performed from left to right, and that they are at the same level of precedence.
  • One participant expresses confusion about why addition is not performed before subtraction in this context.
  • A later reply reiterates that subtraction is essentially addition of a negative number, which may contribute to the confusion regarding the order of operations.

Areas of Agreement / Disagreement

Participants express differing views on the correct application of the order of operations, with some asserting the answer is 7 and others suggesting it could be 5. The discussion remains unresolved regarding the final answer.

Contextual Notes

The discussion highlights potential misunderstandings regarding the precedence of operations, particularly the treatment of addition and subtraction as equal in precedence and the left-to-right evaluation rule. There are no bracketing symbols or exponents in the expression, which may affect interpretations.

Rachel1
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6 - 1 × 0 + 2 ÷ 2 =
Hi :) I was hoping someone could explain this equation? Using PEMDAS the answer came to 5 for me but I have been told the correct answer is 7? Why is this?
 
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Re: Simple equation help

I'm not sure why the multiply sign is showing as a different symbol...
 
Re: Simple equation help

Hello and welcom to MHB, Rachel! (Wave)

I've moved your thread here, because our Challenge Questions and Puzzles forum is for presenting problems to the community as a challenge to solve.

I believe your expression is:

$$6-1\times0+2\div2=$$?

First, we carry out the multiplication and division from left to right:

$$6-0+1=$$?

Now we carry out the addition/subtraction from left to right to obtain:

$$7$$

Does that make sense?
 
Re: Simple equation help

Thank you!
 
Re: Simple equation help

When using PEMDAS it states that addition comes before subtraction.
Why is it that the 0 + 1 is not done first and then finally the 6 - 1 ?
That's the part that confuses me lol
 
Re: Simple equation help

Rachel said:
When using PEMDAS it states that addition comes before subtraction.
Why is it that the 0 + 1 is not done first and then finally the 6 - 1 ?
That's the part that confuses me lol

Addition and subtraction are at the same level, and are done from left to right. Subtraction is really just the addition of a negative number, much like division is just multiplication by the reciprocal (multiplicative inverse). :D

So, in an expression like you posted, where there are no bracketing symbols (parentheses, etc.) and no exponents, we first do the multiplication/division from let to right, then we do the addition/subtraction from left to right. Multiplication and division have the same precedence as do addition and subtraction. :D
 
Re: Simple equation help

Oh ok cool, that makes sense.Thank you so much for explaining!
 

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