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

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In summary, the equation 6 - 1 × 0 + 2 ÷ 2 = has a correct answer of 7, not 5 as initially thought. This is because, according to the PEMDAS order of operations, we first carry out the multiplication and division from left to right, resulting in 6 - 0 + 1 = ? Next, we do the addition and subtraction from left to right, giving us a final answer of 7. The symbols for multiplication and division may appear differently, but they still follow the same rules of precedence.
  • #1
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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  • #2
Re: Simple equation help

I'm not sure why the multiply sign is showing as a different symbol...
 
  • #3
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:

\(\displaystyle 6-1\times0+2\div2=\)?

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

\(\displaystyle 6-0+1=\)?

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

\(\displaystyle 7\)

Does that make sense?
 
  • #4
Re: Simple equation help

Thank you!
 
  • #5
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
 
  • #6
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
 
  • #7
Re: Simple equation help

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

1. What is the correct order of operations when solving an equation like 6-1x0+2÷2=7?

The correct order of operations, also known as PEMDAS, is to first solve any parentheses or brackets, then exponents, followed by multiplication and division from left to right, and finally addition and subtraction from left to right.

2. Why does the equation 6-1x0+2÷2=7 appear to have two different answers?

This equation appears to have two different answers because of a common misconception about the order of operations. Many people incorrectly assume that multiplication should always be performed before division, leading them to solve the equation as 6-1x0+1=7. However, according to the correct order of operations, division should be performed before multiplication, resulting in the correct answer of 6-0+1=7.

3. Can the equation 6-1x0+2÷2=7 be solved using a calculator?

Yes, this equation can be solved using a calculator as long as the calculator follows the correct order of operations. Most modern calculators are programmed to follow the order of operations, but it is always important to double check and use parentheses if necessary to ensure the correct answer.

4. Is there any situation where the order of operations would not apply?

In most mathematical equations, the order of operations must be followed to arrive at the correct answer. However, there are some specific cases, such as when using scientific notation or calculating with matrices, where the order of operations may differ slightly. In these cases, it is important to follow the specific rules for those operations.

5. How can understanding the order of operations help me in my everyday life?

Understanding the order of operations is an essential skill in many areas of life, such as cooking, budgeting, and organizing tasks. It allows us to perform multiple calculations in the correct order, leading to accurate results. It also helps us to solve problems efficiently and effectively, making it a valuable skill in both academic and real-world settings.

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