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'''6÷2(1+2)=?''' is the pre-algebra question that a majority of many Internet respondents seem to get wrong. If you are in the camp that knows the correct answer is 1, read no further. If you believe the answer is 9, you should probably review this document -- {{highlight|there is only one number that 6 can be divided by to result in 9, and that number is 2/3.}}

We substitute x for 2(1+2) from the given equationand backtest the equation with the result of 9:

there is a Common Denominator common divisor of 3 so we reduce the fraction...

Now we compare the value given in the equation to the value we find found (above) for x.

<p style="text-align:center;"> {{highlight|Without fail, 2(1+2) will always equal (2*1 + 2*2), this is the '''Distributive Law.'''}}</p>

''Encyclopedia Britannica'' on parenthetical expressions:

In the majority of incorrect proofs the respondent will cite PEMDAS or BODMAS, we all agree that parenthesis parentheses or brackets are processed first. However, these solvers some respondents incorrectly resolve the [P]arenthesis arentheses or [B]rackets of PEMDAS - BODMAS. For , for some reason, these solvers believe that they can resolve within the parenthesisparentheses, but ignore neglect to multiply the adjacent and dependent coefficient.

=== Parenthetical expressions Parentheses ===

6÷2(1+2) has two EXPLICIT operators, division and addition. However, IMPLIED multiplication tells us to IMPLICITLY multiply (, [2 * (2+1))], normally in the P step of PEMDAS. Then in In the division step, we must apply division to the (entire) implicitly connected termparenthetical expression. We cannot apply division to the coefficient (2) and then not apply division to the factor (2+1). '''Incorrect:''' (''because division is not EXPLICITLY applied to the entire parenthetical expression'')<div style="color:red;"><div style="width:60px; text-align:center; float:left;">6 ---- 2 </div><div style="width:60px; text-align:center; float:left;"><br/><nowiki>*</nowiki><br/></div>

'''Incorrect:''' (''because division is not EXPLICITLY applied to (1+2) '')<div style="width:200px60px; text-align:center; float:left; color:red;">::6 <br/>:--------- * (2+1+2)::2 <br/>

<div style="color:green;"><div style="width:200px60px; text-align:center; float:left; color:green;">6 ---- 1 </div><div style="width:60px; text-align:6 &nbspcenter;&nbspfloat:left;&nbsp"><br/>÷<br/></div> <div style="width:60px;&nbsptext-align:center;&nbsp;&nbsp;&nbsp;&nbspfloat:left;">2(1+2) :--------- ÷ ---------1 </div> <div style="width:60px; text-align:2 &nbspcenter;&nbspfloat:left;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1"><br/>=<br/>

'''Correct:''' (''For multiplication, inverting the denominator will maintain its value.'') <div style="width:200px60px; text-align:center; float:left; color:green;">::6 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2 * (1+2) :--------- 6 * ---------1 </div>::2 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (1+2)</div>

'''SolutionTraditional solution:'''

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1*(1+2)

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If we insist on a left to right solution, ignoring both PEMDAS and the Distributive Law, we can do this with by expressing the Least Common Denominator rulecommon divisor first. However, division is sustained and must be applied to everything to the right of the explicit division operator.

When we reduce by the common denominatordivisor, this does not complete the division operation, division it simply reduces the coefficient to one. Division must be applied to both the factor and the coefficientof the parenthetical expression. Division  ==The equation is not ambiguous =====6÷2(1+2) is sustained not equal to 6÷2*(1+2)===Standing alone, 6 will always equal 6 and 2(1+2) will also always equal 6, so dividing these two terms will always equal 1.  We would not write 2(a+b) as (2(a+b)), nor can we re-write the given equation as 6÷2*(a+b) and must be applied maintain the same value. We can however, rewrite the full equation to everything include an explicit multiplier if we take care to maintain the parenthetical expression with additional bracketing 6÷(2*(a+b)). === Obelus ===Granted, the [https://web.archive.org/web/20210417145938/https://www.wyzant.com/resources/blogs/14831/the_obelus_for_division obelus (÷)] is an archaic symbol for division, it visually represents a fraction with one dot being the numerator and the other being the right of denominator. Computers use the explicit forward slash for division operatorbecause the standard keyboard does not have an obelus key.  For those who claim that the obelus is outdated, why then is it present on virtually every modern calculator?

Entering the equation into a programming language, or low quality calculator, requires the explicit multiplication symbol and outer parenthesis to maintain value of the groupingparenthetical expression.

Other calculators, including Google and Wolfram will simply strip the parenthesis and solve a different equation, 6÷2*3. This is because within the programming, the open parenthesis (bracketing) triggers a different function within the programming, an open parenthesis tells the compiler to find the innermost parenthesized term and work outwards. Thus , to get the correct answer from inferior calculators , the input must be formalized with correct bracketing. I.e. 6÷(2*(1+2))