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Please could someone help me and my brother settle our dispute?

We have been looking at the following equation: $$3-3\times 6+2=$$

This may look familiar but I have yet to find a fully conclusive explanation. We are both using BODMAS, might I add. My answer to this is $-13$, my calculation is as follows: $$-3\times 6=-18$$ $$-18+2=-16$$ Which then leaves us with $3-16=-13$

That is how I worked this out and I'm not sure if it's correct but nearly every other website I have viewed has also come to the same conclusion as me. A lot of these other sites were also mathematics websites.

My brother has come to the conclusion that the answer is $-17$. He worked this put by the following calculation:

$$3\times 6=18$$ $$18+2=20$$ $$3-20=-17$$

Please inform us of which is the correct answer, and I would be very grateful if you could provide us with an explanation.

If the answer is $-13$ then why do we use the $-3$ instead of the $3$?

All info would be greatly appreciated.

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  • $\begingroup$ $-18-18+2=-34$ not $-16$. $\endgroup$ Feb 19, 2016 at 22:10
  • $\begingroup$ You are correct. Your brother's calculation is for $3-3\times 6-2$ whereas he should be doing $3-3\times 6+2$ $\endgroup$
    – Arkady
    Feb 19, 2016 at 22:11
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    $\begingroup$ Because it's from Facebook $\endgroup$ Feb 19, 2016 at 22:15
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    $\begingroup$ This may be a ridiculous question but do we have to use parentheses? Can we not get a conclusive answer just as it is written? If we can choose where to put the parentheses then does this not make this all subjective and without one single answer? $\endgroup$
    – R Alqo
    Feb 19, 2016 at 22:22
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    $\begingroup$ @PhillipHamilton how does it being from facebook make it a problem? Maybe they saw it on there and it was what started the discussion $\endgroup$
    – Quality
    Feb 19, 2016 at 22:37

5 Answers 5

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Your answer is right. Your brother's is wrong.

$3 - 3*6+2 = $

$3 - 18 + 2 = $

You both agree on this much right?

Your brother's mistake happens here:

$3 - 20$

He's not following bedmas here because he's not working from left to right.

Left to right, we'd calculate 3-18 first, so we get:

$-15+2$

$-13$

Remember in BEDMAS.... the DM (divide multiply) is together...and should be done left to right. So if division appears first you divide first. If a multiplication appears before a division, you multiply first then divide.

Similarly AS (addition,subtraction) is together and should be done left to right in order of appearance. So if a subtraction appears first you should subtract first. If an addition appears first you add first.

ie: DM doesn't mean divide before multiply. AS doesn't mean addition before subtraction. DM and AS are together.

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    $\begingroup$ Ameet Sharma. Thank you so much. You couldn't have answered in a clearer way before us. You have provided everything I asked for. Once again, thank you for answering my question. Also, may I thank everyone else for their input and for their answers too. You have all been a great help $\endgroup$
    – R Alqo
    Feb 19, 2016 at 22:29
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The dispute came from the presence of the minus sign in the expression $3-3 \times 6 +2$. The correct interpretation is that a minus sign means the sum of the opposite of the term that follows, so, in this case we have to learn: $$ 3+(-(3\times6))+2 $$ now, since $3 \times 6=18$, its opposite is $-(3\times6)=-18$ and the sum becomes $3+(-18)+2$. Now we can use associativity and compute $3+(-18)=-15$ than $-15+2=-13$

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There is an agreed convention that, in the absence of brackets, $\times $ and $/$ (division) are done first, in left-to-right order, followed by $+$ and $-$, from left to right.This is a convenience, to reduce the amount of brackets that are needed. Expressions enclosed in brackets are to evaluated within the brackets before combining them with anything outside the brackets. Without the convention we would need to write $((3-(3\times 6))+2 =-13.$

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BODMAS simply stands for brackets, order, division, multiplication, addition, subtraction. The natural implication is that addition comes before subtraction but this is not correct.

As pointed out in previous answers, addition and subtraction should simply be carried out left to right. This key point is seldom taught or remembered.

BODMAS should never be employed as an instruction technique since it does more harm than good.

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  • $\begingroup$ This does not answer the question $\endgroup$
    – Shailesh
    Feb 21, 2016 at 16:57
  • $\begingroup$ The question has already been answered above. Carry out the multiplication first and then work left to right to complete the addition/subtraction. This gives the correct answer of -13. $\endgroup$
    – paulharvey
    Feb 21, 2016 at 22:59
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The only "dispute" arises because of a choice of order in which to perform the operations. You chose one order and your brother chose another : it happens to be the case that the order you performed the operations is the "standard" one. My own view is that it is better to include the brackets in such an expression, so that any necessity for a decision about order is removed.

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