What is the value of $3-3\times 6+2$?

Question

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.

You are correct. Your brother's calculation is for $3-3\times 6-2$ whereas he should be doing $3-3\times 6+2$ — Arkady, Feb 19 '16 at 22:11
Gregory, the format of my question isn't how I wanted it to be. My apologies. There should be a line breakers after the first -18 in my calculation. Yes the question is from Facebook, not that this is relevant in the slightest. Could someone please be kind enough to explain why we use the -3? I don't know why but I just used it as it seemed to look right to me. I guess you could say I was 'winging it' but clarification as to why we use the - would be fantastic. — R Alqo, Feb 19 '16 at 22:15
$3-3(6)+2=3-18+2$ the answer depends on where you will put the parentheses next. You could say $(3-18)+2=(-15)+2=-13$ or you could say $3-(18+2)=3-(20)=-17$, I think that computers do it from left to right, but it all depends on where you put your parentheses. — GuPe, Feb 19 '16 at 22:17
As some evidence for $-13$ , if you simply cut and paste your formula into wolfram alpha you get $-13$. If you cut and paste it into Excel, it first asks if you meant $3*6$ instead of $3x6$ and when you agree it also returns $-13$. — lulu, Feb 19 '16 at 22:19
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? — R Alqo, Feb 19 '16 at 22:22
@PhillipHamilton how does it being from facebook make it a problem? Maybe they saw it on there and it was what started the discussion — Quality, Feb 19 '16 at 22:37
Dear @Emilio: thanks for carefully editing the formulas here. I wonder if you have noticed the title of the post... — , Feb 20 '16 at 00:06

score 3 · Answer 1 · answered Feb 19 '16 at 22:25

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.

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 — R Alqo, Feb 19 '16 at 22:29

score 0 · Accepted Answer · answered Feb 19 '16 at 22:30

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 $-15+2=-13$

score 0 · Answer 3 · answered Feb 19 '16 at 22:35

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 $((3-(3\times 6))+2 =-13.$

score 0 · Answer 4 · answered Feb 21 '16 at 16:51

0

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.

answered Feb 21 '16 at 16:51

paulharvey

11

This does not answer the question – Shailesh Feb 21 '16 at 16:57
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. – paulharvey Feb 21 '16 at 22:59

score 0 · Answer 5 · answered Feb 21 '16 at 16:59

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.

What is the value of $3-3\times 6+2$?

5 Answers5