# Order of operations (BODMAS)

$$40-20/2+15\times1.5\\\hspace{.1in}\\40-20/2+15\times1.5=\\ 40-10+22.5=7.5$$

I'm studying and this is from an example.

In BODMAS, aren't addition and subtraction have same level?

So, in the 3rd line, it should be from left to right, correct?

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The last equation is quite wrong, should be $52.5$. –  Gerry Myerson May 19 '13 at 0:51
Yeah, that's what I think too. I'm actually preparing for an apt exam and I was given some review notes. –  Stalker ka NOOB May 19 '13 at 0:54
Rearrange the $3^{\text{rd}}$ line to $40+22.5-10$ and then apply BODMAS rule. –  Maazul May 19 '13 at 0:56
Rolled back; this version is true to the original image. –  Douglas S. Stones May 19 '13 at 1:02
A relevant video appeared in minutephysics –  Vijay Murthy May 19 '13 at 8:14

$$40-10+22.5=52.5$$

You're correct, subtraction and addition have the same level of priority, so when both exist, then you operate from left to right. You are entirely correct about that. If you were puzzled when you saw the "answer" $\,7.5$, good for you, since $\;\;40-10+22.5\neq 7.5!$

Now, note: $$40-(10+22.5)=7.5$$

because operations in "brackets" (or parentheses) have greatest priority.

So let's be forgiving: perhaps the author of the problem statement/review notes forgot parentheses!

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Yeah.. perhaps. I am just paranoid so I posted it. lol –  Stalker ka NOOB May 19 '13 at 1:26
Gets a $\cos^2 x + \sin^2 x$! –  Amzoti May 19 '13 at 1:30
@Stalker: I know exactly what you mean. I myself have a chronic habit of second-guessing myself! –  amWhy May 19 '13 at 1:31

I think you have your answer but still I want to clear this thing to you. $$40-10+22.5$$ you are writing it as $40-(10+22.5)$ but if you try to remove this you will get $40-10-22.5$ which is not same as previous line so if you want to do add and subtraction in a line (they have same priority) you can think as $10$ and $22.5$ have opposite sign so we write their difference and put the sign of bigger number to the difference so here we get

$-10+22.5=12.5$

then we solve this

$40+12.5=52.5$

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"The claim is that the error was not by OP, but was contained in notes given to OP" –  amWhy May 19 '13 at 1:24
@amWhy yeah that's good but I just want clear that thing completely –  iostream007 May 19 '13 at 1:26
Actually, this is an example from the review notes I received. I did not write it. –  Stalker ka NOOB May 19 '13 at 1:27
@StalkerkaNOOB means you knew that there is an error in solution and you just checked it with other am I right? –  iostream007 May 19 '13 at 1:29
@iostream007 Yes. Actually, I've been preparing for the exam for days now and tried to answer the examples by myself and if I got it wrong I google it for step by step explanation or post it here. –  Stalker ka NOOB May 19 '13 at 1:39

$\boxed{40-20/2+15\times1.5}$

Using brackets we can remove ambiguity:

$40+(-20/2)+(15\times1.5)$

$=40+(-10)+(22.5)$

$=(40+22.5)+(-10)$

$=62.5-10$

$=52.5$

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The example is incorrect under BODMAS, but typically, people use a different set of rules, to the effect of creating implied brackets.

• Brackets unchanged
• Of (ie functions) unchanged.
• M Multiplication of close-fit numbers.
• D If there is a horizontal fraction, then this is evaluated first. For example, $/$ only is evaluated here.
• MD Multiplication and division are evaluated equally when set with equal-height signs. This is a different division $\div$. So $120/2 \div 60/2=2$ means 60/30, but $120 \div 2 \div 60 \div 2=0.5$. This is a product of numbers, where $\div$ is read as a unitary inverse. Rather like AS, really.
• AS addition and subtraction are equally evaluated, as if the sign were attached to the number, when set with equal-height signs. eg 5-2+3 = 6

Here is an example of how this works.

$F = c/4\pi þ^2 * M^2/R^2$

In this equation, the multiplication represented by * is a lower operation (MD) then the multiplications represented by {4\pi þ^2}. That is we see this as this, with the close-fit or inner multiplication, being developed done before the division /. In turn, once these are evaluated, the product occurs from left to right in the manner of computers.

$F = (c/(4\pi þ^2)) * (M^2/R^2) = c/4/\pi \ þ^2 * M^2 / R^2$

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It's worth noting that blanks break up the "close-fit" numbers that have priority over "/". Thus, "1/2π" would be "1/(2π)", but "1/2 π" would more likely be read as "(1/2)π" [parentheses should be used if there's any possibility that spaces may be misjudged]. –  supercat Mar 4 '14 at 21:19

As @GerryMyerson noted, there was indeed an error. The last two terms were grouped, which changed the expression to $40 - (10 + 22.5)$, which is entirely different from the correct expression. This is equivalent to $40 + (-1)(10 + 22.5)$, or $40 - 10 - 22.5$. Note how the second plus sign has become a minus sign.

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The claim is the the error was not by OP, but was contained in notes given to OP. –  Gerry Myerson May 19 '13 at 0:58
I have fixed this. –  Lee Sleek May 19 '13 at 1:09
You're still suggesting that OP grouped the last two terms, where OP claims to be presenting the work as OP received it. –  Gerry Myerson May 19 '13 at 1:54
I have fixed this. –  Lee Sleek May 19 '13 at 15:27

You can type this BODMAS mathematical expressions in http://www.careerbless.com/calculators/ScientificCalculator/ and click on solve and see how these are processed

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