BODMAS Rule for simple calculations

Question

I was helping my little sister solve a sixth grade math problem which went something like this -

Z = 4 + 3 - 3 + 2 What is the final value of Z ?

In this case , my brain directly jumped to the BODMAS and I did the addition part first. I thus got -

(4+3) - (3+2) = 7 - 5 = 2

I got to know that this answer was WRONG and I had to just follow it through without considering the BODMAS. And the answer would be something like this -

Z = 4 + 3 - 3 + 2 = 7 - 3 + 2 = 4 + 2 = 6

Which obviously gives 6.

This confused me. Is BODMAS a conditional rule ?? When is it used then ? ( Btw it is quite kiddish but I have the doubt anyways )

For example I checked on the net and I got something like this,

To calculate == 5 + 3 * 2 We use the BODMAS here, == 5 + 6 = 11.

Well if I would have just followed it through here I would get 16.

Any clarification about the BODMAS idea please ?? There is clearly a HUGE misconception.

(For god's sake don't downvote my question, please answer if you can)

Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to. — José Carlos Santos, Mar 26 '20 at 08:16
You have done the wrong bracketing in your first calculation i.e., $4+3-3+2 \ne (4+3)-(3+2)$. Rather, $4+3-3+2 = (4+3)-(3-2)$. Hope this helps. — Rick, Mar 26 '20 at 08:21
If you have an expression like $$ Z = 4+3-3+2 $$ you cannot just arbitrarily add parentheses around the terms - or if you do so, you must be very careful! When you changed it to $$ Z = (4+3)-(3+2) $$ you have already made a mistake and changed the value of the expression. Why? Because you have flipped the sign of the last $+2$. Now it's actually $-2$ due to the minus-sign in front of the parentheses. So don't do this. — Matti P., Mar 26 '20 at 08:22
Welcome to Math SE. With your example of $5 + 3 * 2$, note that multiplication has a higher priority than addition. In BODMAS, as shown in BODMAS - What does BODMAS stand for? The Free Dictionary, the priorities are Brackets Order, Division & Multiply, then Add & Subtract. Thus, you do the multiplication before the addition, which is why you get $5 + 6 = 11$, as you noted. In particular, you don't do the addition first, then multiplying, as you indicated where you would then get $(5 + 3) * 2 = 8 * 2 = 16$. — John Omielan, Mar 26 '20 at 08:26
Thanks to everyone who took the time here. It is very clear now what I was doing wrong. — Aurav S Tomar, Mar 26 '20 at 08:54

score 0 · Accepted Answer · answered Mar 26 '20 at 08:20

If you want to compute $4+3-3+2$, since you only have additions and subtrations (which have the same priority level) and there are no parenthesis, you just do\begin{align}\overbrace{4+3}^{\phantom7=7}-3+2&=\overbrace{7-3}^{\phantom4=4}+2\\&=4+2\\&=6.\end{align}Your mistake consisted in adding parenthesis when there were none.

BODMAS Rule for simple calculations

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