basics first

okay. let's first review what we were being taught in school in doing the famous four operations; + - x /. during those time, i thought that BODMAS is the proper way of doing the four operations. the fact is...it is misleading IF we are not familiar with number concepts. we were taught - do the brackets first, then division, then multiply, then addition and lastly we must do the subtraction. this is very incorrect.

the proper way of viewing order of these operations is, yes we must do the brackets first, then either division OR multiplication, and either subtraction OR addition comes last, doing the ones that comes first from the left of the expression.

1. BRACKETS
2. DIVISION OR MULTIPLICATION
3. ADDITION OR SUBTRACTION

take a look at this example. 10 - 3 + 5. looks simple? personally, i don't think so. one time (last year if i'm not mistaken) i gave this question to my form 1 (year 7) students, and out of 24 students, only 2 got it right. what was their response?

10 - 3 + 5
= 10 - 8
= 2

can you spot what is wrong?

some people thought this is funny, but believe it or not, i did try giving this same question to my form 3 students (year 9) and form 5 students (year 11) from my tutorial school, and yes some of them still got this wrong. the response? as shown above.

so, how did they end up having this as their answer? BODMAS!!! According to this system, we must do addition first, so they added 3 to 5 to get 8, then they do the subtraction to obtain 2 as their answer. I am not saying they are wrong, this is what they called misconception.

if you are very familiar with directed numbers, even if you follow the BODMAS system, you will get the correct answer. why?

10 - 3 + 5

[by directed numbers, we MUST take note of the sign in front of the number. in this case, 3 is not a positive number. instead, it is a NEGATIVE number. so we have - 3 + 5 to obtain 2.]

= 10 + 2
= 12 ans.

we will obtain the same answer if we follow the order of operations properly, i.e. addition OR subtraction, which comes first from the left should be done first. in this case, subtraction comes first, so we do them first.

10 - 3 + 5
= 7 + 5
= 12 ans.

And this morning, i purposely gave the question below to my form 4 students. believe me, out of a total of about 60 students from 3 different classes, only about 20 of them got it right. the question?

7 - 2 x 3 - 2

what is your answer? drop them in the message board and see if you got it right. of course, no calculator. hehe...cheers