Solving equations

[JeffM]

I = indices, exponents, powers.

Please advise what is the correct order of using BEDMAS

Regards

Prob

At least in the US, "index" is not s synonym of "exponent" or "power." Actually, I doubt that it is in any English-speaking country, but I may be in error.

The WHOLE point of the acronym BEDMAS is to give you the proper order.

First, you do everything inside brackets or parentheses, working from the inside out if they are nested. So B for "brackets" comes first.

Second, you do all exponentiation proceeding from left to right. So E for "exponentiation" comes second.

Third, you do all division proceeding from left to right. So D for "division" comes third.

Fourth. you do all multiplication proceeding from left to right. So M for "multiplication" comes fourth.

Fifth, you do all addition proceeding from left to right. So A for "addition" comes fifth.

Sixth, you do all subtraction proceeding from left to right. So S for "subtraction" comes sixth.

then working down the list 5/4 by division before adding or subtracting = wrong answers.

Notice that \(\displaystyle \dfrac{-1 - 5}{4} = (- 1 - 5) / 4.\)

When you have fractions, numerators and denominators are not covered by BEMDAS. To use BEMDAS, you have to put everything into the format
using brackets, ^, /, *, +, and -. This was your problem at the very first when you did not put your fraction into proper form by using grouping symbols (parentheses or brackets.) Another way to say the same thing is to treat the numerator and the denominator of each fraction as though they were surrounded with grouping symbols.

 

[Probability]

At least in the US, "index" is not s synonym of "exponent" or "power." Actually, I doubt that it is in any English-speaking country, but I may be in error.

The WHOLE point of the acronym BEDMAS is to give you the proper order.

First, you do everything inside brackets or parentheses, working from the inside out if they are nested. So B for "brackets" comes first.

Second, you do all exponentiation proceeding from left to right. So E for "exponentiation" comes second.

Third, you do all division proceeding from left to right. So D for "division" comes third.

Fourth. you do all multiplication proceeding from left to right. So M for "multiplication" comes fourth.

Fifth, you do all addition proceeding from left to right. So A for "addition" comes fifth.

Sixth, you do all subtraction proceeding from left to right. So S for "subtraction" comes sixth.



Notice that \(\displaystyle \dfrac{-1 - 5}{4} = (- 1 - 5) / 4.\)

When you have fractions, numerators and denominators are not covered by BEMDAS. To use BEMDAS, you have to put everything into the format
using brackets, ^, /, *, +, and -. This was your problem at the very first when you did not put your fraction into proper form by using grouping symbols (parentheses or brackets.) Another way to say the same thing is to treat the numerator and the denominator of each fraction as though they were surrounded with grouping symbols.

Many thanks for taking the time to explain the above, which is the way our books explain it as I had advised before, i.e. B is first following down the list until s = 6 being the last.

The problem now highlighted by you was in the final part of the understanding, as you wrote above;

\(\displaystyle \dfrac{-1 - 5}{4} = (- 1 - 5) / 4.\)

I could of added 1 to 5 and then divided second, then I could have subtracted before division, but not understanding I followed BIDMAS, which (I) does indicate Indices, powers and exponents in the UK. I can see there are other ways of defining it, and maybe a SI International agreement would be better for the use of it to ensure we all sing from the same hymm sheet.

 

[JeffM]

Many thanks for taking the time to explain the above, which is the way our books explain it as I had advised before, i.e. B is first following down the list until s = 6 being the last.

The problem now highlighted by you was in the final part of the understanding, as you wrote above;

\(\displaystyle \dfrac{-1 - 5}{4} = (- 1 - 5) / 4.\)

I could of added 1 to 5 and then divided second, then I could have subtracted before division, but not understanding I followed BIDMAS, which (I) does indicate Indices, powers and exponents in the UK. I can see there are other ways of defining it, and maybe a SI International agreement would be better for the use of it to ensure we all sing from the same hymm sheet.

I believe that \(\displaystyle \dfrac{-1 - 5}{4} = (-1 - 5)/4 = (- 6) / 4 = -1.5\) is already a global convention of notation. I must admit that I know nothing about educational methods in the UK so you should discuss this with your teacher.

 

[mmm4444bot]

the way our books explain [Order of Operations] as I had advised before, i.e. B is first following down the list until s = 6 being the last.

But I advised you above, we do NOT do division before multiplication, and we do NOT do addition before subtraction. Did you miss the following?

I'm concerned that you wrote "and finally subtraction".

Addition and subtraction are done, in order as they appear, from left to right.

Multiplication and division are done, in order as they appear, from left to right.

 

[Probability]

But I advised you above, we do NOT do division before multiplication, and we do NOT do addition before subtraction. Did you miss the following?

No I didn't miss what you wrote, and that same information is written into our books, however for me the confusion arrives here;

1 + or - 5 divided by 4

BIDMAS says;

D = division, so looking at the quadratic we have addition and subtraction and division, but BIDMAS says the third order is division before addition and subtraction, so this is where my problems occured.

If I say 5/4 - 1 = 1/4 or

If I say 5/4 + 1 = 2 /1/4, then both these answers using division first by inexperience would be seen as correct, but if addition and subtraction are completed first, then a different answer altogether is seen;

1 + or - 5/4 = - 6/4 = -3/2 or

1 + or - 5/4 = -4/4 = 1

I see what is being said about starting from the left to the right, this I have seen with linear equations, but I have never see this with maths using fractions combined, so based on little knowledge I followed what I thought was correct, that being BIDMAS starting at B working down the list until finally using S, which now seems not the case where fractions are included because addition or subtraction is carried out before division, which I admit I did not know, it's not in the books and I have not been advised until now.

Thank you.

P.S. Anyone care to give me a crash course in latex on here as I can't get it to work?

Probability:smile:

 

[mmm4444bot]

1 + or - 5 divided by 4

BIDMAS says;

D = division, so looking at the quadratic we have addition and subtraction and division, but BIDMAS says the third order is division before addition and subtraction, so this is where my problems occured.

Your phrase "divided by" constitutes a grouping symbol. (You are also continuing to leave off the negative sign in front of 1; you've done this three times now.)

The quadratic formula says that the expression on top is divided by 2a; in other words, the fraction bar (shown below) is a grouping symbol.

\(\displaystyle \dfrac{-1 \pm 5}{4}\)

Because the fraction bar is a grouping symbol, we do the arithmetic on top first, then divide by 4.

 

[Probability]

Your phrase "divided by" constitutes a grouping symbol. (You are also continuing to leave off the negative sign in front of 1; you've done this three times now.)

The quadratic formula says that the expression on top is divided by 2a; in other words, the fraction bar (shown below) is a grouping symbol.

\(\displaystyle \dfrac{-1 \pm 5}{4}\)

Because the fraction bar is a grouping symbol, we do the arithmetic on top first, then divide by 4.

Thanks for that, its all a learning curve.:cool:

 

[mmm4444bot]

You're most welcome.

That curve is surely steeper in the beginning, seemingly like an escarpment sometimes (eg: Abert Rim near NW Nevada), but with practice the slope begins to decrease.

By the way, many people often perceive ambiguity when they see either of the following two math symbols. This ambiguity is why we need to use grouping symbols when texting mathematical expressions.

/

÷


Considering again the expression that you posted (showing usage of both symbols above).

-1 ± 5 / 4

-1 ± 5 ÷ 4

The Order of Operations tells us to do division before addition or subtraction. Therefore, the meaning for both of those expressions is:

\(\displaystyle -1 \pm \frac{5}{4}\)


With practice, you will read texting like 16-3*5 as meaning "multiply three by five and subtract the result from 16".

If people intend to say differently, then they must text it properly, like this:

(-1 ± 5)/4

{-1 ± 5}÷4

[16-3]*5


You may think of grouping symbols as forcing a change to the normal order of things.

The symbols / and ÷ do not have sufficient face-value to display grouping-symbol information (thanks to computer pioneers with a mechanical-typewriter mindset); we must use brackets, parentheses, or curly braces.

See ya. :cool:

 

[mmm4444bot]

i = indices, exponents, powers.

bidmas, bedmas, pemdas, boo!