To Summarize:

The answer 1 and 16 can be given and support can be produced for each of them ... the equation should not really be written like it is ... if I had to give only one answer and couldn't explain it I would give 16. And if I could explain it I would also give 16. But it isn't the "only" possible answer if proper explanation is given since we don't have a universal standard for dealing with it. To make it clear it needs more parentheses/brackets.

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Using PEMDAS/BODMAS/BEDMAS you have:

8÷2(1+3) =

8÷2(4) =

4(4) =

16

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If we use an outdated way of dealing with this where everything on the left side of the divide sign is divided by the right side of the divide sign we have:

8÷2(1+3) =

8÷2(4) =

8÷8 =

1

This is outdated for many reasons ... first let us look at what would happen here ... this was done in the past for some simple equations where people were trying to convey what the answer here shows ...

2+3÷3+2 =

5÷5 =

1

However this is so far away from PEMDAS/BODMAS/BEDMAS which would be

2+3÷3+2 =

2+1+2 =

3+2 =

5

So everyone who used this way of doing 8÷2(1+3) = 1 do you want to also say 2+3÷3+2 = 1 ???

And when there are multiple divisions to be done in an equation well I think you could start getting confused ... what would you do with ...

2-4÷6+7x5+3÷17x5-3÷6÷12+3 =

yea I guess it could be done ... but again wouldn't be PEMDAS/BODMAS/BEDMAS and well it isn't how it would be done these days or I think even in the past

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Then we have a modified form of PEMDAS/BODMAS/BEDMAS which is used by mostly physicists ... it has to do with implied multiplication having higher precedence over explicit multiplication and division. Parentheses can be one way for multiplication to be implied but it is not the only way. So it is not because of the parentheses but because of the implied multiplication caused by the parentheses that would give you this.

8÷2(1+3) =

8÷2(4) =

8÷8 =

1

I would think if you gave the reasoning that PEMDAS/BODMAS/BEDMAS requires you to do parentheses (brackets) first and the 2 is part of the brackets you wouldn't get full credit for this ... if you said that implied multiplication has higher precedence over explicit multiplication and division you have a good chance to get full credit. Some calculators have implied multiplication having higher precedence than explicit multiplication and division and will give the answer 1 to the OP equation as posted.

So let's look at another equation and see what you would come up with SINCE parentheses (brackets) are not always necessary for implied multiplication.

A ÷ BC =

Where A = 3 , B = 2, C = 30 ... what would be your answer?

If you say 0.05 then you are being consistent with the modified form of PEMDAS/BODMAS/BEDMAS and with an answer of 1 for the OP, since in the equation BC is implied multiplication it needs to be done first.

3 ÷ 60 =

0.05

If you say 45 then you are being consistent with the "normal" PEMDAS/BODMAS/BEDMAS and with an answer of 16 for the OP. Here division and multiplication are done in the order from left to right that they appear with no precedence for implied multiplication.

1.5 x 30 =

45

Big difference between 0.05 and 45 ... and yes I tried to make it simple to illustrate the difference between PEMDAS/BODMAS/BEDMAS and the modified form of PEMDAS/BODMAS/BEDMAS. I will see if I can get better examples ... but you see this has nothing to do with parentheses (brackets) but with whether the multiplication is implied and not explicit.

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And it's been over 36 hours since I have had any sleep so I hope I didn't mess any of that up and I hope I explained adequately. The answer 1 and 16 can be given and support can be produced for each of them ... the equation should not really be written like it is ... if I had to give only one answer and couldn't explain it I would give 16. And if I could explain it I would also give 16. But it isn't the "only" possible answer if proper explanation is given since we don't have a universal standard for dealing with it. To make it clear it needs more parentheses/brackets.