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### Topic: 48÷2(9+3) = ? (Read 11190 times)previous topic - next topic

#### Nick Gammon

#60
##### Apr 21, 2011, 11:57 pm

I've just googled this and a site pointed out that implied multiplication has a higher precedence than division. For example, 2/5x would normally be interpreted as 2/(5x)

Reference?

I have seen it claimed that 3-1+5 equals -3 on the basis that you evaluate it as 3 - (1 + 5). The reason given is that BODMAS (or BIDMAS/BEDMAS) stands for Brackets, Exponents, Division, Multiplication, Addition, Subtraction. Therefore since addition is before subtraction you add 1 to 5, and then you subtract that from 3, giving -3.

However this is wrong. Multiplication/division, and addition/subtraction have equal priority and are evaluated left to right.
Please post technical questions on the forum, not by personal message. Thanks!

http://www.gammon.com.au/electronics

#### Nick Gammon

#61
##### Apr 22, 2011, 12:52 am
Wikipedia:

Quote
Many programming languages use precedence levels that conform to the order commonly used in mathematics, though some, such as APL or Smalltalk, have no operator precedence rules (in APL evaluation is strictly right to left, in Smalltalk it's strictly left to right).

Not everybody agrees with that.

Yes, I see that.

Well the question is undefined then. Without specifying the base of the numbers, the domain in which we are working (eg. maths, APL, Smalltalk, C, Swahili, Martian) it cannot be answered.
Please post technical questions on the forum, not by personal message. Thanks!

http://www.gammon.com.au/electronics

#### retrolefty

#62
##### Apr 22, 2011, 01:01 am
Quote
And that is the fundamental issue. Not everybody agrees with that.

Heck, we can't all even agree on which side of a road to drive on.

#### biocow

#63
##### Apr 22, 2011, 02:15 pm

Quote
And that is the fundamental issue. Not everybody agrees with that.

Heck, we can't all even agree on which side of a road to drive on.

Now you're trying to confuse things with geometry.

Vehicle A belongs to me
Road B is bisected by line C
Therefore vehicle A may drive on either side of line C
10 PRINT CHR\$(7)
20 GOTO 10

#### mowcius

#64
##### Apr 22, 2011, 04:53 pm
Quote
Heck, we can't all even agree on which side of a road to drive on.

Depends which way you're travelling

#### retrolefty

#65
##### Apr 22, 2011, 05:47 pm

Quote
Heck, we can't all even agree on which side of a road to drive on.

Depends which way you're travelling

Well that would be my way or the highway.

#### chol215

#66
##### Apr 23, 2011, 07:24 pm
shouldn't it be following order of operations so that inside the parenthesis is first this would make it two, but as for the other approaches, I did not really get them.

#### westfw

#67
##### Apr 23, 2011, 08:06 pm
Quote
I did not really get them.

It all boils down to whether you do the un-parthenthesized multiplication or division first:
48÷(2(9+3)) or (48÷2)(9+3)
and THAT depends on whether you believe that implied multiplication (2x) has a different precedence than explicit multiplication (2*x), whether there's an explicit precedence of multiplication vs division, and/or whether you believe in left-to-right evaluation or something else.  All of which are NOT consistently defined.

#### Onions

#68
##### Apr 23, 2011, 09:48 pmLast Edit: Apr 23, 2011, 10:18 pm by Onions Reason: 1

I've just googled this and a site pointed out that implied multiplication has a higher precedence than division. For example, 2/5x would normally be interpreted as 2/(5x)

48÷2(9+3) = y
If we say that (9+3) is x, then x = 12.
That makes it 48÷2x, or 48*(2*12)
2*12 is 24.
48÷24=2, so 2 is my answer.

Arduino disagrees though:

Code: [Select]
`void setup(){  Serial.begin(9600);  Serial.print(48/2*(9+3));}void loop(){}`

Serial output: 288.

Onions.
My website: http://www.harryrabbit.co.uk/electronics/home.html Up and running now! (Feel free to look round!)

#### cyberteque

#69
##### Apr 24, 2011, 04:31 am
I just keyed the equation, exactly as it is written and got 2!

That was after I got 2 solving it in my head and then reading the rest of the posts!

AS an aside for all the weird little varmints going on about which base...

In maths if it's a different base other than 10, then there is a little subscript notation of base, ie

1010
0A16
128
10102

#70
##### Apr 24, 2011, 04:36 am
Excel says an operator is missing, I am going with that: unclear formula presented.

Otherwise, it wants to correct it to
=48/2*(9+3), for result of 288.
And microsoft is never wrong ...
Designing & building electrical circuits for over 25 years.  Screw Shield for Mega/Due/Uno,  Bobuino with ATMega1284P, & other '328P & '1284P creations & offerings at  my website.

#### Nick Gammon

#71
##### Apr 24, 2011, 05:27 am

I just keyed the equation, exactly as it is written and got 2!

Into what?
Please post technical questions on the forum, not by personal message. Thanks!

http://www.gammon.com.au/electronics

#### cyberteque

#72
##### Apr 24, 2011, 05:40 am
A Casio fx-100AU calculator.

48÷2(9+3) = 2

obviously it's evaluating the bracket argument first.
QBasic on a PC gave the same answer, so did Apple basic on an Apple II.
FPC (free pascal compiler) under Linux also gave 2.
USCD Pascal on an Apple 2 gave 2.

I didn't try any other flavours yet.

But 2 was the answer I got when I evaluated it in my head initially.

#### Nick Gammon

#73
##### Apr 24, 2011, 06:37 am
I'm most impressed that you have got things like UCSD Pascal on an Apple 2. Sadly my Apple 2 has gone away.

I can confirm that on the following calculators I also got the answer 2:

• Sharp EL-531WH

• Casio CFX-9850GB Plus

My Casio fx-115 gave the answer 4.
My TI-nspire CAS gave the answer 288.
My HP 50g gave the answer 288.

Interesting.
Please post technical questions on the forum, not by personal message. Thanks!

http://www.gammon.com.au/electronics

#### retrolefty

#74
##### Apr 24, 2011, 06:42 am
Are we done yet.

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