48÷2 (9+3) argument

[Archer]

Let's just all agree that it's a crap way of writing an equation in the first place. Life is too short to get hung up on sh*t like this.

(my) Work is too boring to leave it alone

 

[Barilak]

What do you do in case you have unlike terms inside the brackets ? :erm:

Remember the example given is a simple arithmetic sum with only numbers but you might have a problem once you start working with variables.

But in this example we have like terms inside the bracket. I'll get completely befuzzled if I start thinking of "what if."

 

[Archer]

Have you forgotten about BODMAS now? How can you do division before brackets ?

So you are telling me that a÷b(x+y) does not equal a÷b(x+y) ?

edit: counter point - how do you do multiplication before brackets?

 

[HapticSimian]

It's poor notation, and in an ideal world that realisation would herald the end of the discussion.

 

[Chevron]

nvm

 

[Archer]

So you're saying

48/2(9+3) could be 2/48(9+3)

No..

When will you answer the following?
48*0.5(9+3)=

 

[JungleBoy]

So you are telling me that a÷b(x+y) does not equal a÷b(x+y) ?

edit: counter point - how do you do multiplication before brackets?

In your example a÷b(x+y) = z(x+y) the z is a quotient of a ÷ b not so ?
If yes then you can't do division before brackets

On you counter point - you don't do multiplication before brackets. But you distribute the multiplication inside the brackets then you add the two terms.

 

[Archer]

In your example a÷b(x+y) = z(x+y) the z is a quotient of a ÷ b not so ?
If yes then you can't do division before brackets

I merely made a substitution, I have not evaluated anything yet. Your point is mute (or moot, I never rememeber). So we are back to you are telling me that a÷b(x+y) does not equal a÷b(x+y) but does equal a÷(b(x+y)). You are magically putting in brackets that are only implied. Math doesnt deal with "implied" functions, in which case the logical thing is to not imply anything

On you counter point - you don't do multiplication before brackets. But you distribute the multiplication inside the brackets then you add the two terms.

Hint - the entire part before the brackets is one term, hence you distribute the entire thing into the brackets. Go look up what defines a single mathematical term

In elementary mathematics, a term is either a single number or variable, or the product of several numbers or variables, separated from another term by a + or − sign in an overall expression

So go do your distributive thing properly

 

[JungleBoy]

No..

When will you answer the following?
48*0.5(9+3)=

Nice try but
48 * 0.5 = 0.5 * 48
whereas
48 ÷ 0.5 <> 0.5 ÷ 48 .

Multiplication has commutative properties and division does not. So you can't just switch the two and expect to follow the same rule.

 

[Archer]

48 ÷ 0.5 <> 0.5 ÷ 48 .

Multiplication has commutative properties and division does not. So you can't just switch the two and expect to follow the same rule.

I did not change the order of anything, so again your point is moot.

Unless you are telling me that 1/2 does not equal 0.5 ?
In other words...
You are saying that 100/2 does not equal 100*0.5 ?? <- see, order of stuff is unchanged.

 

[JungleBoy]

I merely made a substitution, I have not evaluated anything yet. Your point is mute (or moot, I never rememeber). So we are back to you are telling me that a÷b(x+y) does not equal a÷b(x+y) but does equal a÷(b(x+y)). You are magically putting in brackets that are only implied. Math doesnt deal with "implied" functions, in which case the logical thing is to not imply anything



Hint - the entire part before the brackets is one term, hence you distribute the entire thing into the brackets. Go look up what defines a single mathematical term


So go do your distributive thing properly

See above about the non commutative properties of division (and subtraction). You cannot substitute a÷b with an arbitrary z without evaluating it first.

 

[Archer]

See above about the non commutative properties of division (and subtraction). You cannot substitute a÷b with an arbitrary z without evaluating it first.

See above the order was not changed...
And yes, you can substitute stuff before evaluating... its a substition where one thing is exactly equal to another... Come on, you must give me this one at least...

 

[JungleBoy]

See above the order was not changed...
And yes, you can substitute stuff before evaluating... its a substition where one thing is exactly equal to another... Come on, you must give me this one at least...

I think that is where the problem is. Division and Subtraction have different properties to Multiplication and Addition. The later are commutative which means that the order does not matter eg. 2*3 = 3*2 and 2+3 = 3+2 ; however 2÷3 <> 3÷2 and 2-3 <> 3-2
You can therefore not substitute a ÷ b with z the same you can substitute a*b. Here is the problem - once you have the z how do you ensure that you can get back to your original a ÷ b without the ambiguity of of ending up with b ÷ a instead?

 

[BeLgaRiOn]

BODMAS: 48÷2(9+3) = 48÷2(12) = 48÷24 = 2

 

[Archer]

I think that is where the problem is. Division and Subtraction have different properties to Multiplication and Addition. The later are commutative which means that the order does not matter eg. 2*3 = 3*2 and 2+3 = 3+2 ; however 2÷3 <> 3÷2 and 2-3 <> 3-2
You can therefore not substitute a ÷ b with z the same you can substitute a*b. Here is the problem - once you have the z how do you ensure that you can get back to your original a ÷ b without the ambiguity of of ending up with b ÷ a instead?

I did not fiddle with anything that requires you to even think about commutative laws. Just read...
I literally did the following
48/2 = 48*0.5 Show me exactly where I did anything commutative in this line... You keep spouting some nonsense about me saying 48/2 = 2/48. Where in the name of creation do you get that??

You're making up random stuff. I might as well say that JungleBoy says 1+3 = 62 and therefore he is wrong. Absolutely ludicrous

And your silly example about substitutions.
If you cant handle let z=a÷b, and therefore a÷b(x+y) = z(x+y) and then know how to sub a÷b back in at the end, then you are a lost cause. There is zero ambiguity in there. Only an idiot would end up with (x+y)a÷b after subbing the values back in

 

[ponder]

B - Brackets first
O - Orders (ie Powers and Square Roots, etc.)
DM - Division and Multiplication (left-to-right)
AS - Addition and Subtraction (left-to-right)

 

[Archer]

B - Brackets first
O - Orders (ie Powers and Square Roots, etc.)
DM - Division and Multiplication (left-to-right)
AS - Addition and Subtraction (left-to-right)

/highfive

 

[a'zombi]

BODMAS: 48÷2(9+3) = 48÷2(12) = 48÷24 = 2

Hi

You were correct in your first step. But in your second step, 48÷2(12), the 2(12) is considered as multiplication and NOT brackets*. Therefore you work from left to right resulting in 24(12).

Hope that helps.

*Brackets in BODMAS means calculating what's INSIDE the brackets.

 

[Africaner]

Some people in here confuse arithmetic and algebraic rules - big time
@JungleBoy With the way you reason you'll be better off residing where your name suggests. WTF
Won't surprise me if he is a maths teacher.

 

[Mike Hoxbig]

The notation sucks, let it go guys. You're arguing over an equation that's poorly defined.