Thread: Solve This Math Problem

Multiplication has 4 properties:
Commutative property: 4 * 2 = 2 * 4
Associative Property: (2 * 3) * 4 = 2 * (3 * 4)
Multiplicative Identity Property: 5 * 1 = 5
Distributive property: 4 * (6 + 3) = 4*6 + 4*3



In our case 2 outside of the parenthesis follows the distributive property of multiplication (which can not be avoided). You HAVE TO factor and simplify 2(9+3) before performing any other operations on the equation. You can not start calculation from left to right unless you do this. Therefore there is no other way to see this besides:
48÷2(9+3) -> 48÷(2*9+2*3) -> 2

Any other answer doesn't take into consideration the Distributive property of multiplication and is absolutely wrong

Originally Posted by papamin

Multiplication has 4 properties:
Commutative property: 4 * 2 = 2 * 4
Associative Property: (2 * 3) * 4 = 2 * (3 * 4)
Multiplicative Identity Property: 5 * 1 = 5
Distributive property: 4 * (6 + 3) = 4*6 + 4*3

In our case 2 outside of the parenthesis follows the distributive property of multiplication (which can not be avoided). You HAVE TO factor and simplify 2(9+3) before performing any other operations on the equation. You can not start calculation from left to right unless you do this. Therefore there is no other way to see this besides:
48÷2(9+3) -> 48÷(2*9+2*3) -> 2

Any other answer doesn't take into consideration the Distributive property of multiplication and is absolutely wrong

Any chance you ignoring basic step that solving brackets always comes first? :S
And, is there any such list for properties of division? There must be one. :/

Originally Posted by exhumare

Any chance you ignoring basic step that solving brackets always comes first? :S
And, is there any such list for properties of division? There must be one. :/

Solving brackets doesn't necessarily mean you have to add the numbers, remember 4 * (6 + 3) is ALWAYS 4*6 + 4*3 . What you are saying is that 4*(6+3) = 4*(9) but that is a different thing, not what the distributive property says.
if you choose to ignore the distributive property it's like saying that 4 * (6 + 3) is not the same as 4*6 + 4*3 which is obviously wrong.

Division has its own properties but you only care about dividing AFTER you are done with the 2(9+3) bit (brackets always comes first)

Order of Operations (the basis of basic alegbra) says:
terms inside brackets
exponents and roots
multiplication and division
addition and subtraction

Therefore 48 / 2 (9+3)
Step 1: 48 / 2 (12)

Proper scientific calculation order is
1) exponentials - right to left
2) multiplication and division left to right
3) addition and subtraction left to right.

Step 2: 48 / 2 = 24 (12)
Step 3: 24 * 12 = 288

Done

You ONLY prioritize what is INSIDE the brackets. Which means once the (9 + 3) is done, you just treat the (12) as a " * 12."

Also - Google Never Lies.
http://lmgtfy.com/?q=48+%2F+2+(+9+%2B+3+)

Originally Posted by papamin

Solving brackets doesn't necessarily mean you have to add the numbers, remember 4 * (6 + 3) is ALWAYS 4*6 + 4*3 . What you are saying is that 4*(6+3) = 4*(9) but that is a different thing, not what the distributive property says.
if you choose to ignore the distributive property it's like saying that 4 * (6 + 3) is not the same as 4*6 + 4*3 which is obviously wrong.

Division has its own properties but you only care about dividing AFTER you are done with the 2(9+3) bit (brackets always comes first)

I would multiply out 4 into brackets first if there were some variables inside brackets but in this case both are constants and so adding them together first makes more sense (to me)

In case of computer programs (like google) you have to explicitly formulate things.
There is a difference between 48 / 2 * (9+3) and 48 / 2(9+3)
The first notation reads 48 / 2 * 1(9+3)
The second notation reads 48 / (2*9+2*3)

So if the original quatation given was 48 / 2 * (9+3) or (48 / 2)* (9+3) or (48 / 2)(9+3) then the result would have been 288
In our case it is given as 48/2(9+3) which in our case equals 2

Originally Posted by papamin

In case of computer programs (like google) you have to explicitly formulate things.
There is a difference between 48 / 2 * (9+3) and 48 / 2(9+3)
The first notation reads 48 / 2 * 1(9+3)
The second notation reads 48 / (2*9+2*3)

So if the original quatation given was 48 / 2 * (9+3) or (48 / 2)* (9+3) or (48 / 2)(9+3) then the result would have been 288
In our case it is given as 48/2(9+3) which in our case equals 2

There is no difference between
48 / 2 ( 9 + 3 )
and
48 / 2 * ( 9 + 3 )
It will still be 48 / 2 * 12

Proper scientific order with multiplication and division is left to right.

The only possible way to get 2 as an answer is if you group the part after the division like so: ( 2 ( 9 + 3 ) )

Mhm, it's settled. Answer is 288, close thread.

*running for cover*

Originally Posted by freu0047

There is no difference between
48 / 2 ( 9 + 3 )
and
48 / 2 * ( 9 + 3 )

Yes there is, if you wanted to formulate this in a computer program you wouldn't get away by writing the equation like this: 48 / 2 ( 9 + 3 ) you'd have to use an operator between the 2 and the bracket. Now if you write 48 / 2 *( 9 + 3 ) in a program you'd probably get 288 as a result (although i've used in the past compilers that would require you to properly define this using brackets but that was ages ago).
In our case it's like having the equation 48/2x (replace x with 9+3). To me this reads 48/(2*x) to you (48/2)*x
If you choose to add the missing * operator, in order to run this against a compiler then you'd get your result.
However to me, the absence of * from the initial problem (which is not formulated in order to run in a program) shows me that 2x is part of the divisor. If the * operator was given and the question was 'what result would you get if you run this in x compiler' i'd tell you it's 288
In any case this would have been a great thread in the new thebigdebate forum :)