5-12x=8-7x-[6÷3(2+5³)+5x]
5-12x=8-7x-[6÷3(127)+5x]
5-12x=8-7x-[6÷381+5x]
5-12x=8-7x-[63.5+5x]
5-12x=8-7x-63.5-5x
-12x+5=-12x-55.5
Ø=60.5
There are two important things to say here.
First: If just the 3 is under the 6, you can't multiply the 3 with 127. This is because 127 in itself is equal to 127/1, and if you are going to multiply a fraction you have to multiply the numbers "above" and the numbers "below" separately. A simple example would be 2/3*3, which is the same as 2/3*3/1. We multiply 2 by 3, and 3 by 1. The result is 6/3, which is the same as 2.
It may be easier to understand this if i write it such as:
We multiply the numbers "above" with the other numbers "above", and the numbers "below" with the numbers "below".
In this math problem, it would be 6*127 and 3*1. The result is 762/3, which is equal to 254.
Check it out:
However, this is a longer road to reach the result.
If you divide 6 per 3 in itself, the result is 2.
2*127 is equal to 254.
I will explain why you can do this down below, in the second part of my post.
DO keep attention that i am considering that only 3 is under the 6.
Second: the number you ( incorrectly) reached was 6/381, and when you did the division you came to the result 63.5. The problem here is that it is the 6 being divided by 381, and not the inverse. 6 divided by 381 is equal to 0,0157.
6 = 0,0157
381
One thing I have noticed is there seems to be some inconsistencies between here and what I've been taught on order of operations. What I have been taught is to do in this order: Parentheses, exponents, multiplication, division, addition, subtraction. Which it makes a big difference dividing 381 by 6 or by 2.
Actually, the order is more like: parentheses, exponents, multiplication/division,addition/subtraction.
The slashes are important, because otherwise you would think that multiplication takes precedence over division, and this is not true.
In this particular case, the parentheses was just a leftover.
In this sort of math problem, when you reach a single number inside a parathenses, it is the same as if you didn't have a parantheses anymore.
Examples:
10 * ( 30 ) is the same thing as 10 * 30.
5 * ( 2 ) is the same thing as 5 * 2.
And as such, the number inside the parentheses loses its priority.
Going back to the original problem:
6/3*(127) is the same thing as 6/3*127.
So we have a division AND a multiplication here, and you can solve this in whatever order you prefer. I highly recommend you to always solve divisions first WHEN you have a "clear" division, such as: 6/3, 81/9,49/7, and so on. This is simply because you will have to handle smaller numbers.
Example:
25 * 99
5
If you divide first ( which will take you a mere second ) you will end up with 5 * 99. 5*99=495. This is pretty simple.
If you multiply first ( which will take you many seconds ) you will end with 2475/5. And you will have yet to divide those numbers ( which takes several more seconds ) to end up with 495.
The result is the same, but one way is quicker and easier to do.
).
