= 6/2*3
= 3*3
= 9
My cat vigorously disagrees. But I’m sticking to the answer is 9.
Posted on 12/28/2024 8:35:57 AM PST by Jonty30
I am getting a lot of people who say the answer is 9, but you can get 9 from 6/2(1+2) if you separate the 2 from the 2(1+2), which seems incorrect to me. I view the 2(1+2) as a complete phrase within the mathematical question, so I think it needs to be solved before you move left to right.
6/2(1+2) = 6/2(3) = 6/6 = 1 But there are a lot of people who want to write the question as 6/2 x (1+2), which is the only way you will get 9.
You seem to have (1+3) in the title, but (1+2) in the body.
My mistake. It should have been written 6/2(1+2)
The parentheses are evaluated first, then division and multiplication are processed left to right.
But the fact that there appears to be ambiguity means that the expression is poorly written. This example is a teaching lesson and a warning in making one’s intent clear.
You’re supposed to reduce the fractional value to it’s lowest common denominator before you multiply it times the sum.
When I broke it down algebraically, it took this form.
F / b(a+b) = (F / ab + b^2) = 6 / (2+4) = 6/6 = 1.
Order of precedence is: 1. parenthesis, 2. exponentiation, 3. multiplication and division, and 4. addition and subtraction. Additionally, equal operations are performed left to right.
In your example, 1 + 2 is done first, and then the remaining division and multiplication are done in order from left to right.
So you have 6/2=3 x 3 = 9.
There is no ambiguity. There is only one way to evaluate the parens first and then evaluate multiplications and divisions from left to right.
The OP is mistaken in wanting to evaluate 2(1+2) first, because doing so means that a multiplication is done prior to a division that is to its left, which violates the laft-to-right rule.
My cat vigorously disagrees. But I’m sticking to the answer is 9.
However, a(b+c) = ab +ac.
Using the principle, 6/2(1+2) = 6/(2+4)
You would need another set of parentheses for that to be true. The problem is the implied multiplication. If the problem was written
F/b×(a+b) or
F/(b(a+b)) or
F/(b×(a+b))
The intent would clear. In a computer program, or Excel, implied multiplication does not exist.
The implied multiplication makes the problem somewhat ambiguous.
No it doesn’t. Left to right (after the parens). Nothing changes if the implied multiplication is made explicit by insertion of a multiplication symbol.
It’s the old “order of operations.” Things get solved in this order: Parentheses, Exponents, Multiplication, Division, Addition, then Subtraction. So, it looks like:
6/2(1+3) = 6/2*4 = 3*4 = 12
However, if you then solve it left to right, I don’t know how you get 9 out of this.
OP meant (1+2) which gives 9.
I agree with you, but it appears some are under the impression that implied multiplication trumps the standard math rules.
The explicit use of ‘×’ would solve any ambiguity regardless of the rules being used.
This. The example given by the OP is one I've seen numerous times in computer programming code. Despite the fact that computer languages follows the order of precedence listed above, using those assumptions can lead to confusing code that can be tricky to debug and sometimes is actually wrong. Use extra parenthesis to make the intent clear.
👍
I got 43.
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