6 ÷ 2(2+1) = ??
People are incorrectly separating the 2 from the parentheses. It is a factor of the 2 numbers inside it. People are trying to solve this as a calculator would, but that is the wrong way. Solve it using algebra techniques with a pen & paper (See URL at the bottom)
Now, think of the Identity Law: a = 1a = 1(a)
Ask yourself: what is a ÷ a = ?? Ans: 1
a ÷ a = 1
Now, Identity Law says any variable that has no coefficient actually has a 1, whether it is written or not. So,
a ÷ 1a = 1 ALWAYS. It is NOT a ÷ 1 * a = a² That is ridiculous.
This proves that 1a = (1a) and (1 * a). 1a is not the same meaning as 1 * a.
Therefore,
a ÷ 2a = 1/2
6 ÷ 2a = 3/a
Let a = 2+1.
6 ÷ 2a = 3 /a
6 ÷ 2(2+1) = 3/(2+1)
6 ÷ 2(2+1) ? Ans: 1 Proven with the laws of math.
6 ÷ 2(2+1) = 1
And…
6 ÷ (2+1)2 = 1
(6 ÷ 2)*(2+1) = 9
6(2+1) ÷ 2 = 9
~caper