2(1+3) is one number. Why? 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 = 3+1.
6 ÷ 2a = 3 /a
6 ÷ 2(3+1) = 3/(3+1)
6 ÷ 2(3+1) ? Ans: 3/4 Proven with the laws of math.
6 ÷ 2(3+1) = 3/4
And…
6 ÷ (3+1)2 = 3/4
(6 ÷ 2)*(3+1) = 12
6(3+1) ÷ 2 = 12