Does omitting the multiplication operator have an effect on order of operations When you write a mathematical expression like this:
$4:2(1+1)$,
does the fact that the multiplication operator is not explicitly written has any bearing on the precedence? What is the order of operations in this case?
Is it:
$4:4=1$ (order: parenthesized addition, implicit multiplication, division)
or
$2(1+1)=4$ (order division, parenthesized addition, implicit multiplication).
If the explicit operator has no effect, this would be $4\div2\cdot(1+1)$ and calculated from left to right (because of the no precedence between division and multiplication). Result woud then be $4$.

The right way to do it, I think, would be as follows: 
$$ 4 \div 2 (1 + 1) = 4 \div 2 \times (2) = 4 \div 2 \times 2 = (4 \div 2) \times 2 = 2 \times 2 = 4. $$
However, one can also proceed as follows:
$$ 4 \div 2(1+1) = (4 \div 2) \times (1+1) = 2 \times (1+1) = 2 \times 2  = 4. $$
Note that parentheses carry the topmost precedence. 
Except for the grouping operators such as the parentheses, the multiplication --- whether expressed with or without the sign --- and division have equal precedence, followed by addition and subtraction, which also have the same precedence. However, operators (of the same precedence) are to be evaluated from left to right. 
Hope this helps. 
