Question

How do you solve `4-(2-12\div 6)`?

Answer 1

The expression simplifies to 4.

Explanation:

The Order of Operations, offered referred to as "PEMDAS," must be followed. This is a 4-part rule that is applied to all expressions.

The first part (P for parentheses) requires that any operations offset by a grouping symbol must be done first, and that such operations also have to follow the Order of Operations. Grouping symbols are parentheses ( ), brackets [ ], the radical sign `sqrt`, absolute value bars | |, and the fraction bar -, among others.

The second part (E for exponents) requires that any power expression (`a^n`) be evaluated next.

The third part (M for multiplication and D for division) requires that any multiplication and/or division be completed In the order it occurs from left to right in the expression.

The fourth part (A for addition and S for subtraction) requires that any addition and/or subtraction be completed in the order it occurs from left to right in the expression.

Therefore, in `4 - (2 - 12-:6)`, we must begin by simplifying the portion in the parenthesis first, and follow the Order of Operations:
`4 - (2 - 12-:6)`
`4 - (2 - 2)`
`4 - 0`
`4`

Properly following the Order of Operations gives the simplified form of the expression, 4.