# Order of Operations

The “Order of Operations” is a convention that ensures everyone interprets algebraic notation the same way. It is used in conjunction with the properties of each operation (addition, subtraction, multiplication, division, and exponentiation). I summarize the order of operations for myself as “do the most powerful operations first”.

The answer shown below is wrong.  Try working your way through the problem backwards, from the answer up. As you find each mistake, try to identify the thinking behind it… what perspective led to the mistake? What should have been done instead?

$3+2(15 \div 3-1)^2$

$=5(15 \div 3-1)^2$

$=(75 \div 15-5)^2$

$=(5-5)^2$

$=0^2$

$=0$

.

..

Hint 1: The correct answer to the original problem is: $35$

Hint 2: What if the problem had been written
$3+2\cdot (15 \div 3-1)^2$

Hint 3: Two mistakes have been made in the work above