Why is the Order of Operations important?
The Order of Operations is just an agreement that allows us all to do a problem the same
way so we get the same answer. Without the Order of Operations, one person might
simplify 3 + 4 x 5 as 35 by adding first. Another person might simplify 3 + 4 x 5 as 23 by
multiplying first. Having two answers for the same problem would be very confusing.
So as we make arrangement to all drive on the right side of the road, to wear wedding
bands on our left hand, to list home teams last in sports, we make agreements in math for
consistency as well.
The agreement is to do from left to right all groupings first, followed by exponentials,
then multiplication and division third, and finally all additions and subtractions.
Example: 3 + 12 ÷ 2 x 3 = 21. Since there were no groupings or exponentials, we
started with multiplications or divisions from left to right. That resulted in us dividing 12
by 2 before multiplying.