Order of Operations
(Priority Rules for Arithmetic)
One way to remember the operation priority rules is to use the
acronym BEDMAS, meaning
B (rackets) first
E (xponents) next
M (ultiply) and D (ivide)
next
and
A (dd) and S (ubtract) last
of all.
Here are a few more examples:
Example 1:
| 35 × 16 - 96 + 14 |
= |
560 - 96 + 14 |
Do the single multiply first – it
has the highest priority present. |
| |
= |
464 + 14 |
Do the left-most of the two add/subtract
operations. They have the same level of priority, so the
left-most one is done first |
| |
= |
478 |
Finally, do the remaining addition, to
get the correct final result of 478. |
Example 2:
3 – 5(4 – 6 x 2 – 5 + 7) + 8 × 3
| = 3 – 5(4 – 12
– 5 + 7) + 8 × 3 |
We need to start with the expression
inside the brackets, which has the highest priority.
Inside the brackets, the multiply operation has the
highest priority. |
| = 3 – 5(-8 – 5 +
7) + 8 × 3 |
Now, do the leftmost subtract inside the
brackets, since the two subtracts and one add otherwise
are at the same priority level. |
| = 3 – 5(-13+7) + 8 × 3 |
Again, leftmost subtract inside the
brackets. |
| = 3 – 5(-6) + 8 × 3 |
And, the last add in the brackets. |
| = 3 +30 + 24 |
Both of the multiplies are at the same
priority level – here they don’t interfere with
each other, so we can do both at the same step. We can
regard the first one as being -5 times -6, giving the
positive result +30. |
| = 33 + 24 |
Now the remaining two adds can be done to
get the final answer. |
| = 57 |
|
We’ve shown the steps above in a little more detail than
one might normally employ, just to show the application of the
priority rules very precisely.
Example 3:
| 2 – 5(6 – 9)
3 |
= |
2 – 5(-3) 3 |
Evaluation of the bracketed expression
takes priority over every other operation present. |
| |
= |
2 – 5 × (-27) |
The exponentiation is done next, since it
is the highest priority of the remaining operations. The
power 3 is applied to the entire contents of the
brackets: (-3) × (-3) × (-3) |
| |
= |
2 + 135 |
The multiplication has the next highest
priority. |
| |
= |
137 |
|
|
