The order of operations followed in simplifying a mathematical expression is illustrated by the acronym PEMDAS, which stands for Parenthesis > Exponent > Multiplication > Division > Addition > Subtraction. First, the mathematical expression should be grouped by parenthesis. Each parenthesis group should be evaluated individually. Then, the parenthesis groups are grouped by exponent; each exponent group should be evaluated individually. When it comes down to the levels of multiplication-division, these two operations are interchangeable in order of execution; similarly, addition and subtraction are interchangeable in order. However, it should be noted that multiplication-division have higher precedence than addition-subtraction, which have the lowest precedence. Therefore, execute the multiplication-division operations first, then the addition-subtraction. When MDAS is finished, evaluations of the exponent groups can be initiated; then finally, evaluation of the parenthesis groups are executed.
One common mathematical function that emphasizes the importance of these rules is the conversion of Fahrenheit to Celsius temperature scales. The formula is:
For instance, let the Fahrenheit temperature equal to 68℉. The correct implementation of the formula is:
℃=5968-32=5936=5×369=5×4=20℃
However, if the order PEMDAS is not followed, for instance the evaluation of the values are from left to right:
℃=5968-32=5÷9×68-32=0.5555×68-32=37.77778-32=5.7778℃
The result is way off the correct one. This shows the importance of following the correct order of operations in simplifying mathematical expressions.
Original Mathematical Expression:
8-4÷23+12÷3+5×3-83
Evaluation (From Left to Right; Incorrect):
8-4÷23+12÷3+5×3-83
→4÷23+12÷3+5×3-83
→23+12÷3+5×3-83
→8+12÷3+5×3-83
→92÷3+5×3-83→81÷3+5×3-83
→27+5×3-83
→32×3-83
→96-83
→883→681472
