What is PEMDAS? - Definition, Rules, and Examples

When playing with numbers, we often encounter a string of numbers and operators, and the solution of such an expression is done using the PEMDAS rule.

Indeed it is essential to know how to do the operations itself, so, for example, one should first learn perhaps using first or 2nd grade math worksheets addition, subtraction, multiplication, division, and exponent to solve any expression but just knowing how to do an operation is not enough as it is also essential to know in what order should the operations be carried out as operators in operation are calculated in a different order the final result can change. For example, consider an expression like 2 + 3 × 5.

One way to solve it would be to solve it from right to left, whichever operator comes first, or another way can be to solve it from left to right, just the reverse of the first method. Another way can be to solve any operator randomly; this method can only work if the order of solving the operations is optional, but as was pointed out before, it does.

So, if one goes from right to left, then we do the addition first that is 2 + 3 * 5 = 5 * 5

In this case, the answer we get is 25. If we go from left to right, we do the multiplication first, which is 2 + 3 * 5 = 2 + 15. In this case, the answer is 17.

Thus, the order of operations makes a difference, so let's know how to find in which order the operators should be solved.

The PEMDAS rule says that parentheses come first in an expression in the order of operations. If something is inside the brackets or parentheses, solve them first. For example,

• = (4 - 4) × 1 (solve the parentheses) = 0 × 1 = 0

Any exponential values in the equation solve them next, for example.

• 23 + 3 = 8 + 3 = 11 (solve the exponent)

After going through with parentheses and exponents, any multiplications or divisions in the expression, solve the next. It will depend upon what comes first when reading from left to right. So, in PEMDAS, ' M' comes before D, but it does not necessarily mean multiplication will precede division. For example,

• = (10 - 6)/2 × 1 + 23 + 3 (First: solve the parentheses)
• = 4/2 × 1 + 8 + 3 (Second: solve the exponent)
• = 2 × 1 + 8 + 3 (Third: solve multiplication or division)
• = 2 + 8 + 3 (Fourth: solve the multiplication) = 13

The same principle goes for addition or subtraction; whichever comes first is calculated. For example,

• = (8-8) × 1 - 3 + 22 / 2 + 3 (First : solving the parentheses)
• = 0 × 1 - 3 + 22 / 2 + 3 (Second : solve the exponent)
• = 0 × 1 - 3 + 4 / 2 + 3 (Third : solve the multiplication)
• = 0 - 3 + 2 + 3 (Fourth : solve the division) = 0 - 3 + 4 (Fifth : solve the subtraction) = 1 (Sixth: solve the addition)

These examples help us understand how to handle the order of operations using the elegant rule of PEMDAS. Visit Cuemath for more information and practice worksheets related to PEMDAS.