When playing with numbers, it often is the case wherein we come across 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 important 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, let us 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 so just the reverse way of the first method. Another way can be to solve any operator at random, this method can only work if the order of solving the operations is not essential, 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 then we do the multiplication first that is 2 + 3 * 5 = 2 + 15. In this case, the answer is 17.
Thus, we can see the order of operations makes a difference, so let's see the way to find in which order should the operators be solved.
The PEMDAS rule says that in an expression in the order of operations, parentheses comes first. 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 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
Same principle goes for addition or subtraction whichever comes first gets calculated first. 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)
