Final answer:
The importance of the order of operations lies in ensuring consistent results across mathematical calculations. Without this order, outcomes vary significantly, such as the difference between 3 x (2 + 5) and 3 x 2 + 5, which highlight the use of parentheses.
Step-by-step explanation:
The order of operations is essential in mathematics to ensure that equations are solved in a systematic and universally agreed-upon manner. This set of rules dictates the sequence in which operations should be performed in an expression to obtain the correct result.
For example, consider the expression 3 + 4 x 2. Without applying the order of operations, one might simply calculate from left to right, yielding (3 + 4) x 2 = 7 x 2 = 14. However, according to the order of operations, multiplication comes before addition. Therefore, the correct calculation is 3 + (4 x 2) = 3 + 8 = 11.
Parentheses indicate which operations should be carried out first but, in their absence, we use the established sequence: multiplication and division before addition and subtraction.
Incorrectly using or not using parentheses can lead to different outcomes. For instance, 3 x (2 + 5) and 3 x 2 + 5 would yield different results as parentheses change the order in which the operations are performed.