PEMDAS/BODMAS/BIDMAS and Verbal Math Problems - Do the Rules Still Apply?

When a math problem is stated verbally, does the order of operations, as guided by PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction), or BIDMAS (Brackets, Indices, Division and Multiplication, Addition and Subtraction), still apply? The answer is yes, but it depends on how the problem is presented.

The Role of PEMDAS/BODMAS/BIDMAS

These acronyms help remember the order of operations which is crucial for solving mathematical equations correctly. The order of operations dictates the sequence in which mathematical operations should be performed:

Parentheses/Brackets: Solve expressions in parentheses or brackets first. Exponents/Orders/Indices: Next, solve exponents or powers. Multiplication and Division: Perform these operations from left to right. Addition and Subtraction: Finally, perform these operations from left to right.

Verbal vs. Written Problems

Whether a math problem is written down or stated verbally, the same rules of PEMDAS/BODMAS/BIDMAS apply. However, the key lies in how the problem is framed in the verbal statement:

Written Example: 3 – 4 x 5

If you solve this following the left-to-right rule, you add first and then multiply:

3 – 4 x 5 3 – 20 -17

However, using PEMDAS/BODMAS/BIDMAS, the order of operations is:

1. Parentheses/Brackets (none here) 2. Exponents/Orders/Indices (none here) 3. Multiplication and Division (from left to right): 4 x 5 20, then 3 – 20 -17

Verbal Example: “3 plus 4 times 5”

When presented as a verbal statement, “3 plus 4 times 5,” the implicit rules of PEMDAS/BODMAS/BIDMAS come into play:

1. Exponents/Orders/Indices (none here) 2. Multiplication and Division (from left to right): 4 x 5 20, then 3 20 23

Implications of Verbal Presentation

When a problem is presented verbally, the way it is stated can influence how the order of operations is applied. Consider these two scenarios:

Scenario 1: Add 3, then multiply by 5

In this case, you should not apply the order of operations. Instead, perform the operations in the order they are presented:

1. Add 3 and 4: 3 4 7 2. Multiply 7 by 5: 7 x 5 35

Scenario 2: 3 plus 4 times 5

Here, the verbal statement “3 plus 4 times 5” implies an implicit pair of brackets around 3 4, making it equivalent to 3 (4 x 5). Using the order of operations:

1. Exponents/Orders/Indices (none here) 2. Multiplication: 4 x 5 20, then 3 20 23

Conclusion

To summarize, the rules of PEMDAS/BODMAS/BIDMAS do apply when a math problem is stated verbally. However, the key is in how the problem is presented. If the problem is clearly stated with an order that directly follows the operations, the rules of order of operations may still hold. If the verbal statement implicitly groups operations, the order of operations should be applied accordingly.

The order of operations is a fundamental concept in mathematics that ensures consistency in solving problems. Understanding how these rules apply to both written and verbal problems is crucial for accurate mathematical communication.