Who Decided That 13x3 10 Instead of 12 and Why?

The answer to this question might surprise you. The concept of mathematical operations and their order, known as BODMAS, has been a fundamental aspect of mathematics for centuries. However, the origin of BODMAS and its specific order of operations is a mystery often steeped in historical context and practical necessity.

The Rule of BODMAS: A Historical Look

The BODMAS rule is a mnemonic for the order of operations in mathematics. It stands for B - Brackets, O - Orders (exponents and roots), D - Division, M - Multiplication, A - Addition, and S - Subtraction. This rule ensures consistency in solving mathematical expressions, making them solvable in a standardized manner.

The Importance of BODMAS

The choice of multiplication over addition in BODMAS might seem arbitrary, but it has practical roots. Consider a practical scenario where you are buying apples for your family. If your father asks you to buy 2 apples per person, for 3 family members, and for 3 meals a day, you would calculate it as follows:

Representing the Problem Mathematically:

2 apples x 3 persons x 3 times a day 233 18

Alternatively, you can solve it step-by-step:

2 apples eaten by you in the morning, 2 eaten by your first brother in the morning, and 2 eaten by your second brother in the morning 2 2 2 6 (morning total)

Similarly, total in the evening 2 2 2 6 (evening total)

Total in the night 2 2 2 6 (night total)

Total in a day 6 6 6 18

Complex Calculations in BODMAS

Consider a more complex scenario where your father also eats an apple in the morning:

2 apples 1 (your father's) in the morning 2 apples x 2 brothers x 2 times a day (evening and night) 2 1 22222 22222 19

When you express it as a single operation using BODMAS,

2331 19

This example clearly illustrates why BODMAS is necessary. The rule ensures that multiplications and divisions are solved first, followed by additions and subtractions, thus providing consistent and accurate results.

Alternative Order: BODAMS?

If you were to challenge the conventional BODMAS rule and propose an alternative, like BODAMS (Brackets, Orders, Division, Multiplication, Addition, Subtraction), it could indeed simplify some problems. However, such a change might lead to confusion and inconsistency in mathematical expressions. For instance, consider the following:

1332 (without BODMAS)

If we follow BODMAS, we calculate it as:

13 x 3 39 (multiplication first) then 39 2 41 (addition next)

But if we follow BODAMS, it would be:

13 x 3 39 (multiplication first), then 39 2 41 (addition next)

In this specific case, the results are the same, but in other cases, they might not be. Hence, the BODMAS rule remains a universally accepted standard in mathematics.

Conclusion

Mathematics is as much about practical application as it is about theoretical consistency. The BODMAS rule ensures that mathematical expressions are solved in a systematic and unambiguous manner. While history might not shed light on the specific reasons behind this rule, its effectiveness is evident in the countless practical scenarios it addresses.

So, next time you see an expression like 133, remember why 13 x 3 equals 10, not 12, and appreciate the-order-of-operations rule that keeps mathematics structured and reliable.