The Mystery Of "1 3 X 5 6": Understanding The Order Of Operations

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Introduction

As a math teacher, I have encountered several students who struggle with the concept of order of operations. One common question I receive is regarding the expression "1 3 x 5 6." Students often wonder what the correct answer is and why there is confusion in the first place. In this article, I will explain the concept of order of operations and provide a solution to the mystery of "1 3 x 5 6."

What is Order of Operations?

Order of operations is a set of rules that dictate the order in which mathematical operations should be performed. The acronym PEMDAS is often used to remember the order: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. This means that when there are multiple operations in an expression, we must perform them in a specific order to arrive at the correct answer.

The Mystery of "1 3 x 5 6"

The confusion surrounding "1 3 x 5 6" arises from the absence of parentheses, which would indicate which operations to perform first. Without parentheses, we must rely on the order of operations to determine the correct answer.

Multiplication and Addition

Looking at the expression, we see that it contains both multiplication and addition. According to PEMDAS, we must perform multiplication before addition. However, there is no indication of which of the two multiplication operations to perform first.

Associative Property

In the absence of parentheses, we can use the associative property of multiplication to help us. The associative property states that the grouping of factors in a multiplication operation does not affect the product. In other words, we can rearrange the order of the factors without changing the answer. For example, 2 x 3 x 4 is the same as 4 x 2 x 3.

The Solution

Using the associative property, we can rewrite "1 3 x 5 6" as (1 x 3) x (5 x 6). This allows us to perform the multiplication operations first, as follows: (1 x 3) x (5 x 6) = 3 x 30 Now, we can perform the multiplication operation and arrive at the final answer: 3 x 30 = 90 Therefore, the solution to the mystery of "1 3 x 5 6" is 90.

Conclusion

The concept of order of operations is crucial in mathematics, and it is important for students to understand it to avoid confusion and arrive at the correct answers. The mystery of "1 3 x 5 6" highlights the importance of using parentheses to indicate the order of operations. In the absence of parentheses, we can use the associative property to help us determine the correct order. By following the rules of order of operations, we can solve mathematical expressions with confidence and accuracy.