The phrase "4 5 divided by 3" represents a mathematical expression that can be interpreted in different ways, leading to varying results. To understand the correct approach, we need to consider the order of operations and the intended meaning of the phrase.
Understanding the Order of Operations
The order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), dictates the sequence in which mathematical operations should be performed. According to PEMDAS, multiplication and division have equal precedence and should be performed from left to right.
Possible Interpretations
There are two primary interpretations of the phrase "4 5 divided by 3":
1. "4 times 5, then divided by 3": This interpretation suggests that the multiplication should be performed first, followed by division. In this case, the calculation would be:
(4 * 5) / 3 = 20 / 3 = 6.67 (approximately)
2. "4 divided by 3, then multiplied by 5": This interpretation implies that the division should be performed first, followed by multiplication. In this case, the calculation would be:
(4 / 3) * 5 = 1.33 * 5 = 6.67 (approximately)
Conclusion
While both interpretations yield the same numerical result (approximately 6.67), it is crucial to understand the intended meaning of the phrase "4 5 divided by 3" to determine the correct order of operations. Without clear context, it is difficult to definitively determine which interpretation is accurate.
In general, it is always best to use parentheses or other grouping symbols to clarify the order of operations in mathematical expressions. This ensures that there is no ambiguity and that everyone understands the intended calculation.
