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Chapter 1: Problem 105

Why is the order of operations agreement needed?

Short Answer

Expert verified
The order of operations agreement is needed to ensure consistency and prevent ambiguity in mathematical calculations by specifying the sequence of operations to be performed. It ensures that everyone gets the same result when calculating a mathematical expression.

Step by step solution

01

Explain the Concept

The Order of Operations is a set of rules that dictate the sequence of operations to be performed when simplifying expressions. It is needed due to the different operations that might be used in these expressions - addition, subtraction, multiplication, division, exponentiation, and parentheses.
02

Illustrate the Rule

The acronym PEMDAS is commonly used to remember the order of operations. It stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). Following this rule ensures that everyone gets the same result when calculating a mathematical expression.
03

Provide an Example

Consider the following example: \(7 + 5 \times 2\). Using the PEMDAS rule, we perform multiplication first, followed by the addition. Hence, we calculate \(5 \times 2 = 10\) first, and then add 7 to the result, giving \(7 + 10 = 17\). If operations were done in random order, say addition before multiplication, we would incorrectly get \(7 + 5 = 12\), and then multiply it by 2 to get 24, which is an incorrect result. The order of operations eliminates ambiguity and ensures uniformity in the calculation process, and so it is needed.

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