Question
Explain the correct Order of Operations and given an example in your explanation. (2 points)
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GPT 3.5
The correct order of operations, also known as PEDMAS or PEMDAS, is a set of rules used to determine the sequence in which mathematical operations should be performed in an expression.
The order of operations is as follows:
1. Parentheses: Perform operations within parentheses first. This allows us to simplify expressions within parentheses before applying any other operations. For example, consider the expression 2 * (3 + 4). According to the order of operations, we first evaluate what's inside the parentheses, so 3 + 4 equals 7. Then, we multiply 2 by 7 to get the final result of 14.
2. Exponents: Next, we evaluate any exponentiation operations. If an expression contains an exponent, such as 2^3, we raise the base to the power of the exponent. For instance, 2^3 equals 2 * 2 * 2, resulting in a value of 8.
3. Division and Multiplication: From left to right, perform all division and multiplication operations. These operations are given equal priority. For example, in the expression 8 / 4 * 2, we first divide 8 by 4 to get 2. Then, we multiply 2 by 2, giving us the final answer of 4.
4. Addition and Subtraction: Finally, perform all addition and subtraction operations from left to right. Like division and multiplication, these operations have equal priority. For instance, in the expression 5 - 2 + 3, we first subtract 2 from 5 to get 3. Then, we add 3 to 3, resulting in a final answer of 6.
It is important to follow the correct order of operations to ensure accurate calculations in mathematics. By adhering to these rules, we can avoid confusion and ambiguity when solving complex mathematical expressions.
The order of operations is as follows:
1. Parentheses: Perform operations within parentheses first. This allows us to simplify expressions within parentheses before applying any other operations. For example, consider the expression 2 * (3 + 4). According to the order of operations, we first evaluate what's inside the parentheses, so 3 + 4 equals 7. Then, we multiply 2 by 7 to get the final result of 14.
2. Exponents: Next, we evaluate any exponentiation operations. If an expression contains an exponent, such as 2^3, we raise the base to the power of the exponent. For instance, 2^3 equals 2 * 2 * 2, resulting in a value of 8.
3. Division and Multiplication: From left to right, perform all division and multiplication operations. These operations are given equal priority. For example, in the expression 8 / 4 * 2, we first divide 8 by 4 to get 2. Then, we multiply 2 by 2, giving us the final answer of 4.
4. Addition and Subtraction: Finally, perform all addition and subtraction operations from left to right. Like division and multiplication, these operations have equal priority. For instance, in the expression 5 - 2 + 3, we first subtract 2 from 5 to get 3. Then, we add 3 to 3, resulting in a final answer of 6.
It is important to follow the correct order of operations to ensure accurate calculations in mathematics. By adhering to these rules, we can avoid confusion and ambiguity when solving complex mathematical expressions.
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