Explain how the order of operations determines how you simplify a numeric expression. explain the rules for addition, subtraction, multiplication, division, and the use of grouping symbols.
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The order of operations is a set of rules that determines the sequence in which mathematical operations should be performed to simplify a numeric expression. These rules help ensure consistent and accurate calculation results. The order of operations consists of the following:
1. Parentheses or Grouping Symbols:
Start by simplifying any expressions within parentheses or grouping symbols, such as brackets or braces. Evaluate these expressions first and work from the inside out.
2. Exponents or Powers:
Next, evaluate any exponential expressions or powers. Raise the base number to the given exponent.
3. Multiplication and Division:
Perform multiplication and division from left to right. If an expression contains both multiplication and division, evaluate them in the order they appear (from left to right).
4. Addition and Subtraction:
Finally, perform addition and subtraction from left to right. Similar to multiplication and division, if an expression contains both addition and subtraction, evaluate them in the order they appear (from left to right).
It is important to note that multiplication and division have the same precedence, and addition and subtraction have the same precedence. However, while evaluating an expression, you should always perform multiplication or division before addition or subtraction if they appear together.
To simplify a numeric expression, you need to follow the order of operations. Let's take an example:
2 + 3 × 4 - (8 ÷ 2)
1. Start with parentheses: There's a set of parentheses "(8 ÷ 2)" in the expression. In this step, we simplify the expression within the parentheses. The division 8 ÷ 2 equals 4. So, the expression becomes:
2 + 3 × 4 - 4
2. Next, perform multiplication: Multiply 3 by 4. The result is 12. The expression becomes:
2 + 12 - 4
3. Finally, perform addition and subtraction from left to right: Add 2 and 12, which equals 14. Then, subtract 4 from 14. The final result is:
14 - 4 = 10
So, the simplified value of the original expression is 10.
By following the order of operations, you can systematically solve numeric expressions and avoid any ambiguity or confusion.