Parentheses identify a grouped quantity whose value must be determined before the surrounding operations, so evaluating an expression requires working from the innermost grouping outward and then applying multiplication or division before addition or subtraction, from left to right when operations share precedence. This distinguishes structural grouping from a purely left-to-right calculation and supports later work with algebraic expressions; the scope is numerical expressions with whole numbers and the four operations, excluding variables, negative numbers, and more advanced symbolic forms.
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Detailed Explanation: Evaluate numerical expressions with parentheses
Parentheses show which calculation to do first. To evaluate a numerical expression:
- Calculate inside the parentheses, starting with the innermost group.
- Do multiplication and division from left to right.
- Do addition and subtraction from left to right.
Worked example
Evaluate:
Step 1: Calculate inside the parentheses.
Rewrite the expression:
Step 2: Do division and multiplication from left to right.
First divide:
Then multiply:
Now the expression is:
Step 3: Add.
Therefore,
Always use the parentheses first; do not simply calculate from left to right from the beginning.
Learn by doing: Evaluate numerical expressions with parentheses
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Practice:
Order of Operations - Add, Subtract, Multiply, Divide with Parentheses (5 Numbers)
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Download/Modify Free Grade 6 'Evaluate numerical expressions with parentheses' Worksheet
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This Worksheet Includes:
- Order of Operations - Add, Subtract, Multiply, Divide with Parentheses (5 Numbers)
- Order of Operations - Add, Subtract, Multiply, Divide with Parentheses (4 Numbers)
- Order of Operations - Add, Subtract, Multiply, Divide with Parentheses (3 Numbers)
- Order of Operations - Add, Subtract, Multiply with Parentheses (5 Numbers)
- Order of Operations Priority - All Basic Operators with Parentheses
- Order of Operations - Add, Subtract, Multiply with Parentheses (4 Numbers)
- Order of Operations Priority - Add, Subtract with Parentheses
- Order of Operations - Add, Subtract, Multiply with Parentheses (3 Numbers)
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