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Questions and Answers
The _______________ Property states that the order of addends does not change the result in addition.
Commutative
The _______________ Property states that the order of factors does not change the result in multiplication.
Commutative
In subtraction, the order of operands is _______________ and does change the result.
not commutative
In multiplication, the order in which factors are grouped does not change the result, this is known as the _______________ Property.
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The _______________ Property allows multiplication to be distributed over addition.
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The order of operands in division does _______________ the result.
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Study Notes
Combined Operations
Combined operations involve performing multiple mathematical operations in a specific order to evaluate an expression. The order of operations is crucial to ensure accurate results.
Order of Operations
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate addition and subtraction operations from left to right.
Addition
- Commutative Property: The order of addends does not change the result. (e.g., 2 + 3 = 3 + 2)
- Associative Property: The order in which addends are grouped does not change the result. (e.g., (2 + 3) + 4 = 2 + (3 + 4))
Subtraction
- Not Commutative: The order of operands does change the result. (e.g., 2 - 3 ≠3 - 2)
- Not Associative: The order in which operands are grouped does change the result. (e.g., (2 - 3) - 4 ≠2 - (3 - 4))
Multiplication
- Commutative Property: The order of factors does not change the result. (e.g., 2 × 3 = 3 × 2)
- Associative Property: The order in which factors are grouped does not change the result. (e.g., (2 × 3) × 4 = 2 × (3 × 4))
- Distributive Property: Multiplication can be distributed over addition. (e.g., 2 × (3 + 4) = 2 × 3 + 2 × 4)
Division
- Not Commutative: The order of operands does change the result. (e.g., 2 ÷ 3 ≠3 ÷ 2)
- Not Associative: The order in which operands are grouped does change the result. (e.g., (2 ÷ 3) ÷ 4 ≠2 ÷ (3 ÷ 4))
Remember to follow the order of operations when evaluating expressions that involve multiple combined operations.
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Description
Evaluate mathematical expressions by following the correct order of operations. Learn the rules for combining addition, subtraction, multiplication, and division operations. Practice with examples to master the basics.
