Properties of Multiplication

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What does the commutative property of multiplication state?
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The commutative property of multiplication states that the order of factors does not change the product, such as a × b = b × a.
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Define the associative property of multiplication.
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The associative property of multiplication states that how numbers are grouped in a multiplication problem does not affect the product, like (a × b) × c = a × (b × c).
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What is the identity property of multiplication?
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The identity property of multiplication states that any number multiplied by 1 equals the number itself, such as a × 1 = a.
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Explain the zero property of multiplication.
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The zero property of multiplication states that any number multiplied by zero will result in zero, like a × 0 = 0.
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What is the distributive property of multiplication over addition?
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The distributive property states that a(b + c) = ab + ac. It allows us to multiply a single term by terms inside a parenthesis.
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How can we use the commutative property with larger numbers?
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For larger numbers, we can rearrange factors to make multiplication easier, e.g., 5 × 12 × 2 can become (5 × 2) × 12 = 10 × 12.
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Why is the associative property helpful?
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The associative property helps simplify multiplication by allowing us to regroup numbers, such as calculating (3 × 4) × 5 by first finding 3 × (4 × 5).
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Does the commutative property apply to division?
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No, the commutative property does not apply to division since changing the order of division changes the result.
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Give an example of the identity property using fractions.
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For fractions, (1/2) × 1 = 1/2. The fraction remains the same when multiplied by one.
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Can the zero property be applied to addition?
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No, the zero property is specific to multiplication. In addition, adding zero doesn't change the value (identity property of addition).
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How can the distributive property simplify 4 × (6 + 3)?
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Using the distributive property, 4 × (6 + 3) becomes (4 × 6) + (4 × 3) = 24 + 12 = 36.
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What is a real-life example of the distributive property?
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If you have 4 bags, each with 3 apples and 2 oranges, the total can be found as 4(3 + 2), which is (4 × 3) apples + (4 × 2) oranges.
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Which property would you use to compute 9 × 1 faster?
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The identity property of multiplication states 9 × 1 = 9, simplifying the computation without changes.
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Why does 8 × 0 equal 0?
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Based on the zero property of multiplication, any number multiplied by zero equals zero, so 8 × 0 = 0.
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How can we verify the distributive property with numbers?
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Verify with numbers, e.g., for 2(5 + 3), check that it equals (2 × 5) + (2 × 3), both resulting in 16.
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