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Which properties does multiplication have?
- a)Distributive, Cumulative, Associative
- b)Commutative, Associative, Identity
- c)Associative, Distributive, Identity
- d)Commutative, Cumulative, Identity
Correct answer is option 'A'. Can you explain this answer?
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Which properties does multiplication have?a)Distributive, Cumulative, ...
Multiplication is distributive, cumulative, and associative. It follows the distributive property, meaning a * (b + c) is equal to (a * b) + (a * c). It is also cumulative, as multiplying a number by another number multiple times is equivalent to adding that number repeatedly. Additionally, multiplication is associative, meaning the grouping of numbers being multiplied does not affect the result.
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Which properties does multiplication have?a)Distributive, Cumulative, ...
Understanding Properties of Multiplication
Multiplication is a fundamental mathematical operation that has several important properties. Let's explore these properties in detail.
1. Distributive Property
- This property states that multiplying a number by a sum is the same as multiplying each addend separately and then adding the results.
- For example: \( a \times (b + c) = (a \times b) + (a \times c) \).
2. Commutative Property
- The commutative property indicates that the order of multiplication does not affect the product.
- For example: \( a \times b = b \times a \). This means that \( 3 \times 4 = 4 \times 3 \), both resulting in 12.
3. Associative Property
- According to the associative property, how numbers are grouped in multiplication does not change the product.
- For example: \( (a \times b) \times c = a \times (b \times c) \). This means \( (2 \times 3) \times 4 = 2 \times (3 \times 4) = 24 \).
Conclusion
Each of these properties plays a crucial role in simplifying calculations and understanding multiplication.
- By using the **distributive property**, complex problems can be broken down.
- The **commutative property** allows flexibility in calculation order.
- The **associative property** provides the ability to group numbers for easier computation.
These properties are foundational in mathematics, making option 'A' the correct answer as it encompasses the essential properties of multiplication.
Multiplication is a fundamental mathematical operation that has several important properties. Let's explore these properties in detail.
1. Distributive Property
- This property states that multiplying a number by a sum is the same as multiplying each addend separately and then adding the results.
- For example: \( a \times (b + c) = (a \times b) + (a \times c) \).
2. Commutative Property
- The commutative property indicates that the order of multiplication does not affect the product.
- For example: \( a \times b = b \times a \). This means that \( 3 \times 4 = 4 \times 3 \), both resulting in 12.
3. Associative Property
- According to the associative property, how numbers are grouped in multiplication does not change the product.
- For example: \( (a \times b) \times c = a \times (b \times c) \). This means \( (2 \times 3) \times 4 = 2 \times (3 \times 4) = 24 \).
Conclusion
Each of these properties plays a crucial role in simplifying calculations and understanding multiplication.
- By using the **distributive property**, complex problems can be broken down.
- The **commutative property** allows flexibility in calculation order.
- The **associative property** provides the ability to group numbers for easier computation.
These properties are foundational in mathematics, making option 'A' the correct answer as it encompasses the essential properties of multiplication.
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Which properties does multiplication have?a)Distributive, Cumulative, Associativeb)Commutative, Associative, Identityc)Associative, Distributive, Identityd)Commutative, Cumulative, IdentityCorrect answer is option 'A'. Can you explain this answer?
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