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What property allows you to compute 1/3 × (6 × 4/3) as (1/3 × 6) × 4/3?
- a)Associative Property
- b)Distributive property
- c)Commutative property
- d)None of the above
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
What property allows you to compute 1/3 × (6 × 4/3) as (1/...
Understanding the Associative Property
The Associative Property is a fundamental principle in arithmetic that allows you to group numbers in different ways without changing the result of the operation.
Key Features of the Associative Property:
- It applies to addition and multiplication.
- It states that the way in which numbers are grouped does not affect the sum or product.
Example in Context:
In the expression 1/3 × (6 × 4/3), the operation inside the parentheses (6 × 4/3) is computed first. According to the Associative Property, we can also group the numbers differently:
- (1/3 × 6) × 4/3
Both expressions yield the same final result due to the property of associativity in multiplication.
Why the Correct Answer is 'A':
- The operation you are performing with fractions—multiplying them—allows for regrouping.
- By using the Associative Property, you can rearrange the expression without altering the outcome.
Other Properties Explained:
- Distributive Property: This is used when you multiply a single term by terms in parentheses, but it does not apply here.
- Commutative Property: This property states that changing the order of numbers does not affect the sum or product, but it does not explain regrouping.
In conclusion, the ability to regroup numbers in multiplication is what identifies the Associative Property, making option 'A' the correct answer to the question.
The Associative Property is a fundamental principle in arithmetic that allows you to group numbers in different ways without changing the result of the operation.
Key Features of the Associative Property:
- It applies to addition and multiplication.
- It states that the way in which numbers are grouped does not affect the sum or product.
Example in Context:
In the expression 1/3 × (6 × 4/3), the operation inside the parentheses (6 × 4/3) is computed first. According to the Associative Property, we can also group the numbers differently:
- (1/3 × 6) × 4/3
Both expressions yield the same final result due to the property of associativity in multiplication.
Why the Correct Answer is 'A':
- The operation you are performing with fractions—multiplying them—allows for regrouping.
- By using the Associative Property, you can rearrange the expression without altering the outcome.
Other Properties Explained:
- Distributive Property: This is used when you multiply a single term by terms in parentheses, but it does not apply here.
- Commutative Property: This property states that changing the order of numbers does not affect the sum or product, but it does not explain regrouping.
In conclusion, the ability to regroup numbers in multiplication is what identifies the Associative Property, making option 'A' the correct answer to the question.
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Community Answer
What property allows you to compute 1/3 × (6 × 4/3) as (1/...
The property used here is the Associative Property of Multiplication. This property states that the grouping of numbers in multiplication does not affect the product. In other words, for any numbers a, b, and c, we have:
a × (b × c) = (a × b) × c
In this case:
1/3 × (6 × 4/3) = (1/3 × 6) × 4/3
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