Question
Identify the property that justifies each step about the answer and the area below. Line 1: (10x)(5y) line 2: 10*(x*5)*y line 3: 10*(5*x)*y line 4: (10*5)(x*y) line 5: 50xy line one to line is: associative property of addition associative property of multiplication commutative property of addition. Commutative property of multiplication or disruptive property. Line 2 to line 3 is: associative property of addition associative property of multiplication commutative property of addition. Commutative property of multiplication or disruptive property. Line 3 to 4 is: associative property of addition associative property of multiplication commutative property of addition. Commutative property of multiplication or disruptive property.
Answers
Answered by
GPT-4o mini
Let's analyze each of the steps and identify the appropriate properties that justify the transitions between them:
1. **Line 1: (10x)(5y)**
**Line 2: 10*(x*5)*y**
**Justification:** This step is justified by the **Associative Property of Multiplication**. It rearranges the grouping of the factors but does not change their product.
2. **Line 2: 10*(x*5)*y**
**Line 3: 10*(5*x)*y**
**Justification:** This step is justified by the **Commutative Property of Multiplication**. It changes the order of the factors inside the parentheses (5 and x).
3. **Line 3: 10*(5*x)*y**
**Line 4: (10*5)(x*y)**
**Justification:** This step is again an application of the **Associative Property of Multiplication**. It groups the factors 10 and 5 together, while also combining x and y.
4. **Line 4: (10*5)(x*y)**
**Line 5: 50xy**
**Justification:** This final step simplifies the product by calculating the multiplication of 10 and 5, which results in 50, and combines that with the product of x and y.
To summarize the properties used for each transition:
- Line 1 to Line 2: **Associative Property of Multiplication**
- Line 2 to Line 3: **Commutative Property of Multiplication**
- Line 3 to Line 4: **Associative Property of Multiplication**
- Line 4 to Line 5: Basic multiplication/combination of terms.
The mention of "distributive property" seems to be a misunderstanding, as it is not applicable in the steps provided.
1. **Line 1: (10x)(5y)**
**Line 2: 10*(x*5)*y**
**Justification:** This step is justified by the **Associative Property of Multiplication**. It rearranges the grouping of the factors but does not change their product.
2. **Line 2: 10*(x*5)*y**
**Line 3: 10*(5*x)*y**
**Justification:** This step is justified by the **Commutative Property of Multiplication**. It changes the order of the factors inside the parentheses (5 and x).
3. **Line 3: 10*(5*x)*y**
**Line 4: (10*5)(x*y)**
**Justification:** This step is again an application of the **Associative Property of Multiplication**. It groups the factors 10 and 5 together, while also combining x and y.
4. **Line 4: (10*5)(x*y)**
**Line 5: 50xy**
**Justification:** This final step simplifies the product by calculating the multiplication of 10 and 5, which results in 50, and combines that with the product of x and y.
To summarize the properties used for each transition:
- Line 1 to Line 2: **Associative Property of Multiplication**
- Line 2 to Line 3: **Commutative Property of Multiplication**
- Line 3 to Line 4: **Associative Property of Multiplication**
- Line 4 to Line 5: Basic multiplication/combination of terms.
The mention of "distributive property" seems to be a misunderstanding, as it is not applicable in the steps provided.
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