Question
For the following problem, match the name of the number property that was used to get to each step from the previous step.
37 · 2 · (-5 + 1^2 + 5)
1. 37 · 2 · (-5 + 5 + )
commutative property
2. 37 · 2 · (0 + )
identity property of addition
3. 37 · 2 ·
inverse property of multiplication
4. 37 · 1
identity property of multiplication
5. 37
inverse property of addition
37 · 2 · (-5 + 1^2 + 5)
1. 37 · 2 · (-5 + 5 + )
commutative property
2. 37 · 2 · (0 + )
identity property of addition
3. 37 · 2 ·
inverse property of multiplication
4. 37 · 1
identity property of multiplication
5. 37
inverse property of addition
Answers
GPT-4o mini
Let's break down the steps and match them with the appropriate properties:
1. **Step: 37 · 2 · (-5 + 5 + 0)**
- **Description**: In this step, the +1^2 (which equals 1) is replaced by +5 (from -5 + 5 = 0) and it adds 0.
- **Property Used**: **Commutative Property** (to change the order of addition).
2. **Step: 37 · 2 · (0 + 0)**
- **Description**: Simplifying -5 + 5 to 0.
- **Property Used**: **Identity Property of Addition** (adding 0 does not change the value).
3. **Step: 37 · 2 · (0)**
- **Description**: Since anything added to zero remains zero.
- **Property Used**: **Inverse Property of Addition** (adding the inverse (5 and -5) results in zero).
4. **Step: 37 · 1**
- **Description**: Since multiplying by zero gives zero.
- **Property Used**: **Identity Property of Multiplication** (multiplying 1 does not change the value).
5. **Step: 37**
- **Description**: Finally simplifying just to 37.
- **Property Used**: **Inverse Property of Multiplication** (removing the one from multiplication leaves the original number).
Here is the corrected list with matched properties:
1. **Commutative Property**
2. **Identity Property of Addition**
3. **Inverse Property of Addition**
4. **Identity Property of Multiplication**
5. **Inverse Property of Multiplication**
Please note that in the original assignment of properties above the steps, there might be some mismatches based on the typical properties used in addition and multiplication—much of this interpretation depends on the specific operations leading to the final value.
1. **Step: 37 · 2 · (-5 + 5 + 0)**
- **Description**: In this step, the +1^2 (which equals 1) is replaced by +5 (from -5 + 5 = 0) and it adds 0.
- **Property Used**: **Commutative Property** (to change the order of addition).
2. **Step: 37 · 2 · (0 + 0)**
- **Description**: Simplifying -5 + 5 to 0.
- **Property Used**: **Identity Property of Addition** (adding 0 does not change the value).
3. **Step: 37 · 2 · (0)**
- **Description**: Since anything added to zero remains zero.
- **Property Used**: **Inverse Property of Addition** (adding the inverse (5 and -5) results in zero).
4. **Step: 37 · 1**
- **Description**: Since multiplying by zero gives zero.
- **Property Used**: **Identity Property of Multiplication** (multiplying 1 does not change the value).
5. **Step: 37**
- **Description**: Finally simplifying just to 37.
- **Property Used**: **Inverse Property of Multiplication** (removing the one from multiplication leaves the original number).
Here is the corrected list with matched properties:
1. **Commutative Property**
2. **Identity Property of Addition**
3. **Inverse Property of Addition**
4. **Identity Property of Multiplication**
5. **Inverse Property of Multiplication**
Please note that in the original assignment of properties above the steps, there might be some mismatches based on the typical properties used in addition and multiplication—much of this interpretation depends on the specific operations leading to the final value.