Question

The Commutative Property
a+ b=b+=____
5-4 ? 4-5
1≠ -1
5 + (-4) = (__)+5
1 = 1

Answer 1

Let's break down each part of your prompt using the Commutative Property and basic arithmetic concepts:

1. **Commutative Property**:
The Commutative Property states that for addition and multiplication, changing the order of the operands does not change the result. That is:
- For addition: \( a + b = b + a \)
- For multiplication: \( a \times b = b \times a \)

Given the expression you provided, it looks like there is a small error in the notation: `a + b = b += ____`. This should likely read as \( a + b = b + a \).

2. **Evaluating \( 5 - 4 ? 4 - 5 \)**:
To evaluate \( 5 - 4 \) and \( 4 - 5 \):
- \( 5 - 4 = 1 \)
- \( 4 - 5 = -1 \)
Thus, \( 5 - 4 \neq 4 - 5 \) because \( 1 \neq -1 \). So, the correct relationship is:
\( 5 - 4 \neq 4 - 5 \).

3. **Filling in the Blank - \( 5 + (-4) = (__)+5 \)**:
Here, we are looking to maintain equality with \( 5 + (-4) \):
- \( 5 + (-4) = 1 \)
To keep the equation true, we can use the commutative property:
- Since \( 5 + (-4) = (-4) + 5 = 1 \)
Thus, \( 5 + (-4) = __ + 5 \) where the blank can be filled with \( -4 \):
- Therefore, the answer is \( 5 + (-4) = (-4) + 5 \).

4. **Final Statement**:
The statement \( 1 = 1 \) is a true statement, indicating equality.

Putting it all together:

1. \( a + b = b + a \)
2. \( 5 - 4 = 1, \quad 4 - 5 = -1 \quad (1 \neq -1) \)
3. \( 5 + (-4) = -4 + 5 \)
4. \( 1 = 1 \)

If there are any more specific questions or if you'd like further clarification, feel free to ask!