Answer :
To determine which equation reflects the inverse property of multiplication, let's briefly recall what this property states:
The inverse property of multiplication asserts that for any nonzero number [tex]\( a \)[/tex], there exists a number [tex]\( \frac{1}{a} \)[/tex] such that:
[tex]\[ a \cdot \frac{1}{a} = 1 \][/tex]
Now, let's analyze the given equations one by one:
Option 1: [tex]\( 4 + (-4) = 0 \)[/tex]
- This represents the inverse property of addition, not multiplication. It shows that adding a number and its additive inverse (negative) results in zero.
Option 2: [tex]\( -8 + (-3) = -3 + (-8) \)[/tex]
- This equation demonstrates the commutative property of addition, where the order of adding two numbers does not change the result. It doesn't involve multiplication.
Option 3: [tex]\( 2 \cdot \frac{1}{2} = 1 \)[/tex]
- This equation can be rewritten as:
[tex]\[ 2 \cdot \frac{1}{2} = 1 \][/tex]
- Here, the product of 2 and its multiplicative inverse [tex]\( \frac{1}{2} \)[/tex] equals 1, which is exactly the inverse property of multiplication.
Option 4: [tex]\( \frac{8}{5} + 0 = \frac{8}{5} \)[/tex]
- This shows the identity property of addition, which states that adding zero to a number does not change its value. It also does not involve multiplication.
After carefully reviewing each option, none of them explicitly demonstrate the inverse property of multiplication except for reinterpreting part of Option 3. Since the clear, direct representation of [tex]\( a \cdot \frac{1}{a} = 1 \)[/tex] is not present, we conclude:
None of the given equations show the inverse property of multiplication directly.
The inverse property of multiplication asserts that for any nonzero number [tex]\( a \)[/tex], there exists a number [tex]\( \frac{1}{a} \)[/tex] such that:
[tex]\[ a \cdot \frac{1}{a} = 1 \][/tex]
Now, let's analyze the given equations one by one:
Option 1: [tex]\( 4 + (-4) = 0 \)[/tex]
- This represents the inverse property of addition, not multiplication. It shows that adding a number and its additive inverse (negative) results in zero.
Option 2: [tex]\( -8 + (-3) = -3 + (-8) \)[/tex]
- This equation demonstrates the commutative property of addition, where the order of adding two numbers does not change the result. It doesn't involve multiplication.
Option 3: [tex]\( 2 \cdot \frac{1}{2} = 1 \)[/tex]
- This equation can be rewritten as:
[tex]\[ 2 \cdot \frac{1}{2} = 1 \][/tex]
- Here, the product of 2 and its multiplicative inverse [tex]\( \frac{1}{2} \)[/tex] equals 1, which is exactly the inverse property of multiplication.
Option 4: [tex]\( \frac{8}{5} + 0 = \frac{8}{5} \)[/tex]
- This shows the identity property of addition, which states that adding zero to a number does not change its value. It also does not involve multiplication.
After carefully reviewing each option, none of them explicitly demonstrate the inverse property of multiplication except for reinterpreting part of Option 3. Since the clear, direct representation of [tex]\( a \cdot \frac{1}{a} = 1 \)[/tex] is not present, we conclude:
None of the given equations show the inverse property of multiplication directly.
