Sure, let's analyze each of the equations to determine which one demonstrates the inverse property of multiplication.
1. Equation: [tex]\(4 + (-4) = 0\)[/tex]
- This equation shows the inverse property of addition. It indicates that adding a number and its additive inverse (or opposite) results in zero. In this case, 4 and -4 are additive inverses.
2. Equation: [tex]\(-8 + (-3) = -3 + (-8)\)[/tex]
- This equation shows the commutative property of addition. It demonstrates that the sum remains the same regardless of the order in which the numbers are added.
3. Equation: [tex]\(2 \cdot \frac{1}{2} = 1\)[/tex]
- This equation accurately represents the inverse property of multiplication. According to this property, the product of a non-zero number and its multiplicative inverse (or reciprocal) is always 1. Here, 2 multiplied by [tex]\(\frac{1}{2}\)[/tex] equals 1, indicating that [tex]\(\frac{1}{2}\)[/tex] is the reciprocal of 2.
4. Equation: [tex]\(\frac{8}{5} + 0 = \(\frac{8}{5}\)[/tex]
- This equation demonstrates the identity property of addition, which states that any number added to zero remains unchanged. Here, adding zero to [tex]\(\frac{8}{5}\)[/tex] does not change its value.
Based on this detailed analysis, the equation that shows the inverse property of multiplication is:
[tex]\[ 2 \cdot \frac{1}{2} = 1 \][/tex]
Therefore, the correct answer is the third equation.
