Which equation demonstrates the multiplicative identity property?
[tex](-2+8)+0-4+6[/tex]
[tex](-3+6)(1)-3+61[/tex]
[tex](-3+6)(3+5)-10+30[/tex]
Answer (2)
The equation that demonstrates the multiplicative identity property is ( − 3 + 6 ) ( 1 ) − 3 + 61 because it includes a multiplication by 1, affirming that a × 1 = a . The other equations do not exhibit this property as they lack this specific multiplication. Thus, the correct choice is the second equation.
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The multiplicative identity property states that a × 1 = a .
The first equation ( − 2 + 8 ) + 0 − 4 + 6 does not involve multiplication by 1.
The second equation ( − 3 + 6 ) ( 1 ) − 3 + 61 demonstrates the property because ( − 3 + 6 ) × 1 = ( − 3 + 6 ) .
The third equation ( − 3 + 6 ) ( 3 + 5 ) − 10 + 30 does not involve multiplication by 1.
Therefore, the equation that demonstrates the multiplicative identity property is ( − 3 + 6 ) ( 1 ) − 3 + 61 .
Explanation
Understanding the Multiplicative Identity Property The question asks us to identify which equation demonstrates the multiplicative identity property. This property states that any number multiplied by 1 equals itself, i.e., a × 1 = a . We need to check each given equation to see if it fits this property.
Analyzing the First Equation Let's analyze the first equation: ( − 2 + 8 ) + 0 − 4 + 6 . This equation involves addition and subtraction. There is no multiplication by 1, so it does not demonstrate the multiplicative identity property.
Analyzing the Second Equation Now, let's examine the second equation: ( − 3 + 6 ) ( 1 ) − 3 + 61 . This equation includes multiplication by 1. Let's simplify the expression ( − 3 + 6 ) .
( − 3 + 6 ) = 3
Verifying the Multiplicative Identity Now, let's multiply the result by 1: 3 × 1 = 3
Since ( − 3 + 6 ) ( 1 ) = ( − 3 + 6 ) , this equation demonstrates the multiplicative identity property. The rest of the terms in the equation, − 3 + 61 , do not affect whether the multiplicative identity property is demonstrated within the first part of the expression.
Analyzing the Third Equation Finally, let's analyze the third equation: ( − 3 + 6 ) ( 3 + 5 ) − 10 + 30 . This equation involves multiplication, but not by 1. Therefore, it does not demonstrate the multiplicative identity property.
Conclusion Therefore, the equation that demonstrates the multiplicative identity property is ( − 3 + 6 ) ( 1 ) − 3 + 61 .
Examples
The multiplicative identity property is fundamental in algebra and arithmetic. For example, when scaling a recipe, if you multiply the amount of each ingredient by 1, you keep the recipe the same. Similarly, in computer graphics, multiplying a vector by an identity matrix (which contains 1s along the diagonal) leaves the vector unchanged, preserving the object's shape and position.
