Identify the property of integers being illustrated in each of the following:
a:(-2)(3) �(the "E" letter) element of I
b: (-4)0=0
c: -2(3+4)=-2(3) + (-2)4
d: (-2)3=3(-2)
Identify the property of integers illustrated by the following
a: The property illustrated in this case is the closure property of integers. To identify this property, we need to understand that multiplying two integers always results in another integer. The expression (-2)(3) is the product of -2 and 3, and since (-2)(3) equals -6, which is an integer, it satisfies the closure property.
b: The property illustrated in this case is the zero property of multiplication. The zero property of multiplication states that any number multiplied by zero equals zero. So, when we have (-4) multiplied by 0, the result is always 0.
c: The property illustrated in this case is the distributive property of multiplication over addition. The distributive property states that when we multiply a number by the sum of two other numbers, it is the same as multiplying the number by each of the two numbers individually and then adding the results. In the expression -2(3+4), we can distribute -2 over the parentheses to get -2(3) + -2(4). This expression is equal to -6 + (-8), which simplifies to -14. On the other side of the equation, -2(3) equals -6 and -2(4) equals -8. So, the equation -2(3+4) = -2(3) + (-2)(4) is an example of the distributive property.
d: The property illustrated in this case is the commutative property of multiplication. The commutative property states that the order of multiplication does not affect the result. In the expression (-2)3 = 3(-2), we can see that the order of -2 and 3 is switched, but the result remains the same. Both expressions equal -6, which shows the commutative property of multiplication.
c - distributive
d - commutative