To identify which equations illustrate the commutative, identity, and associative properties, we need to understand what each property means:
1. Commutative Property: This property states that the order of the operands does not affect the result of addition or multiplication. For example, a + b = b + a and a * b = b * a.
2. Identity Property: This property states that there exist special values (called identity elements) such that when they are combined with any other value through addition or multiplication, the result remains unchanged. For example, a + 0 = a and a * 1 = a.
3. Associative Property: This property states that the grouping of operands does not affect the result of addition or multiplication. For example, (a + b) + c = a + (b + c) and (a * b) * c = a * (b * c).
Now let's examine each equation one by one to determine the property they illustrate:
-7 . 1 = -7: This equation illustrates the identity property for multiplication because any number multiplied by 1 remains unchanged.
3 + (7+19) = (3+7)+19: This equation illustrates the associative property for addition because changing the grouping of the parentheses does not affect the sum.
8 . 7 . 6 = 8 7 6: This equation does not illustrate any specific property. It is simply a multiplication expression.
99+0=99: This equation illustrates the identity property for addition because adding 0 to any number does not change its value.
2 (4 . 11) = 2 (4 . 11): This equation illustrates the commutative property for multiplication because the order of the operands does not affect the result.
5-3-=3-5: This equation does not illustrate any specific property. It is an incorrect equation and does not follow the rules of arithmetic.
1 (-99) = 99: This equation does not illustrate any specific property. It is a multiplication expression.
0.4 + 2.3 = 2.3 + 0.4: This equation illustrates the commutative property for addition because the order of the operands does not affect the sum.
Therefore, to summarize:
- Identity property: -7 . 1 = -7, 99+0=99
- Associative property: 3 + (7+19) = (3+7)+19
- Commutative property: 2 (4 . 11) = 2 (4 . 11), 0.4 + 2.3 = 2.3 + 0.4
- None of the above properties: 8 . 7 . 6, 5-3-=3-5, 1 (-99)