Identify the properties
( 5 + 3) + 4 = ( 3 + 5) + 4 = Communitive property
( 3 × 2) × 8 = 3 × ( 2 × 8) = associative property
To identify the properties used in the provided equations, let's break it down step by step:
Equation 1: (5 + 3) + 4 = (3 + 5) + 4
This equation demonstrates the commutative property of addition. The commutative property states that the order of the numbers being added does not affect the result. In this case, regardless of whether we add 5 and 3 first or 3 and 5 first, the sum will be the same.
To verify this property, you can simplify both sides of the equation:
Left side: (5 + 3) + 4 = 8 + 4 = 12
Right side: (3 + 5) + 4 = 8 + 4 = 12
Since both sides of the equation simplify to the same value, we can conclude that the commutative property is applied.
Equation 2: (3 × 2) × 8 = 3 × (2 × 8)
This equation demonstrates the associative property of multiplication. The associative property states that the grouping of numbers being multiplied does not affect the result. In this case, regardless of whether we multiply 3 and 2 first or 2 and 8 first, the product will be the same.
To verify this property, you can simplify both sides of the equation:
Left side: (3 × 2) × 8 = 6 × 8 = 48
Right side: 3 × (2 × 8) = 3 × 16 = 48
Both sides of the equation simplify to the same value, confirming that the associative property is applied.
By understanding these properties, we can identify and explain how the given equations represent the commutative and associative properties.