Identify the property illustrated in each statement. Assume all variables represent real numbers. 5(t+3) = (t+3)∙5

Verified step by step guidance

1. Observe the given equation: \(5(t+3) = (t+3) * 5\). This shows that the order of multiplication between the number 5 and the expression \((t+3)\) can be switched without changing the result.
2. Recall the properties of real numbers, specifically the Commutative Property of Multiplication, which states that for any real numbers \(a\) and \(b\), \(a \times b = b \times a\).
3. Compare the given equation to the Commutative Property of Multiplication: here, \(a = 5\) and \(b = (t+3)\), so \(5(t+3) = (t+3)5\) fits the property exactly.
4. Conclude that the property illustrated by the equation \(5(t+3) = (t+3) * 5\) is the Commutative Property of Multiplication.
5. Remember that this property allows us to multiply numbers or expressions in any order without affecting the product.

Key Concepts

Properties of Real Numbers

Properties of real numbers are rules that govern arithmetic operations. They include commutative, associative, distributive, identity, and inverse properties, which help simplify and manipulate expressions.

Commutative Property of Multiplication

The commutative property of multiplication states that changing the order of factors does not change the product. For example, a × b = b × a for any real numbers a and b.

Algebraic Expressions and Variables

Algebraic expressions combine variables and constants using operations. Understanding how to manipulate expressions with variables is essential for applying properties like commutativity correctly.