Math / Numbers & Operations

Question27 Which property does the equation below demonstrate? $3(-5 \cdot 10)=(-5 \cdot 10) 3$ (A) Commutative Property of Multiplication (B) Associative Property of Multiplication (C) Identity Property of Multiplication (D) Distributive Property

Studdy Solution

STEP 1

1. We are given the equation $3(-5 \cdot 10) = (-5 \cdot 10)3$ .
2. We need to identify which property of multiplication the equation demonstrates.
3. The options provided are standard properties of multiplication.

STEP 2

1. Understand the properties of multiplication.
2. Analyze the given equation.
3. Identify the property demonstrated by the equation.

STEP 3

Review the properties of multiplication: - Commutative Property of Multiplication: $a \cdot b = b \cdot a$ - Associative Property of Multiplication: $(a \cdot b) \cdot c = a \cdot (b \cdot c)$ - Identity Property of Multiplication: $a \cdot 1 = a$ - Distributive Property: $a(b + c) = ab + ac$

STEP 4

Examine the given equation:
$3(-5 \cdot 10) = (-5 \cdot 10)3$
Notice that the order of multiplication is changed, but the grouping of numbers remains the same.

STEP 5

Identify the property:
The equation demonstrates the Commutative Property of Multiplication because the order of the numbers being multiplied is changed, but the result remains the same.
The property demonstrated by the equation is:
$\boxed{\text{(A) Commutative Property of Multiplication}}$

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