Question

study paths > tx math bridge - stage 1 topic test: associative, commutative, and distributive prope...
associative, commutative, and distributive propen
topic: associative, commutative, and distributive properties
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match each equation on the left to the mathematical property it uses on the right
(1 + 4) + 3 = 1 + (4 + 3) \t\t\tcommutative property of addition
(2 · x) · 5 = 2 · (x · 5) \t\t\tcommutative property of multiplication
3(x + 2) = 3x + 6 \t\t\t\tassociative property of addition
(8 · x · 2) = (x · 8 · 2) \t\t\tassociative property of multiplication
(6 + 5) + 3 = 3 + (6 + 5) \t\t\tdistributive property
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Explanation:

Step1: Identify associative addition

$(1 + 4) + 3 = 1 + (4 + 3)$ groups addition differently: associative addition.

Step2: Identify associative multiplication

$(2 \cdot x) \cdot 5 = 2 \cdot (x \cdot 5)$ groups multiplication differently: associative multiplication.

Step3: Identify distributive property

$3(x + 2) = 3x + 6$ distributes 3 over $x+2$: distributive property.

Step4: Identify commutative multiplication

$(8 \cdot x) \cdot 2 = (x \cdot 8) \cdot 2$ swaps 8 and $x$: commutative multiplication.

Step5: Identify commutative addition

$(6 + 5) + 3 = 3 + (6 + 5)$ swaps $(6+5)$ and 3: commutative addition.

Answer:

$(1 + 4) + 3 = 1 + (4 + 3)$ → associative property of addition
$(2 \cdot x) \cdot 5 = 2 \cdot (x \cdot 5)$ → associative property of multiplication
$3(x + 2) = 3x + 6$ → distributive property
$(8 \cdot x) \cdot 2 = (x \cdot 8) \cdot 2$ → commutative property of multiplication
$(6 + 5) + 3 = 3 + (6 + 5)$ → commutative property of addition