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Math  /  Algebra

QuestionWhich of the following illustrates the commutative property of multiplication?
Enter a, b, c, d, or e. a. zy=yzz y=y z b. a+(c+d)=(a+c)+da+(c+d)=(a+c)+d c. y+a=a+yy+a=a+y d. (db)(e+f)=d[b(e+f)](d b)(e+f)=d[b(e+f)] e. (ac+de)(ef)=(de+ac)(ef)(a c+d e)(e f)=(d e+a c)(e f)

Studdy Solution

STEP 1

1. The commutative property of multiplication states that for any numbers x x and y y , the equation x⋅y=y⋅x x \cdot y = y \cdot x holds true.
2. We need to identify which option demonstrates this property.

STEP 2

1. Review each option to determine if it demonstrates the commutative property of multiplication.
2. Identify the correct option.

STEP 3

Review option (a): zy=yz z y = y z .
This option shows that the order of multiplication does not affect the product, which is the commutative property of multiplication.

STEP 4

Review option (b): a+(c+d)=(a+c)+d a + (c + d) = (a + c) + d .
This option demonstrates the associative property of addition, not the commutative property of multiplication.

STEP 5

Review option (c): y+a=a+y y + a = a + y .
This option demonstrates the commutative property of addition, not multiplication.

STEP 6

Review option (d): (db)(e+f)=d[b(e+f)] (d b)(e+f) = d[b(e+f)] .
This option involves distribution and does not demonstrate the commutative property of multiplication.

STEP 7

Review option (e): (ac+de)(ef)=(de+ac)(ef) (a c + d e)(e f) = (d e + a c)(e f) .
This option shows the commutative property of addition within the multiplication context, but not directly the commutative property of multiplication itself.
The correct option that illustrates the commutative property of multiplication is a \boxed{a} .

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