Question

algebra 1-study gu1. $(x + y) + z = x + (y + z)$2. $0 \div 5 = 0; 5 \div 0 = \text{undefined}$3. $x \cdot 0 = 0$4. $x + -x = 0$5. $(x \cdot y) \cdot z = x \cdot (y \cdot z)$6. $x \cdot y = y \cdot x$7. $x \div 1 = x$8. $x + 0 = x$9. $x - 0 = x$10. $x + y = y + x$11. $x(y + z) = xy + xz$12. $x \cdot 1 = x$13. $x - y = x + (-y)$a. addition property of zerob. addition property of oppositesc. commutative property of additiond. associative property of additione. subtraction property of zerof. subtraction property of regroupingg. multiplication property of zeroh. multiplication property of onei. commutative property of multiplicationj. associative property of multiplicationk. distributive property of multiplicationl. division property of zerom. division property of one

Explanation:

Step1: Match associative addition

The equation $(x + y) + z = x + (y + z)$ is the definition of the Associative Property of Addition, so it pairs with d.

Step2: Match division property of zero

The equations $0 \div 5 = 0; 5 \div 0 = \text{undefined}$ describe the Division Property of Zero, so it pairs with l.

Step3: Match multiplication zero property

The equation $x \cdot 0 = 0$ is the Multiplication Property of Zero, so it pairs with g.

Step4: Match addition opposites property

The equation $x + -x = 0$ is the Addition Property of Opposites, so it pairs with b.

Step5: Match associative multiplication

The equation $(x \cdot y) \cdot z = x \cdot (y \cdot z)$ is the Associative Property of Multiplication, so it pairs with j.

Step6: Match commutative multiplication

The equation $x \cdot y = y \cdot x$ is the Commutative Property of Multiplication, so it pairs with i.

Step7: Match division property of one

The equation $x \div 1 = x$ is the Division Property of One, so it pairs with m.

Step8: Match addition property of zero

The equation $x + 0 = x$ is the Addition Property of Zero, so it pairs with a.

Step9: Match subtraction property of zero

The equation $x - 0 = x$ is the Subtraction Property of Zero, so it pairs with e.

Step10: Match commutative addition

The equation $x + y = y + x$ is the Commutative Property of Addition, so it pairs with c.

Step11: Match distributive property

The equation $x(y + z) = xy + xz$ is the Distributive Property of Multiplication, so it pairs with k.

Step12: Match multiplication property of one

The equation $x \cdot 1 = x$ is the Multiplication Property of One, so it pairs with h.

Step13: Match subtraction regrouping property

The equation $x - y = x + (-y)$ is the Subtraction Property of Regrouping, so it pairs with f.

Answer:

1. d. Associative Property of Addition
2. l. Division Property of Zero
3. g. Multiplication Property of Zero
4. b. Addition Property of Opposites
5. j. Associative Property of Multiplication
6. i. Commutative Property of Multiplication
7. m. Division Property of One
8. a. Addition Property of Zero
9. e. Subtraction Property of Zero
10. c. Commutative Property of Addition
11. k. Distributive Property of Multiplication
12. h. Multiplication Property of One
13. f. Subtraction Property of Regrouping