Identify the correct property of real numbers in this math worksheet.

Let’s go step by step through each problem to identify the correct property of real numbers.

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a. 5 + (-5) = 0
This shows that adding a number and its opposite gives zero. That’s the Additive Inverse Property.

b. 1 • (6y) = 4Y → Wait, this looks like a typo. It should probably be:
1 • (6y) = 6y — because multiplying by 1 doesn’t change the value. That’s the Multiplicative Identity Property.
But as written, “= 4Y” is incorrect unless it’s a trick or error. Since we’re identifying properties, and assuming it’s meant to show identity, we’ll assume it’s a typo and treat it as 1 • (6y) = 6y → Multiplicative Identity.

Actually — looking again: maybe it’s 1 • (6y) = 6y, but written with a capital Y? Or perhaps it’s testing if you notice the mismatch? But in standard worksheets, this is likely intended to be Multiplicative Identity. Let’s proceed under that assumption.

Wait — actually, let me check all problems carefully.

Looking at the worksheet layout:

Left column:
- a: 5 + (-5) = 0 → Additive Inverse
- c: -√2 + 2 = 0 → Also Additive Inverse
- e: 8c = 8c → Reflexive Property (or sometimes called Identity for equality)
- g: x • (1/x) = 1 → Multiplicative Inverse (assuming x ≠ 0)
- i: (-2·8), 3 = -2(8·3) → Associative Property of Multiplication
- k: 9m = 9m → Again, Reflexive

Right column:
- b: 1 • (6y) = 4Y → This must be a typo. Probably meant 1 • (6y) = 6y → Multiplicative Identity
- d: 3x + 0 = 3x → Additive Identity
- f: 5n = 5n → Reflexive
- h: 8x + 2 = 2 + 8x → Commutative Property of Addition
- j: 2 • (1/2) = 1 → Multiplicative Inverse
- l: 4x + 0 = 4x → Additive Identity

Now let’s assign proper names:

Standard Properties:

- Additive Inverse: a + (-a) = 0
- Additive Identity: a + 0 = a
- Multiplicative Inverse: a • (1/a) = 1 (a ≠ 0)
- Multiplicative Identity: a • 1 = a
- Commutative Property of Addition: a + b = b + a
- Associative Property of Multiplication: (a•b)•c = a•(b•c)
- Reflexive Property: a = a

So now matching:

→ a: 5 + (-5) = 0 → Additive Inverse

→ b: 1 • (6y) = 4Y → Hmm… this is problematic. If it's truly "4Y", then it’s false. But since it’s a property identification sheet, it’s almost certainly a typo. Likely meant 1 • (6y) = 6y → Multiplicative Identity

We’ll go with that.

→ c: -√2 + √2 = 0 → Additive Inverse

→ d: 3x + 0 = 3x → Additive Identity

→ e: 8c = 8c → Reflexive Property

→ f: 5n = 5n → Reflexive Property

→ g: x • (1/x) = 1 → Multiplicative Inverse (for x ≠ 0)

→ h: 8x + 2 = 2 + 8x → Commutative Property of Addition

→ i: (-2·8), 3 = -2(8·3) → The comma might be a typo; probably meant: (-2 • 8) • 3 = -2 • (8 • 3) → Associative Property of Multiplication

→ j: 2 • (1/2) = 1 → Multiplicative Inverse

→ k: 9m = 9m → Reflexive Property

→ l: 4x + 0 = 4x → Additive Identity

Note: Some properties repeat — that’s okay. Worksheets often have repeats to reinforce learning.

Also note: For item i, the notation “(-2 . 8), 3 = -2(8 . 3)” — the comma is likely a misprint for parentheses or multiplication dot. We interpret as grouping: ((-2)(8))3 = (-2)((8)(3)) → associative.

Final mapping:

a: Additive Inverse
b: Multiplicative Identity *(assuming typo)*
c: Additive Inverse
d: Additive Identity
e: Reflexive
f: Reflexive
g: Multiplicative Inverse
h: Commutative (Addition)
i: Associative (Multiplication)
j: Multiplicative Inverse
k: Reflexive
l: Additive Identity

All make sense except possibly b — but given context, we accept it as Multiplicative Identity.

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Final Answer:
a: Additive Inverse
b: Multiplicative Identity
c: Additive Inverse
d: Additive Identity
e: Reflexive Property
f: Reflexive Property
g: Multiplicative Inverse
h: Commutative Property of Addition
i: Associative Property of Multiplication
j: Multiplicative Inverse
k: Reflexive Property
l: Additive Identity