This engaging worksheet helps students practice identifying properties of real numbers through a fun color-by-number activity.

Let’s go step by step to match each equation with the correct property from the word bank.

We’ll look at each problem and think: “What is happening here?” Then we’ll find the matching property name.

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Problem 1: a · 0 = 0

This says any number multiplied by zero equals zero. That’s called the Multiplication Property of Zero.
→ Matches option f) → color maroon (but we just need the property name)

✔ Answer: Multiplication Property of Zero

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Problem 2: a · b = b · a

The order of multiplication doesn’t change the result. That’s the Commutative Property of Multiplication.
→ Matches option j) → aqua blue

✔ Answer: Commutative Property of Multiplication

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Problem 3: a + b = b + a

Order doesn’t matter in addition either — that’s the Commutative Property of Addition.
→ Matches option g) → yellow

✔ Answer: Commutative Property of Addition

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Problem 4: a · (1/a) = 1

Multiplying a number by its reciprocal gives 1. That’s the Multiplicative Inverse of a Number.
→ Matches option c) → black

✔ Answer: Multiplicative Inverse of a Number

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Problem 5: a · 1 = a

Multiplying by 1 leaves the number unchanged — that’s the Identity Property of Multiplication.
→ Matches option e) → purple

✔ Answer: Identity Property of Multiplication

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Problem 6: a + 0 = a

Adding zero doesn’t change the number — that’s the Identity Property of Addition.
→ Matches option a) → maroon

✔ Answer: Identity Property of Addition

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Problem 7: (a + b) + c = a + (b + c)

Grouping changes, but not the order — this is the Associative Property of Addition.
→ Matches option d) → yellow

✔ Answer: Associative Property of Addition

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Problem 8: a + (-a) = 0

A number plus its opposite equals zero — that’s the Additive Inverse of a Number.
→ Matches option h) → purple

✔ Answer: Additive Inverse of a Number

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Problem 9: a · (b · c) = (a · b) · c

Grouping changes in multiplication, but not the order — that’s the Associative Property of Multiplication.
→ Matches option b) → yellow

✔ Answer: Associative Property of Multiplication

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Problem 10: a(b + c) = ab + ac

You’re distributing the ‘a’ across the parentheses — that’s the Distributive Property.
→ Matches option i) → black

✔ Answer: Distributive Property

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Now let’s double-check all answers against the word bank to make sure no mistakes:

Word Bank Recap:
- a) Identity Property of Addition → #6 ✔
- b) Associative Property of Multiplication → #9 ✔
- c) Multiplicative Inverse → #4 ✔
- d) Associative Property of Addition → #7 ✔
- e) Identity Property of Multiplication → #5 ✔
- f) Multiplication Property of Zero → #1 ✔
- g) Commutative Property of Addition → #3 ✔
- h) Additive Inverse → #8 ✔
- i) Distributive Property → #10 ✔
- j) Commutative Property of Multiplication → #2 ✔

All matched correctly!

Final Answer:
1. Multiplication Property of Zero
2. Commutative Property of Multiplication
3. Commutative Property of Addition
4. Multiplicative Inverse of a Number
5. Identity Property of Multiplication
6. Identity Property of Addition
7. Associative Property of Addition
8. Additive Inverse of a Number
9. Associative Property of Multiplication
10. Distributive Property