Let’s go through each property one by one, fill in the blanks correctly, and solve all the example problems.
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1. Commutative Property
Definition: When adding or multiplying, the
order does not matter.
Examples:
- 2 + 3 =
5
- 3 + 2 =
5 → Same as above! Order changed, result same.
- 4 • 5 =
20
- 5 • 4 =
20 → Again, same result even though order flipped.
✔ So definition blank:
order
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2. Associative Property
Definition: When adding or multiplying, it doesn’t matter how the numbers are
grouped.
Examples:
- 3 + (2 + 1) = 3 + 3 =
6
- (3 + 2) + 1 = 5 + 1 =
6 → Same total, different grouping.
- 2 • (4 • 6) = 2 • 24 =
48
- (2 • 4) • 6 = 8 • 6 =
48 → Same product, different grouping.
✔ Definition blank:
grouped
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3. Distributive Property
Definition: When multiplying by a sum, you can multiply each
term separately and add.
Example:
- 3(2 + 4) = 3•2 + 3•4 = 6 + 12 =
18
Alternatively, do inside first: 2+4=6, then 3•6=18 → same answer.
✔ Definition blank:
term
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4. Identity Property
Two parts:
Additive Identity: The sum of any number and
0 is that number.
→ Example: 4 + 0 =
4
Multiplicative Identity: The product of any number and
1 is that number.
→ Example: 8 • 1 =
8
✔ Blanks:
0 and
1
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5. Inverse Property
Additive Inverse: The sum of any number and the negative of that number is
0.
→ Example: 7 + (-7) =
0
Multiplicative Inverse: The product of any number and its reciprocal is
1.
→ Example: 3 • (1/3) =
1
✔ Blanks:
0 and
1
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Now let’s write out all completed answers clearly for the worksheet:
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Commutative Property
Definition: When adding or multiplying, the
order does not matter.
Examples:
2 + 3 =
5
3 + 2 =
5
4 • 5 =
20
5 • 4 =
20
Associative Property
Definition: When adding or multiplying, it doesn’t matter how the numbers are
grouped.
Examples:
3 + (2 + 1) =
6
(3 + 2) + 1 =
6
2 • (4 • 6) =
48
(2 • 4) • 6 =
48
Distributive Property
Definition: When multiplying by a sum, you can multiply each
term separately and add.
Example:
3(2 + 4) =
18
Identity Property
The sum of any number and
0 is that number. → 4 + 0 =
4
The product of any number and
1 is that number. → 8 • 1 =
8
Inverse Property
Additive Inverse: The sum of any number and the negative of that number is
0. → 7 + -7 =
0
Multiplicative Inverse: The product of any number and its reciprocal is
1. → 3 • 1/3 =
1
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Final Answer:
All blanks filled and examples solved as shown above.
Parent Tip: Review the logic above to help your child master the concept of properties of equality worksheets.
