Properties of Operations
A free Pre-Algebra lesson from the “Algebra Readiness” unit, with a worked example and practice problems including step-by-step solutions.
The commutative property says order does not matter for addition or multiplication (a + b = b + a, a * b = b * a). The associative property says grouping does not matter ((a + b) + c = a + (b + c)). The identity property: a + 0 = a and a * 1 = a. The distributive property: a(b + c) = ab + ac.
What you'll learn
- Identify the commutative, associative, identity, and distributive properties
- Use properties of operations to simplify expressions
- Justify each step of a calculation by naming the property used
Worked example
Problem. Use the distributive property to compute 6(20 + 3).
- Distributive: a(b + c) = ab + ac.
- 6(20) + 6(3) = 120 + 18.
- 120 + 18 = 138.
- Connect the calculation back to Properties of Operations so the method, not just the arithmetic, is clear.
Answer: 138
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (multiple choice and typed response). Counts include repeated prompts and variants.
Practice problems
1. Which property is shown by 3 + 7 = 7 + 3?
Choices: Commutative · Associative · Identity · Distributive
Show solution
- The order of the two addends switched but the values stayed the same.
- That is the commutative property of addition.
Answer: Commutative
2. Which property is shown by 2(5x) = 10x?
Choices: Commutative · Associative · Identity · Distributive
Show solution
- The grouping (2 * 5) * x became 10 * x.
- That regrouping is the associative property of multiplication.
Answer: Associative
3. Use the distributive property to expand 5(x + 4).
Show solution
- Multiply 5 by each term inside.
- 5 * x + 5 * 4 = 5x + 20.
Answer: 5x + 20
4. Expand 3(2x - 7).
Show solution
- Distribute the 3: 3 * 2x - 3 * 7.
- = 6x - 21.
Answer: 6x - 21
5. Use the commutative property: 4 + x = ___ + 4. Enter what fills the blank.
Show solution
- Commutative lets you swap order.
- 4 + x = x + 4.
Answer: x
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