Distributive Property Practice
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Distributive Property Practice
📚 Part 1: Apply the Distributive Property
a) 6 × (3 + 4) = _____ × _____ + _____ × _____ = _____
b) 5 × (8 - 2) = _____ × _____ - _____ × _____ = _____
c) 7 × (4 + 5) = _____ × _____ + _____ × _____ = _____
For 4 × (6 + 3):
Draw an area model for 3 × (5 + 2) in the box below, then write the distributive expression:
3 × (5 + 2) = _____ × _____ + _____ × _____ = _____
🔍 Part 2: Error Analysis & Word Problems
Marcus solved 8 × (4 + 1) like this:
Marcus's work: 8 × (4 + 1) = (8 × 4) + 1 = 32 + 1 = 33
What did Marcus do wrong?
Show the correct solution: ________________________________
Emma buys 6 packs of supplies. Each pack contains 4 pencils and 3 erasers. Use the distributive property to find the total number of items.
Total items: _____ pencils + _____ erasers = _____ items
✏️ Part 3: Challenge & Reflection
Write a distributive property expression using subtraction and solve it:
_____ × (_____ - _____) = _____ × _____ - _____ × _____ = _____
A movie theater has 12 rows of seats. Each row has 8 regular seats and 2 premium seats. Use the distributive property to find the total number of seats.
Expression: ________________________________
Total seats: _____
How does the distributive property help you solve multiplication problems? Give an example.
✅ Answer Key
a) 6 × (3 + 4) = 6 × 3 + 6 × 4 = 18 + 24 = 42
b) 5 × (8 - 2) = 5 × 8 - 5 × 2 = 40 - 10 = 30
c) 7 × (4 + 5) = 7 × 4 + 7 × 5 = 28 + 35 = 63
For 4 × (6 + 3): (4 × 6) + (4 × 3)
3 × (5 + 2) = 3 × 5 + 3 × 2 = 15 + 6 = 21
Marcus's mistake was not distributing the 8 to both terms inside the parentheses. The correct solution is:
8 × (4 + 1) = (8 × 4) + (8 × 1) = 32 + 8 = 40
Emma buys 6 packs of supplies. Each pack contains 4 pencils and 3 erasers.
Total items: 6 × 4 pencils + 6 × 3 erasers = 24 pencils + 18 erasers = 42 items
Correct answers: (9 × 7) - (9 × 3) and 9 × 4
Example: 5 × (10 - 3) = 5 × 10 - 5 × 3 = 50 - 15 = 35
Expression: 12 × (8 + 2) = 12 × 8 + 12 × 2 = 96 + 24 = 120
Total seats: 120
The distributive property allows you to break down complex multiplication problems into simpler parts. For example, instead of calculating 6 × 14 directly, you can use 6 × (10 + 4) = 6 × 10 + 6 × 4 = 60 + 24 = 84.
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