Distributive Property Introduction

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📚 Part 1: Understanding the Distributive Property

1. Look at this example: 4 × 5 + 4 × 2 = 4 × (5 + 2)

What is the common factor in the expression 4 × 5 + 4 × 2?

2. Which expression shows the distributive property correctly?

3 × 6 + 3 × 4 = 3 × (6 + 4)

3 × 6 + 4 × 4 = 3 × (6 + 4)

3 × 6 + 3 × 4 = 6 × (3 + 4)

3 × 6 + 3 × 4 = 3 + (6 × 4)

3. Calculate both ways to check: 5 × 7 + 5 × 2

Method 1: 5 × 7 + 5 × 2 = _____ + _____ = _____

Method 2: 5 × (7 + 2) = 5 × _____ = _____

4. True or False: The distributive property helps us group numbers to make multiplication easier.

True

False

5. Rewrite using the distributive property:

a) 6 × 3 + 6 × 1 = 6 × (_____ + _____) = 6 × _____ = _____

b) 8 × 4 + 8 × 5 = _____ × (_____ + _____) = _____ × _____ = _____

c) 7 × 2 + 7 × 6 = _____ × (_____ + _____) = _____ × _____ = _____

6. Circle the common factor in each expression:

a) 9 × 3 + 9 × 7

b) 4 × 8 + 4 × 2

c) 12 × 5 + 12 × 1

7. Show your work to solve: 3 × 9 + 3 × 1

8. Explain in your own words: How does the distributive property make math easier?