Teaching the distributive property using GCF with prime factorization of 20 and 15.

Let's solve the problem step by step using the information provided in the image.

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Problem:

We are given the expression:

$$
20 + 15 = \_\_\_\_ (\_\_\_\_ + \_\_\_\_)
$$

We need to factor out the Greatest Common Factor (GCF) of 20 and 15 and rewrite the sum as a product using the distributive property.

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Step 1: Prime Factorization

From the image, we see:

- $ 20 = 2 \times 2 \times 5 $
- $ 15 = 3 \times 5 $

Now, identify the common prime factors.

- Both numbers have one 5 in common.
- So, the GCF = 5

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Step 2: Use the GCF to factor the sum

We now factor out the GCF (which is 5) from both terms:

$$
20 + 15 = 5 \times (4 + 3)
$$

Because:
- $ 20 ÷ 5 = 4 $
- $ 15 ÷ 5 = 3 $

So,

$$
20 + 15 = 5(4 + 3)
$$

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✔ Final Answer:

$$
\boxed{20 + 15 = 5(4 + 3)}
$$

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Explanation:

This uses the distributive property:
$$
a(b + c) = ab + ac
$$

Here:
- $ a = 5 $
- $ b = 4 $
- $ c = 3 $

So:
$$
5(4 + 3) = 5 \times 4 + 5 \times 3 = 20 + 15
$$

Thus, we’ve rewritten the sum as a product using the GCF.

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✔️ Summary:

- GCF of 20 and 15 is 5
- Factoring gives: $ 20 + 15 = 5(4 + 3) $
- This demonstrates the distributive property with the GCF

✔ Answer:
$$
\boxed{20 + 15 = 5(4 + 3)}
$$