Question: Use the GCF and the distributive property to write $45 + 90$ as a product. What is the GCF of $45$ and $90$? $45$ Write $45 + 90$ as a product using the GCF, $45$, as one of the factors. $45 + 90 = ? ( ? + ? )

1. **State the problem:** We want to write the sum $45 + 90$ as a product using the Greatest Common Factor (GCF) and the distributive property. 2. **Find the GCF of $45$ and $90$:** - Prime factorization of $45 = 3^2 \times 5$ - Prime factorization of $90 = 2 \times 3^2 \times 5$ - Common factors are $3^2$ and $5$ - So, GCF $= 3^2 \times 5 = 9 \times 5 = 45$ 3. **Use the distributive property:** - Express each term as a product of the GCF and another factor: $$45 = 45 \times 1$$ $$90 = 45 \times 2$$ 4. **Rewrite the sum:** $$45 + 90 = 45 \times 1 + 45 \times 2$$ 5. **Factor out the GCF:** $$45 \times 1 + 45 \times 2 = 45 (1 + 2)$$ 6. **Simplify inside the parentheses:** $$45 (1 + 2) = 45 \times 3 = 135$$ **Final answer:** $$45 + 90 = 45 (1 + 2)$$