1. **Problem:** Calculate the products and estimate ranges for the following multiplications: 2. **Calculate $24.09 \times 12.57$:** - Approximate $24.09 \approx 24$ and $12.57 \approx 13$. - Multiply the approximations: $24 \times 13 = 312$. - Now calculate the exact product: $$24.09 \times 12.57 = 302.8713$$ - So, the exact answer is $302.8713$, close to the estimate $312$. 3. **Calculate $3.29 \times 3.81$:** - Approximate $3.29 \approx 3$ and $3.81 \approx 4$. - Multiply the approximations: $3 \times 4 = 12$. - Use the breakdown given: - $3 \times 3 = 9$ - $8 \times 2 = 16$ - $9 \times 1 = 9$ - Calculate the exact product: $$3.29 \times 3.81 = 12.5349$$ - The exact answer $12.5349$ is close to the estimate $12$. 4. **Calculate $4.1 \times 13.5$:** - Approximate $4.1 \approx 4$ and $13.5 \approx 13$. - Multiply the approximations: $4 \times 13 = 52$. - Add the extra part: - $5 \times 1 = 5$ - Calculate the exact product: $$4.1 \times 13.5 = 55.35$$ - The exact answer $55.35$ is close to the estimate $52 + 5 = 57$. 5. **Calculate $16.12 \times 3.55$:** - Approximate $16.12 \approx 16$ and $3.55 \approx 4$. - Multiply the approximations: $16 \times 4 = 64$. - Calculate the exact product: $$16.12 \times 3.55 = 57.226$$ - The exact answer $57.226$ is slightly less than the estimate $64$. **Summary:** - $24.09 \times 12.57 = 302.8713$ - $3.29 \times 3.81 = 12.5349$ - $4.1 \times 13.5 = 55.35$ - $16.12 \times 3.55 = 57.226$ Estimation helps to quickly find a range for the product before calculating the exact value.