Estimate 83 x 21 by first rounding each number to the nearest ten.Which of the following 3 numbers is a reasonable estimate of the product?1600, 1800, 2400

1. Break Down the Problem

To estimate the product $83 \times 21$, we will round each number to the nearest ten and then multiply the rounded numbers.

2. Relevant Concepts

• Rounding to the nearest ten:
  • For $83$: The nearest ten is $80$.
  • For $21$: The nearest ten is $20$.

3. Analysis and Detail

Now we will multiply the rounded numbers: $80 \times 20 = 1600$

4. Verify and Summarize

We confirmed that:

• Rounding $83$ gives $80$.
• Rounding $21$ gives $20$.
• Therefore, the estimated product is $1600$.

Final Answer

The reasonable estimate of the product $83 \times 21$ is 1600.