Question

How is the quotient of 2,001 and 87 determined using an area model? Enter your answers in the boxes to complete the equations.

Answer 1

To determine the quotient of 2,001 and 87 using an area model, you can represent the division in a visual format. Let's break this down step by step:

1. **Set Up the Problem**: You're trying to find how many times 87 fits into 2,001.

2. **Breaking Down the Numbers**: Start by approximating how many times 87 goes into 2,001. A good first step is to find multiples of 87 that are easier to work with.

- 87 × 20 = 1,740
- 87 × 30 = 2,610 (which is too high)
- So, we can start with 20, then refine our estimate.

3. **Finding the Area**:
- Assume 87 goes into 2,001 about 20 times. Thus, the area of our model would help confirm this. You can write:
\[
87 \times 20 = 1,740
\]
- Now, we calculate how much remains after subtracting this area from the total area:
\[
2,001 - 1,740 = 261
\]

4. **Continuing the Division**: Since we still have 261 left:
- We can now calculate how many times 87 goes into 261:
\[
87 × 3 = 261
\]

5. **Final Calculation**: Combine the results:
- \(20\) times (for the first area) plus \(3\) times (for the second area) gives you:
\[
20 + 3 = 23
\]

6. **Write the Equations**: You can fill in the boxes like this:
\[
2,001 = 87 \times 23
\]

Therefore, the completed equations are:
- \(2,001 = 87 \times (20 + 3)\)
- \(2,001 = 87 \times 23\)

In summary, the quotient of 2,001 and 87 is 23, using the area model approach to break down the calculation into manageable parts.