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:
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Set Up the Problem: You're trying to find how many times 87 fits into 2,001.
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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.
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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: \[ 2,001 - 1,740 = 261 \]
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Continuing the Division: Since we still have 261 left:
- We can now calculate how many times 87 goes into 261: \[ 87 × 3 = 261 \]
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Final Calculation: Combine the results:
- \(20\) times (for the first area) plus \(3\) times (for the second area) gives you: \[ 20 + 3 = 23 \]
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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.
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