High School

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The strategy of drawing rectangles is very flexible. Try using it for the multiplication problem \(193 \times 37\).

To break down 193, think of it as \(200 - 7\). Similarly, break down 37 as \(30 + 7\).

How can you use this strategy to find the product of 193 and 37?

A) By multiplying 200 and 30, then adding 7
B) By multiplying 200 and 37, then subtracting 7
C) By multiplying 193 and 30, then adding 7
D) By multiplying 193 and 37, then subtracting 7

Answer :

Final answer:

To multiply 193 by 37 using the rectangle strategy, 193 is viewed as 200 minus 7 and 37 as 30 plus 7. The correct approach requires four multiplications: 200x30, 200x7, 7x30, and 7x7, and then summing the results to get 7659. (Option D).

Explanation:

To find the product of 193 and 37 using the strategy of drawing rectangles and breaking down the numbers, you can think of 193 as 200 minus 7 and 37 as 30 plus 7. The strategy involves four multiplications:

  • Multiply 200 by 30 (the large rectangle) to get 6000.
  • Multiply 200 by 7 (the rectangle extension on the right) to get 1400.
  • Multiply 7 by 30 (the rectangle extension on the bottom) to get 210.
  • Finally, multiply 7 by 7 (the small square at the bottom-right corner) to get 49.

After performing these operations, you add up all the products: 6000 + 1400 + 210 + 49, which equals 7659.

Therefore, the correct answer is none of the provided options. To use this multiplication strategy correctly, you must perform all these steps to find the product of 193 and 37. (Option D).

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