Question 74

436

The number represented by three flats, twelve rods, and sixteen cubes is 436. Each flat represents 100, each rod represents 10, and each cube represents 1, leading to the total of 400 (3 flats) + 120 (12 rods) + 16 (16 cubes) = 436.

A) 328

This option is incorrect because it does not accurately reflect the values of the base-ten blocks. With three flats (300), twelve rods (120), and sixteen cubes (16), the total would exceed 328.

B) 436

This option is correct as it accurately sums the values of the three flats, twelve rods, and sixteen cubes. The calculation confirms that 3 flats (300) plus 12 rods (120) and 16 cubes (16) equals 436.

C) 516

This choice is incorrect as it overestimates the total value derived from the base-ten blocks. The sum of the three flats, twelve rods, and sixteen cubes does not reach 516.

D) 580

This option is also incorrect. The total derived from three flats, twelve rods, and sixteen cubes is significantly lower than 580, making this a false representation of the number.

Conclusion

The correct answer, 436, is determined by the accurate calculation of the values of the flats, rods, and cubes represented in the question. All other options fail to represent the correct total, as they either undercount or overcount the contributions from the base-ten blocks, illustrating a misunderstanding of how to calculate the total number represented by these components.