What three-digit number is represented by three flats, twelve rods, and sixteen cubes from a set of base-ten blocks?

Rationale

Three flats, twelve rods, and sixteen cubes represent the number 436.

In base-ten blocks, flats represent hundreds, rods represent tens, and cubes represent units. Therefore, three flats equal 300, twelve rods equal 120, and sixteen cubes equal 16, which together sum up to 436.

A (328) YOUR ANSWER

This choice suggests that the combined value of three flats, twelve rods, and sixteen cubes totals 328. However, calculating the values gives 300 (flats) + 120 (rods) + 16 (cubes) = 436, clearly indicating that this option is too low and thus incorrect.

B (436) CORRECT

This is the correct answer, as it accurately represents the total derived from the three components: 300 from three flats, 120 from twelve rods, and 16 from sixteen cubes. The addition of these values results in 436, aligning perfectly with the representation from the base-ten blocks.

C (516) YOUR ANSWER

Choosing 516 suggests that the total from the blocks exceeds the correct sum. With three flats contributing 300, twelve rods 120, and sixteen cubes 16, the maximum total is only 436, making this option incorrect and exceeding the actual total.

D (580) YOUR ANSWER

This option implies an even higher total than 516. The calculations for three flats, twelve rods, and sixteen cubes yield a maximum of 436, confirming that this choice is incorrect as it misrepresents the sum of the values represented by the blocks.

Conclusion

The representation of three flats, twelve rods, and sixteen cubes in base-ten blocks correctly totals 436. Each component contributes to the final sum: 300 from flats, 120 from rods, and 16 from cubes. Thus, the only accurate representation of this total is reflected in choice B, while all other options miscalculate the values.

What three-digit number is represented by three flats, twelve rods, and sixteen cubes from a set of base-ten blocks?

Three flats, twelve rods, and sixteen cubes represent the number 436.

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