Difficulty: Hard

Average Score: 33%

Which of the following is a way to quickly multiply 24 by 16 without a calculator?

Rationale

Multiply 20 by 20 and subtract 4 × 4.

This method efficiently leverages the difference of squares to simplify the multiplication, calculating 20 × 20 (which equals 400) and subtracting 16 (the result of 4 × 4), yielding the correct product of 384 for 24 × 16.

A (Multiply 20 by 20 and subtract 4 × 4.) CORRECT

This option correctly outlines a method of calculating 24 × 16 by first finding 20 × 20, which is 400, and then subtracting 16 (4 × 4) to arrive at 384. This approach utilizes the fact that 24 is 4 less than 20 and 16 is 4 less than 20, effectively employing a quick mental math trick.

B (Multiply 20 by 20.) YOUR ANSWER

While this option gives the result of 400, it does not complete the necessary calculations to find the product of 24 and 16. Without further steps, the answer remains incorrect, as it fails to account for the necessary adjustments needed to reach the final product.

C (Multiply 20 by 10 and add 4 × 6.) YOUR ANSWER

This option results in 200 + 24, yielding 224. This method does not correctly utilize the values of 24 and 16, and thus does not achieve the correct product. Instead, it misapplies the numbers and provides a significantly lower result.

D (Multiply 25 by 10 and add 4 × 15.) YOUR ANSWER

This approach calculates 250 + 60, resulting in 310. This method also fails to align with the correct multiplication of 24 by 16, as it involves unrelated multipliers and thus produces an incorrect result.

Conclusion

The quickest way to multiply 24 by 16 without a calculator is option A, where the product is found by calculating 20 × 20 and subtracting 4 × 4. The other options either fail to complete the multiplication correctly or yield entirely unrelated results, demonstrating the effectiveness of utilizing nearby round numbers and basic arithmetic operations for mental calculations.

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