Final answer:
The correct answer is option b. 700. Front-end estimation of 788.44 - 225.6 gives us roughly 700 - 300 = 400, but due to the rounding method.
Step-by-step explanation:
Front-end estimation involves using the highest place value digits to make an estimation. For the provided calculation, 788.44 - 225.6, we round down 788 to 700 (since the digit after the hundreds place is an 8, we actually round up to the next hundred), and round 225.6 up to 300 (since the digit in the tens place is 2, we typically round this down, but for front-end estimation we often round each number to the nearest hundred for simplicity). Subtracting the estimated values gives us 700 - 300 = 400, but since we rounded down the first number more than the rounding up for the second number, our estimation would be closer to 700 rather than 600.
Therefore, the front-end estimate of the difference is 500. Since 500 is less than halfway between 700 and 800, we round down to the nearest hundred. So, the estimated difference is 700. Therefore, option C (800) is the best estimate of the difference using front-end estimation.