Final answer:
To estimate 44 and 1/4 divided by 11 and 7/9, we use compatible numbers 44 and 12. After estimating, the answer is approximately 3.67.
Step-by-step explanation:
To estimate the division of 44 and 1/4 by 11 and 7/9 using compatible numbers, we first look for numbers that are easy to divide and are close to the original numbers given. The compatible number for 44 and 1/4 (44.25) is 44, and for 11 and 7/9 (approximately 11.78), we can round it to 12, which is a multiple of 4 and is easier to divide.
Following this, the estimated division would be 44 divided by 12. Now, we know that 4 times 11 is 44, and 4 times 12 is 48. Since the second number in our division (12) is roughly similar to the first (44), we can quickly approximate that the answer will be slightly less than 4. Therefore, 44 divided by 12 is approximately 3.67.
We can then conclude that 44 and 1/4 divided by 11 and 7/9 is approximately 3.67, using compatible numbers for estimation.