To subtract the mixed number 2 1/4 from the fraction 385/132, we first need to convert the mixed number to an improper fraction.
2 1/4 can be written as (2 * 4 + 1) / 4 = 9/4.
Now, we have the subtraction expression: 385/132 - 9/4.
To subtract fractions, we need to have a common denominator. The least common multiple (LCM) of 132 and 4 is 132.
We can convert both fractions to have a denominator of 132:
385/132 - 9/4 = (385/132) * (4/4) - (9/4) * (33/33)
= 1540/528 - 297/132
Now that both fractions have a common denominator of 132, we can subtract them:
1540/528 - 297/132 = (1540 - 297) / 132
= 1243/132
The resulting fraction is 1243/132.
However, we can simplify this fraction further by finding the greatest common divisor (GCD) of the numerator and denominator, which is 17.
Dividing both the numerator and denominator by 17, we get:
1243/132 = (1243/17) / (132/17)
= 73/8
Therefore, the fraction 385/132 - 2 1/4 is equal to 73/8.