To find out how many 1/2 yard increments Anna can cut from her 27 1/4 yards of fabric, we need to divide the total length of the fabric by the length of each increment.
First, we need to convert the mixed number 27 1/4 to an improper fraction.
To do this, we multiply the whole number (27) by the denominator of the fraction (4) and add the numerator (1). This gives us 108 + 1 = 109.
The denominator remains the same, so the improper fraction is 109/4 yards.
Now, we can divide the total length of the fabric (109/4 yards) by the length of each increment (1/2 yard).
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
The reciprocal of 1/2 is 2/1.
So, we have (109/4) * (2/1) = 218/4.
To simplify this fraction, we can divide both the numerator and denominator by their greatest common factor, which is 2.
218/4 simplifies to 109/2.
Therefore, Anna can cut 109/2 or 54 1/2 increments from her 27 1/4 yards of fabric.