A tailor hard 6/ 1/4 m of an embroidery thread to decorate a fabric she used to2/ 1/2 m of thread to decorate the age of the fabric she used a quarter of the remaining thread to make a flower find the remaining peace

To find the remaining piece of the embroidery thread, we will need to subtract the thread used from the initial length of the thread.

Initial thread length = 6 1/4 m

Thread used = 2 1/2 m

Remaining thread = Initial thread length - Thread used

To subtract mixed fractions, we need to have a common denominator.

6 1/4 = (4*6 + 1)/4 = 25/4

2 1/2 = (2*2 + 1)/2 = 5/2

Remaining thread = 25/4 - 5/2

To subtract fractions, we need a common denominator.

The least common multiple of 4 and 2 is 4, so we can combine the fractions as follows:

Remaining thread = (25/4) - (10/4)

Remaining thread = 15/4

Therefore, the remaining piece of embroidery thread is 15/4 meters.