Final answer:
After converting the ribbon's length to feet, we find Mary can cut 30 equal pieces of the ribbon, each piece being 1/14 foot long.
Step-by-step explanation:
To find out how many pieces Mary can cut from a piece of ribbon that is 5/7 yard long, with each piece being 1/14 foot long, we need to ensure that the units are consistent. Since there are 3 feet in 1 yard, we first convert the length of the ribbon to feet using the relation 1 yard = 3 feet. So, 5/7 yard is equivalent to (5/7) * 3 feet.
Next, calculate the length of the ribbon in feet: (5/7) * 3 = 15/7 feet. Now, we have the length of the ribbon and the desired piece length in the same unit (feet).
Then, we need to divide the total length of the ribbon by the length of one piece to find out how many pieces can be cut: (15/7 feet) / (1/14 feet) = (15/7) * (14/1) = 30 pieces.
So, Mary should cut 30 pieces of ribbon.