A piece of fabric measures 6 3/4 yards in length. If it needs to be cut into pieces that are each 2 1/2 yards long, how many pieces can be cut from the fabric?
To find how many pieces can be cut, divide the total length of fabric by the length of each piece: $6 \frac{3}{4} \div 2 \frac{1}{2}=\frac{27}{4} \div \frac{5}{2}.$ To simplify the expression, we multiply by the reciprocal of the divisor: $\frac{27}{4} \div \frac{5}{2}=\frac{27}{4} \cdot \frac{2}{5}.$ $\frac{27}{4} \cdot \frac{2}{5}=\frac{27\cdot2}{4\cdot5}=\frac{54}{20}.$ To get this fraction in simplest form we can divide by 2: $\frac{54}{20}=\frac{27}{10}=\boxed{2\frac{7}{10}}.$
