1. **State the problem:** Lana needs a total of $24 \frac{1}{2}$ yards of fabric to make a tablecloth. She already has two pieces of fabric: one is $3 \frac{1}{4}$ yards and the other is $4 \frac{1}{8}$ yards. We need to find out how many more yards of fabric Lana needs. 2. **Convert mixed numbers to improper fractions:** - $24 \frac{1}{2} = 24 + \frac{1}{2} = \frac{48}{2} + \frac{1}{2} = \frac{49}{2}$ - $3 \frac{1}{4} = 3 + \frac{1}{4} = \frac{12}{4} + \frac{1}{4} = \frac{13}{4}$ - $4 \frac{1}{8} = 4 + \frac{1}{8} = \frac{32}{8} + \frac{1}{8} = \frac{33}{8}$ 3. **Add the two pieces Lana already has:** $$\frac{13}{4} + \frac{33}{8}$$ To add, find a common denominator, which is 8: $$\frac{13}{4} = \frac{13 \times 2}{4 \times 2} = \frac{26}{8}$$ So, $$\frac{26}{8} + \frac{33}{8} = \frac{26 + 33}{8} = \frac{59}{8}$$ 4. **Calculate how much more fabric Lana needs:** $$\frac{49}{2} - \frac{59}{8}$$ Convert $\frac{49}{2}$ to eighths: $$\frac{49}{2} = \frac{49 \times 4}{2 \times 4} = \frac{196}{8}$$ So, $$\frac{196}{8} - \frac{59}{8} = \frac{196 - 59}{8} = \frac{137}{8}$$ 5. **Convert the improper fraction back to a mixed number:** $$\frac{137}{8} = 17 \frac{1}{8}$$ **Final answer:** Lana needs $17 \frac{1}{8}$ more yards of fabric.