Tia uses \( 2 \frac{1}{2} \) meters of fabric for a project. She has \( 1 \frac{1}{8} \) meters of fabric left. How many meters of fabric did Tia start with? Make an equation that represents the word problem. Use \( f \) to represent the amount of fabric, in meters, that Tia started with. Move numbers, a symbol, and \( f \) to the boxes to show the answer.

To find out how much fabric Tia started with, we can set up the equation as follows: \[ f - 1 \frac{1}{8} = 2 \frac{1}{2} \] This means that if we take the amount of fabric she used, \( 2 \frac{1}{2} \), away from what she originally had, \( f \), we will have \( 1 \frac{1}{8} \) meters left. Now let's bring it all together: 1. Convert to improper fractions for easier calculations: - \( f \) (unknown) - \( 1 \frac{1}{8} = \frac{9}{8} \) meters - \( 2 \frac{1}{2} = \frac{5}{2} \) meters 2. The equation becomes: \[ f - \frac{9}{8} = \frac{5}{2} \] 3. To find \( f \), add \( \frac{9}{8} \) to both sides: \[ f = \frac{5}{2} + \frac{9}{8} \] 4. Finding a common denominator (which is 8): - Convert \( \frac{5}{2} = \frac{20}{8} \) 5. So: \[ f = \frac{20}{8} + \frac{9}{8} = \frac{29}{8} \] 6. Therefore, Tia started with \( \frac{29}{8} \), or \( 3 \frac{5}{8} \) meters of fabric. Thus, the finalized equation representing the situation is: \[ f - 1 \frac{1}{8} = 2 \frac{1}{2} \] with the solution indicating Tia started with \( 3 \frac{5}{8} \) meters of fabric.