T-11/18=11/12-5/9

To solve the equation \( t - \frac{11}{18} = \frac{11}{12} - \frac{5}{9} \), we first need to simplify the expression on the right side. 1. Find a common denominator between \( \frac{11}{12} \) and \( \frac{5}{9} \). The least common multiple (LCM) of 12 and 9 is 36. 2. Convert each fraction to have a denominator of 36: - For \( \frac{11}{12} \): \[ \frac{11}{12} = \frac{11 \times 3}{12 \times 3} = \frac{33}{36} \] - For \( \frac{5}{9} \): \[ \frac{5}{9} = \frac{5 \times 4}{9 \times 4} = \frac{20}{36} \] 3. Now, substitute back into the equation: \[ t - \frac{11}{18} = \frac{33}{36} - \frac{20}{36} \] Simplifying the right side: \[ \frac{33}{36} - \frac{20}{36} = \frac{33 - 20}{36} = \frac{13}{36} \] So now we have: \[ t - \frac{11}{18} = \frac{13}{36} \] 4. Next, we need to add \( \frac{11}{18} \) to both sides. First, convert \( \frac{11}{18} \) to a denominator of 36: \[ \frac{11}{18} = \frac{11 \times 2}{18 \times 2} = \frac{22}{36} \] 5. Now add \( \frac{22}{36} \) to \( \frac{13}{36} \): \[ t = \frac{13}{36} + \frac{22}{36} = \frac{35}{36} \] So, the solution is: \[ t = \frac{35}{36} \]