T+25/27-7/9=41/54

To solve the equation \( t + \frac{25}{27} - \frac{7}{9} = \frac{41}{54} \), let's follow these steps:

1. Combine Like Terms: First, simplify the left side of the equation. To subtract \(\frac{7}{9}\) from \(\frac{25}{27}\), we need a common denominator. The least common multiple of 27 and 9 is 27.

   Convert \(\frac{7}{9}\): \[ \frac{7}{9} = \frac{7 \times 3}{9 \times 3} = \frac{21}{27} \]

   Now the equation becomes: \[ t + \frac{25}{27} - \frac{21}{27} = \frac{41}{54} \]

   Simplify the left side: \[ t + \frac{4}{27} = \frac{41}{54} \]

2. Isolate \(t\): Subtract \(\frac{4}{27}\) from both sides: \[ t = \frac{41}{54} - \frac{4}{27} \]

   We need a common denominator to combine these fractions. The least common multiple of 54 and 27 is 54. Convert \(\frac{4}{27}\): \[ \frac{4}{27} = \frac{4 \times 2}{27 \times 2} = \frac{8}{54} \]

   Now substitute this back into the equation: \[ t = \frac{41}{54} - \frac{8}{54} \]

   Combine the fractions: \[ t = \frac{41 - 8}{54} = \frac{33}{54} \]

3. Simplify \(t\): Reduce \(\frac{33}{54}\): \[ \frac{33}{54} = \frac{11}{18} \quad (\text{dividing the numerator and denominator by 3}) \]

Thus, the final solution is: \[ t = \frac{11}{18} \]