1⅑×y+⁷/¹⁸=¼

To solve the equation \( 1 \frac{1}{9} \times y + \frac{7}{18} = \frac{1}{4} \), we can follow these steps:

1. Convert the mixed number \( 1 \frac{1}{9} \) to an improper fraction: \[ 1 \frac{1}{9} = \frac{9}{9} + \frac{1}{9} = \frac{10}{9} \]

2. Substitute the improper fraction into the equation: \[ \frac{10}{9} \times y + \frac{7}{18} = \frac{1}{4} \]

3. Isolate the term involving \( y \): \[ \frac{10}{9} \times y = \frac{1}{4} - \frac{7}{18} \]

4. Find a common denominator for \( \frac{1}{4} \) and \( \frac{7}{18} \). The least common multiple of 4 and 18 is 36. We'll convert both fractions:

   • For \( \frac{1}{4} \): \[ \frac{1}{4} = \frac{9}{36} \]
   • For \( \frac{7}{18} \): \[ \frac{7}{18} = \frac{14}{36} \]

5. Subtract the fractions: \[ \frac{1}{4} - \frac{7}{18} = \frac{9}{36} - \frac{14}{36} = \frac{-5}{36} \]

6. Now we have: \[ \frac{10}{9} y = \frac{-5}{36} \]

7. Multiply both sides by the reciprocal of \( \frac{10}{9} \) to solve for \( y \): \[ y = \frac{-5}{36} \times \frac{9}{10} = \frac{-5 \times 9}{36 \times 10} = \frac{-45}{360} \]

8. Simplify \( \frac{-45}{360} \): \[ \frac{-45}{360} = \frac{-1}{8} \]

Thus, the solution is: \[ y = -\frac{1}{8} \]