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: \[ y = -\frac{1}{8} \]