Question

solve for y.
\\(\frac{2}{3} + y - \frac{1}{9} = \frac{7}{9}\\)
enter your answer as a fraction in simplest form
\\(y = square\\)

Explanation:

Step1: Simplify the left - hand side fractions

First, we need to simplify \(\frac{2}{3}-\frac{1}{9}\). To subtract these two fractions, we find a common denominator. The common denominator of 3 and 9 is 9. So we rewrite \(\frac{2}{3}\) as \(\frac{2\times3}{3\times3}=\frac{6}{9}\). Then \(\frac{6}{9}-\frac{1}{9}=\frac{6 - 1}{9}=\frac{5}{9}\). The original equation \(\frac{2}{3}+y-\frac{1}{9}=\frac{7}{9}\) becomes \(y+\frac{5}{9}=\frac{7}{9}\).

Step2: Solve for y

To isolate y, we subtract \(\frac{5}{9}\) from both sides of the equation. Using the subtraction property of equality, if \(y+\frac{5}{9}=\frac{7}{9}\), then \(y=\frac{7}{9}-\frac{5}{9}\). When we subtract the numerators (since the denominators are the same), we get \(y = \frac{7-5}{9}=\frac{2}{9}\).

Answer:

\(\frac{2}{9}\)