Question

1. \frac{5}{6} = \frac{7n + 9}{9}

Explanation:

Step1: Cross - multiply the fractions

To solve the equation \(\frac{5}{6}=\frac{7m + 9}{9}\), we cross - multiply. Cross - multiplying gives us \(5\times9=6\times(7m + 9)\).
Calculating the left - hand side: \(5\times9 = 45\).
Calculating the right - hand side: \(6\times(7m+9)=6\times7m+6\times9 = 42m+54\). So the equation becomes \(45 = 42m+54\).

Step2: Isolate the variable term

Subtract 54 from both sides of the equation \(45 = 42m+54\) to get \(45-54=42m\).
Calculating \(45 - 54=-9\), so the equation is \(-9 = 42m\).

Step3: Solve for m

Divide both sides of the equation \(-9 = 42m\) by 42. We have \(m=\frac{-9}{42}\).
Simplify the fraction \(\frac{-9}{42}\) by dividing both the numerator and the denominator by 3. \(\frac{-9\div3}{42\div3}=\frac{-3}{14}\).

Answer:

\(m =-\frac{3}{14}\)