Solve the Fraction Equation: Finding 'a' in a/6 = 6/7

To solve this problem, we'll follow these steps:

• Step 1: Start with the given equation.
• Step 2: Use cross-multiplication to eliminate the fractions.
• Step 3: Simplify the resulting expression.
• Step 4: Solve for the variable $a$.

Now, let's work through each step:
Step 1: The equation given is $\frac{a}{6} = \frac{6}{7}$.
Step 2: We apply cross-multiplication: Multiply both sides to get $a \times 7 = 6 \times 6$.
Step 3: Simplify the equation: $7a = 36$.
Step 4: Solve for $a$ by dividing both sides by 7:
$a = \frac{36}{7}$.
This fraction can be converted to a mixed number: $a = 5\frac{1}{7}$.

Therefore, the solution to the problem is $a = 5\frac{1}{7}$.