Solve the Ratio Equation: Simplifying 126/a : 6x/7a

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

• Step 1: Rewrite the division of fractions as multiplication by the reciprocal.
• Step 2: Simplify the resulting expression.
• Step 3: Verify simplification and final form.

Now, let's work through each step:
Step 1: The problem involves dividing $\frac{126}{a}$ by $\frac{6x}{7a}$. Using the property of dividing fractions, we rewrite this as:

$\frac{126}{a} \div \frac{6x}{7a} = \frac{126}{a} \times \frac{7a}{6x}$.

Step 2: Multiply the fractions:

$\frac{126}{a} \times \frac{7a}{6x} = \frac{126 \times 7a}{a \times 6x}$.

Simplify the expression:

Notice that the term $a$ in the numerator and the denominator cancels out, leaving:

$\frac{126 \times 7}{6x}$.

Calculate the number:

$126 \times 7 = 882$.

Divide by 6:

$\frac{882}{6x} = \frac{147}{x}$.

Therefore, the solution to the problem is $\frac{147}{x}$.