Solve the Ratio Equation: Find Proportion Between (3a-12b) and (9x/4y)

To solve the mathematical expression $(3a-12b):(9x/4y)$, follow these steps:

• Step 1: Understand that the notation $(3a-12b):(9x/4y)$ means $(3a-12b) \div \left( \frac{9x}{4y} \right)$.
• Step 2: Migrate from division to multiplication by taking the reciprocal of the divisor: $(3a-12b) \times \left( \frac{4y}{9x} \right)$.
• Step 3: Apply the distributive property:

Multiply $(3a-12b)$ by $\frac{4y}{9x}$:

$(3a \times \frac{4y}{9x}) + (-12b \times \frac{4y}{9x}) = \frac{3a \times 4y}{9x} - \frac{12b \times 4y}{9x}$

Simplify each term:

• First term: $\frac{3a \times 4y}{9x} = \frac{12ay}{9x} = \frac{4ay}{3x}$
• Second term: $\frac{12b \times 4y}{9x} = \frac{48by}{9x} = \frac{16by}{3x}$

Thus, the expression becomes:

$\frac{4ay}{3x} - \frac{16by}{3x} = \frac{4ay - 16by}{3x}$

Therefore, the solution to the problem is $\frac{4ay-16by}{3x}$.