\frac{15}{y} = \frac{5}{3}

["# How to Solve ( \frac{15}{y} = \frac{5}{3} ): A Step-by-Step Guide", "Understanding how to solve equations involving fractions can seem challenging at first, but breaking the process down makes it manageable. In this article, we’ll explore how to solve the equation:", "[\n\frac{15}{y} = \frac{5}{3}\n]", "Whether you're a student learning algebra or simply looking to refresh your math skills, this guide will walk you through each step clearly and simply.", "---", "## Step 1: Understand What the Equation Means", "The equation\n[\n\frac{15}{y} = \frac{5}{3}\n]\nindicates that the ratio of 15 divided by an unknown variable ( y ) is equal to the ratio 5 over 3. To solve for ( y ), our goal is to isolate ( y ) on one side of the equation.", "---", "## Step 2: Use Cross-Multiplication to Eliminate the Fractions", "One of the most effective methods for solving proportions like this is cross-multiplication. This technique avoids changing the original equation while eliminating the denominators:", "[\n15 \ imes 3 = 5 \ imes y\n]", "This step transforms the fraction equation into a simple linear expression.", "---", "## Step 3: Perform the Multiplication", "Now compute both sides:", "- Left side: ( 15 \ imes 3 = 45 )\n- Right side: ( 5 \ imes y = 5y )", "So the equation becomes:", "[\n45 = 5y\n]", "---", "## Step 4: Solve for ( y )", "To isolate ( y ), divide both sides of the equation by 5:", "[\ny = \frac{45}{5} = 9\n]", "---", "## Final Answer", "Therefore, the solution to the equation\n[\n\frac{15}{y} = \frac{5}{3}\n]\nis", "[\n\boxed{y = 9}\n]", "---", "## Why This Method Works", "Cross-multiplication relies on the fundamental property of proportions: when two fractions are equal, the cross products are also equal. This approach simplifies solving for the variable without requiring advanced algebra, making it ideal for beginners and efficient even in intermediate levels.", "---", "## Additional Tips", "- Always verify your solution: Substitute ( y = 9 ) back into the original equation:\n [\n \frac{15}{9} = \frac{5}{3} \quad \Rightarrow \quad \frac{5}{3} = \frac{5}{3} \quad \ ext{(True!)}\n ]\n- Use this method for similar equations involving ratios and fractions.", "---", "## Key Takeaways", "- The fraction equation ( \frac{15}{y} = \frac{5}{3} ) can be solved using cross-multiplication.\n- Cross-multiplying leads to a simple linear equation: ( 45 = 5y ).\n- Solving gives ( y = 9 ), which satisfies the original equation.\n- Practice helps reinforce understanding and builds confidence in solving rational equations.", "---", "If you’re struggling with similar fraction equations, remember: simplify step by step, use cross-multiplication carefully, and always verify your answer. Mastering this skill opens the door to more advanced algebra topics.", "Happy solving!"]