["# Solve the Equation (\frac{5}{3} = \frac{15}{c}): Step-by-Step Explanation", "If you’ve stumbled upon the equation (\frac{5}{3} = \frac{15}{c}), you’re in the right place. This article guides you through solving this proportion using clear math principles and practical techniques—perfect for students, self-learners, or anyone looking to strengthen their algebra skills.", "---", "## What is the Equation (\frac{5}{3} = \frac{15}{c})?", "This equation presents a proportion, meaning two ratios are equal. Here, (\frac{5}{3}) is a fixed ratio, and (\frac{15}{c}) varies with (c)—the unknown variable we want to find.", "---", "## Step-by-Step Solution", "### Step 1: Understand the Proportion Form
\nUse cross-multiplication, the standard method for solving simple proportions:", "[
\n\frac{a}{b} = \frac{c}{d} \quad \Rightarrow \quad a \cdot d = b \cdot c
\n]", "For our equation:
\n[
\n\frac{5}{3} = \frac{15}{c}
\n]", "Apply cross-multiplication:", "[
\n5 \cdot c = 3 \cdot 15
\n]", "---", "### Step 2: Simplify the Right Side
\nCompute (3 \ imes 15):", "[
\n5c = 45
\n]", "---", "### Step 3: Solve for (c)
\nDivide both sides by 5:", "[
\nc = \frac{45}{5} = 9
\n]", "---", "## Verification: Plug (c = 9) Back In
\nCheck if it satisfies the original equation:", "[
\n\frac{5}{3} = \frac{15}{9}
\n]", "Simplify (\frac{15}{9}):", "[
\n\frac{15 \div 3}{9 \div 3} = \frac{5}{3}
\n]", "✔ Confirmed—both sides equal (\frac{5}{3}), so the solution is correct.", "---", "## What Does This Mean?
\nThe value (c = 9) makes the ratio (\frac{15}{c}) exactly match (\frac{5}{3}). This kind of problem is fundamental in understanding equivalent ratios, solving for unknowns in proportions, and real-world applications like scaling recipes, mapping, or finance.", "---", "## Related Concepts & Tips", "- Cross-Multiplication Rule: Always valid for proportions (a/b = c/d) → (ad = bc).
\n- Common Denominators: Avoiding cross-multiplication in complex cases, rewrite both ratios with a common denominator.
\n- Real-World Use: Proportions appear in percentages, unit conversions, and direct variation relationships.", "---", "## Summary", "- Solve (\frac{5}{3} = \frac{15}{c}) by cross-multiplying:
\n [
\n 5c = 45 \Rightarrow c = 9
\n ]
\n- Verify by substituting back into the equation.
\n- This mastery unlocks broader geometric and algebraic problem-solving skills.", "---", "## Related Search Terms
\n- Solve (\frac{5}{3} = \frac{15}{c}),
\n- How to solve proportions,
\n- Algebraic ratios explained,
\n- Cross-multiplying in equations.", "---", "If you enjoyed this breakdown, explore more on solving linear equations, proportions, and algebraic methods—key tools for math success!"]
