If $\frac{3}{5}$ of a number equals $\frac{2}{3}$ of another number, which number is greater?

Step-by-step solution

1. Step 1: Let the numbers be $x$ and $y$. The given condition is $\frac{3}{5}x=\frac{2}{3}y$.
2. Step 2: Solve for the ratio $\frac{x}{y}$ by dividing both sides by $y$ and multiplying both sides by $\frac{5}{3}$: $\frac{x}{y}=\frac{\frac{2}{3}}{\frac{3}{5}}=\frac{2}{3}\cdot \frac{5}{3}=\frac{10}{9}$.
3. Step 3: Since $\frac{10}{9}>1$, it follows that $x>y$.
4. Step 4: Conclude that the first number is greater.

Concept tested: Comparing two numbers using proportion

Published 4 October 2026 · How this solution was prepared and checked