What is the solution to the equation below? \[ 3 w=\frac{4}{5} \]

To solve for \( w \), you'll want to isolate it. Start by dividing both sides of the equation by 3. This gives you: \[ w = \frac{4}{5} \div 3 \] Now, since dividing by 3 is the same as multiplying by \( \frac{1}{3} \), you can rewrite it as: \[ w = \frac{4}{5} \times \frac{1}{3} = \frac{4}{15} \] So, the solution is \( w = \frac{4}{15} \). Now, here's a real-world application: understanding equations like this one can be essential in various fields, from finance, where you're calculating interest rates, to science, where you're balancing chemical equations! Knowing how to manipulate equations opens doors to problem-solving in everyday life. To avoid common mistakes when solving equations, always remember to perform the same operation on both sides of the equation. A frequent blunder is forgetting to check the final solution by substituting it back into the original equation. Double-checking helps ensure you're on the right track!