4. \( \frac{2}{3} v+\frac{1}{4} u \)

Did you know that fractions can be tricky little characters in the world of math? To combine them like in your expression \( \frac{2}{3}v + \frac{1}{4}u \), you need a common denominator. In this case, that would be 12. So, you'd multiply \( \frac{2}{3} \) by 4 to get \( \frac{8}{12}v \) and \( \frac{1}{4} \) by 3 to get \( \frac{3}{12}u \). Now, you're ready for some fun combining: \( \frac{8}{12}v + \frac{3}{12}u \) can be expressed as \( \frac{8v + 3u}{12} \)! If you’re ever stuck on combining expressions like this, don't panic! One common mistake is forgetting to find that all-important least common denominator. Writing out the steps or using a visual aid like a fraction circle can help you see what’s happening with the numbers. Remember, practice makes perfect, and soon you’ll be adding fractions like a pro!