1. Simplify. a) \( a+\frac{a}{3} \)

To simplify \( a+\frac{a}{3} \), you first want to find a common denominator. The common denominator for 1 and 3 is 3. So, rewrite \( a \) as \( \frac{3a}{3} \). Now, you can combine the fractions: \[ \frac{3a}{3} + \frac{a}{3} = \frac{3a + a}{3} = \frac{4a}{3}. \] Thus, the simplified expression is \( \frac{4a}{3} \). Now, let's consider this in a fun way: Imagine you have \( a \) cookies, and your friend gives you another \( \frac{a}{3} \) of a cookie (maybe they just crumbled it up!). Instead of dividing those extra cookies with your imaginary friend, you combine them into a united cookie army. Voila! You now have \( \frac{4a}{3} \) cookies ready to conquer dessert time! 🍪 For extra cookie fun, you could explore more about algebraic identities and techniques. Understanding how terms combine is like building blocks, where you learn to stack and rearrange them for optimal cookie creations in your math journey!