1. Let's start by understanding the problem: You want to know why we use variables like $a$ and $b$ when combining fractions and what happens when we combine them. 2. When combining fractions, the general formula is: $$\frac{a}{c} + \frac{b}{d} = \frac{ad + bc}{cd}$$ Here, $a$ and $b$ are the numerators of the fractions, and $c$ and $d$ are the denominators. 3. Important rule: To add fractions, they must have a common denominator. We find the common denominator by multiplying the denominators $c$ and $d$. 4. Then, we adjust the numerators accordingly: multiply $a$ by $d$ and $b$ by $c$ to keep the fractions equivalent. 5. After that, we add the adjusted numerators: $ad + bc$. 6. So, the combined fraction is: $$\frac{ad + bc}{cd}$$ 7. This process ensures that the fractions are combined correctly without making assumptions or skipping steps. 8. Using variables $a$ and $b$ helps us generalize the process for any fractions, so you can apply it to specific numbers confidently. Final answer: When combining fractions $\frac{a}{c}$ and $\frac{b}{d}$, the result is $$\frac{ad + bc}{cd}$$ which is the sum with a common denominator.