Add or subtract, as indicated. See Example 4. 3 5 —— + —— 2k 3k

Verified step by step guidance

1. Identify the common denominator for the fractions $\frac{3}{2k}$ and $\frac{5}{3k}$. The common denominator is $6k$.
2. Rewrite each fraction with the common denominator $6k$.
3. For $\frac{3}{2k}$, multiply both the numerator and the denominator by 3 to get $\frac{9}{6k}$.
4. For $\frac{5}{3k}$, multiply both the numerator and the denominator by 2 to get $\frac{10}{6k}$.
5. Add the two fractions: $\frac{9}{6k}+\frac{10}{6k}=\frac{9+10}{6k}$.

Key Concepts

Fraction Addition and Subtraction

To add or subtract fractions, they must have a common denominator. The least common denominator (LCD) is the smallest multiple that both denominators share. Once the fractions are expressed with the same denominator, you can combine the numerators while keeping the denominator unchanged. This process is essential for simplifying the operation and obtaining a correct result.

Simplifying Fractions

After performing operations on fractions, it is often necessary to simplify the result. Simplifying involves dividing both the numerator and the denominator by their greatest common divisor (GCD). This step ensures that the fraction is expressed in its simplest form, making it easier to understand and use in further calculations.

Variable Representation in Fractions

In the given problem, variables (like 'k') are used in the denominators of the fractions. Understanding how to manipulate these variables is crucial, as it affects the overall simplification and addition of the fractions. When working with variables, it is important to treat them as algebraic quantities, ensuring that operations respect their properties and relationships.