Give me some problems with equations with fractions

Here are some problems involving equations with fractions for you to solve:

### 1. Solve for \(x\):
\[
\frac{2x}{3} - \frac{3}{4} = \frac{5}{6}
\]

### 2. Solve for \(y\):
\[
\frac{y}{5} + \frac{2}{3} = \frac{7}{15}
\]

### 3. Solve for \(z\):
\[
\frac{4}{z} + \frac{1}{3} = \frac{10}{9}
\]

### 4. Solve for \(x\):
\[
\frac{5x}{6} - \frac{7}{8} = \frac{11}{12}
\]

### 5. Solve for \(a\):
\[
\frac{3}{4a} + \frac{2}{5a} = \frac{1}{2}
\]

Would you like detailed solutions for any of these problems or have questions on how to approach them?

Here are some related problems you could explore:
1. Solve \( \frac{x}{4} + \frac{3x}{2} = \frac{7}{8} \).
2. Solve \( \frac{3}{2y} - \frac{1}{4} = \frac{5}{6y} \).
3. Solve \( \frac{4x}{5} + \frac{6x}{10} = 1 \).
4. Solve \( \frac{2z + 3}{4} = \frac{5}{6} \).
5. Solve \( \frac{3}{x+1} = \frac{7}{2} - \frac{1}{x+1} \).

### Tip:
When solving equations with fractions, a helpful strategy is to eliminate the fractions by multiplying the entire equation by the least common denominator (LCD).

Explore how to solve equations with fractions through these algebra problems. This guide includes multiple examples with detailed solutions, covering the core concepts of rational equations and using the least common denominator. Suitable for Grades 6-8 students.

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