1. **Stating the problem:** We want to learn how to add and subtract positive and negative fractions. 2. **Formula and rules:** To add or subtract fractions, first find a common denominator. Then add or subtract the numerators. Remember: - A positive fraction plus a positive fraction is positive. - A positive fraction plus a negative fraction is like subtracting the smaller absolute value from the larger. - A negative fraction plus a negative fraction is negative. 3. **Example 1: Addition of positive fractions** $$\frac{1}{4} + \frac{1}{2}$$ Find common denominator: 4 $$\frac{1}{4} + \frac{2}{4} = \frac{3}{4}$$ 4. **Example 2: Addition of positive and negative fractions** $$\frac{3}{4} + \left(-\frac{1}{2}\right)$$ Common denominator: 4 $$\frac{3}{4} - \frac{2}{4} = \frac{1}{4}$$ 5. **Example 3: Subtraction of negative fractions** $$\left(-\frac{2}{3}\right) - \left(-\frac{1}{6}\right)$$ Rewrite subtraction as addition: $$-\frac{2}{3} + \frac{1}{6}$$ Common denominator: 6 $$-\frac{4}{6} + \frac{1}{6} = -\frac{3}{6} = -\frac{1}{2}$$ 6. **Summary:** Always find a common denominator, then add or subtract numerators considering signs. Simplify the result if possible.