1. **Problem:** Calculate $-1.3 + 1.3$. 2. **Formula:** Addition of real numbers. 3. **Work:** $$-1.3 + 1.3 = 0$$ 4. **Explanation:** Adding a number and its negative cancels out to zero. --- 1. **Problem:** Calculate $3 \frac{1}{8} - \frac{7}{8}$. 2. **Formula:** Subtract fractions and mixed numbers. 3. **Work:** Convert $3 \frac{1}{8}$ to improper fraction: $$3 \frac{1}{8} = \frac{3 \times 8 + 1}{8} = \frac{25}{8}$$ Subtract: $$\frac{25}{8} - \frac{7}{8} = \frac{25 - 7}{8} = \frac{18}{8} = \frac{9}{4} = 2 \frac{1}{4}$$ 4. **Explanation:** Convert mixed number to improper fraction, subtract numerators, simplify. --- 1. **Problem:** Calculate $0.75 + (-\frac{1}{4})$. 2. **Formula:** Addition of decimals and fractions. 3. **Work:** Convert $-\frac{1}{4}$ to decimal: $$-\frac{1}{4} = -0.25$$ Add: $$0.75 + (-0.25) = 0.5$$ 4. **Explanation:** Convert fraction to decimal, then add. --- 1. **Problem:** Calculate $-1 \frac{1}{6} - 2 \frac{1}{9}$. 2. **Formula:** Subtract mixed numbers. 3. **Work:** Convert to improper fractions: $$-1 \frac{1}{6} = -\frac{7}{6}, \quad 2 \frac{1}{9} = \frac{19}{9}$$ Find common denominator 18: $$-\frac{7}{6} = -\frac{21}{18}, \quad \frac{19}{9} = \frac{38}{18}$$ Subtract: $$-\frac{21}{18} - \frac{38}{18} = -\frac{59}{18} = -3 \frac{5}{18}$$ 4. **Explanation:** Convert mixed numbers to improper fractions, find common denominator, subtract, simplify. --- 1. **Problem:** Calculate $-\frac{3}{10} + (-\frac{1}{10})$. 2. **Formula:** Addition of fractions with same denominator. 3. **Work:** $$-\frac{3}{10} + (-\frac{1}{10}) = -\frac{3+1}{10} = -\frac{4}{10} = -\frac{2}{5}$$ 4. **Explanation:** Add numerators, keep denominator, simplify. --- 1. **Problem:** Calculate $-\frac{4}{9} + \frac{2}{3}$. 2. **Formula:** Addition of fractions with different denominators. 3. **Work:** Find common denominator 9: $$\frac{2}{3} = \frac{6}{9}$$ Add: $$-\frac{4}{9} + \frac{6}{9} = \frac{-4 + 6}{9} = \frac{2}{9}$$ 4. **Explanation:** Convert to common denominator, add numerators. --- 1. **Problem:** Calculate $-1 \frac{1}{5} + 2 \frac{3}{15}$. 2. **Formula:** Addition of mixed numbers. 3. **Work:** Convert to improper fractions: $$-1 \frac{1}{5} = -\frac{6}{5}, \quad 2 \frac{3}{15} = 2 \frac{1}{5} = \frac{11}{5}$$ Add: $$-\frac{6}{5} + \frac{11}{5} = \frac{5}{5} = 1$$ 4. **Explanation:** Convert mixed numbers to improper fractions, add, simplify. --- 1. **Problem:** Calculate $4.2 - (-8.5)$. 2. **Formula:** Subtracting a negative number is addition. 3. **Work:** $$4.2 - (-8.5) = 4.2 + 8.5 = 12.7$$ 4. **Explanation:** Subtracting a negative is the same as adding the positive. --- **Final answers:** 1. $0$ 2. $2 \frac{1}{4}$ 3. $0.5$ 4. $-3 \frac{5}{18}$ 5. $-\frac{2}{5}$ 6. $\frac{2}{9}$ 7. $1$ 8. $12.7$