Question: Activity in Mathematics 7 Directions: Solve each problem involving operations on rational numbers. Show your complete solution in a separate piece of paper. Write your final answer in simplest form. 1. $\frac{3}{4} + \left(-\frac{5}{8}\right) = ____________$ 2. $-2.5 + 4.8 = ____________$ 3. $\frac{7}{9} - \frac{2}{3} = ____________$ 4. $-6.25 - \left(-3.4\right) = ____________$ 5. $-\frac{5}{6} + \frac{1}{3} = ____________$ 6. $\left(-\frac{4}{5}\right) \times \frac{15}{8} = ____________$ 7. $-3.2 \times 2.5 = ____________$ 8. $\frac{7}{10} \times \left(-\frac{20}{21}\right) = ____________$ 9. $-8.4 \div 2.1 = ____________$ 10. $\left(-\frac{9}{10}\right) \div \frac{3}{5} = ____________$ 11. $\frac{3}{5} + \left(-1.8\right) = ____________$ 12. $2.75 - \frac{3}{4} = ____________$ 13. $\left(-\frac{5}{6}\right) + 1.25 = ____________$ 14. $-2.4 + \frac{7}{5} - \frac{3}{10} = ____________$ 15. $\left(-\frac{3}{4}\right) \times 2.4 + \frac{1}{2} = ____________$

1. **Problem:** Calculate $\frac{3}{4} + \left(-\frac{5}{8}\right)$. 2. **Formula:** To add fractions, find a common denominator and add numerators. 3. **Work:** - Common denominator of $4$ and $8$ is $8$. - Convert $\frac{3}{4} = \frac{6}{8}$. - Add: $\frac{6}{8} + \left(-\frac{5}{8}\right) = \frac{6 - 5}{8} = \frac{1}{8}$. 4. **Answer:** $\frac{1}{8}$. 1. **Problem:** Calculate $-2.5 + 4.8$. 2. **Formula:** Add decimal numbers directly. 3. **Work:** - $-2.5 + 4.8 = 4.8 - 2.5 = 2.3$. 4. **Answer:** $2.3$. 1. **Problem:** Calculate $\frac{7}{9} - \frac{2}{3}$. 2. **Formula:** Subtract fractions by finding a common denominator. 3. **Work:** - Common denominator of $9$ and $3$ is $9$. - Convert $\frac{2}{3} = \frac{6}{9}$. - Subtract: $\frac{7}{9} - \frac{6}{9} = \frac{1}{9}$. 4. **Answer:** $\frac{1}{9}$. 1. **Problem:** Calculate $-6.25 - \left(-3.4\right)$. 2. **Formula:** Subtracting a negative is adding the positive. 3. **Work:** - $-6.25 - (-3.4) = -6.25 + 3.4 = -2.85$. 4. **Answer:** $-2.85$. 1. **Problem:** Calculate $-\frac{5}{6} + \frac{1}{3}$. 2. **Formula:** Add fractions with common denominator. 3. **Work:** - Common denominator is $6$. - Convert $\frac{1}{3} = \frac{2}{6}$. - Add: $-\frac{5}{6} + \frac{2}{6} = -\frac{3}{6} = -\frac{1}{2}$. 4. **Answer:** $-\frac{1}{2}$. 1. **Problem:** Calculate $\left(-\frac{4}{5}\right) \times \frac{15}{8}$. 2. **Formula:** Multiply numerators and denominators. 3. **Work:** - Multiply: $\frac{-4 \times 15}{5 \times 8} = \frac{-60}{40}$. - Simplify: $\frac{-60}{40} = \frac{\cancel{-60}^{-3} \times 20}{\cancel{40}^{-2} \times 20} = -\frac{3}{2}$. 4. **Answer:** $-\frac{3}{2}$. 1. **Problem:** Calculate $-3.2 \times 2.5$. 2. **Formula:** Multiply decimals. 3. **Work:** - $-3.2 \times 2.5 = -8.0$. 4. **Answer:** $-8.0$. 1. **Problem:** Calculate $\frac{7}{10} \times \left(-\frac{20}{21}\right)$. 2. **Formula:** Multiply numerators and denominators. 3. **Work:** - Multiply: $\frac{7 \times (-20)}{10 \times 21} = \frac{-140}{210}$. - Simplify: $\frac{-140}{210} = \frac{\cancel{-140}^{-2} \times 70}{\cancel{210}^{-3} \times 70} = -\frac{2}{3}$. 4. **Answer:** $-\frac{2}{3}$. 1. **Problem:** Calculate $-8.4 \div 2.1$. 2. **Formula:** Divide decimals. 3. **Work:** - $-8.4 \div 2.1 = -4$. 4. **Answer:** $-4$. 1. **Problem:** Calculate $\left(-\frac{9}{10}\right) \div \frac{3}{5}$. 2. **Formula:** Dividing fractions is multiplying by reciprocal. 3. **Work:** - $\left(-\frac{9}{10}\right) \times \frac{5}{3} = \frac{-9 \times 5}{10 \times 3} = \frac{-45}{30}$. - Simplify: $\frac{-45}{30} = \frac{\cancel{-45}^{-3} \times 15}{\cancel{30}^{-2} \times 15} = -\frac{3}{2}$. 4. **Answer:** $-\frac{3}{2}$. 1. **Problem:** Calculate $\frac{3}{5} + \left(-1.8\right)$. 2. **Formula:** Convert decimal to fraction or fraction to decimal. 3. **Work:** - Convert $\frac{3}{5} = 0.6$. - Add: $0.6 + (-1.8) = -1.2$. 4. **Answer:** $-1.2$. 1. **Problem:** Calculate $2.75 - \frac{3}{4}$. 2. **Formula:** Convert fraction to decimal or decimal to fraction. 3. **Work:** - Convert $\frac{3}{4} = 0.75$. - Subtract: $2.75 - 0.75 = 2.0$. 4. **Answer:** $2.0$. 1. **Problem:** Calculate $\left(-\frac{5}{6}\right) + 1.25$. 2. **Formula:** Convert decimal to fraction or fraction to decimal. 3. **Work:** - Convert $1.25 = \frac{5}{4}$. - Find common denominator $12$. - Convert $-\frac{5}{6} = -\frac{10}{12}$ and $\frac{5}{4} = \frac{15}{12}$. - Add: $-\frac{10}{12} + \frac{15}{12} = \frac{5}{12}$. 4. **Answer:** $\frac{5}{12}$. 1. **Problem:** Calculate $-2.4 + \frac{7}{5} - \frac{3}{10}$. 2. **Formula:** Convert decimals to fractions or fractions to decimals. 3. **Work:** - Convert $-2.4 = -\frac{12}{5}$. - Common denominator $10$. - Convert: $-\frac{12}{5} = -\frac{24}{10}$, $\frac{7}{5} = \frac{14}{10}$, $\frac{3}{10}$ stays. - Add: $-\frac{24}{10} + \frac{14}{10} - \frac{3}{10} = \frac{-24 + 14 - 3}{10} = \frac{-13}{10} = -1.3$. 4. **Answer:** $-1.3$. 1. **Problem:** Calculate $\left(-\frac{3}{4}\right) \times 2.4 + \frac{1}{2}$. 2. **Formula:** Multiply and then add. 3. **Work:** - Convert $2.4 = \frac{12}{5}$. - Multiply: $-\frac{3}{4} \times \frac{12}{5} = \frac{-36}{20}$. - Simplify: $\frac{-36}{20} = \frac{\cancel{-36}^{-9} \times 4}{\cancel{20}^{-5} \times 4} = -\frac{9}{5}$. - Add $\frac{1}{2}$: find common denominator $10$. - Convert: $-\frac{9}{5} = -\frac{18}{10}$, $\frac{1}{2} = \frac{5}{10}$. - Add: $-\frac{18}{10} + \frac{5}{10} = -\frac{13}{10} = -1.3$. 4. **Answer:** $-1.3$.