Fraction Operations Fc94E9

1. **Problem 1:** Calculate $\frac{4}{21} + \frac{6}{3}$. Formula: To add fractions, find a common denominator and add numerators. Step 1: Simplify $\frac{6}{3} = 2$. Step 2: Convert $2$ to fraction with denominator $21$: $\frac{42}{21}$. Step 3: Add fractions: $\frac{4}{21} + \frac{42}{21} = \frac{46}{21}$. Step 4: Simplify if possible. $\frac{46}{21}$ is in simplest form. **Answer:** $\frac{46}{21}$. 2. **Problem 2:** Calculate $6, \frac{18}{4} \times \frac{6}{5}$. Step 1: Convert mixed number $6, \frac{18}{4}$ to improper fraction. $6 = \frac{24}{4}$, so $6, \frac{18}{4} = \frac{24}{4} + \frac{18}{4} = \frac{42}{4}$. Step 2: Multiply $\frac{42}{4} \times \frac{6}{5}$. Step 3: Multiply numerators and denominators: $$\frac{42 \times 6}{4 \times 5} = \frac{252}{20}$$ Step 4: Simplify fraction by dividing numerator and denominator by 4: $$\frac{\cancel{252}^{63}}{\cancel{20}^{5}} = \frac{63}{5}$$ **Answer:** $\frac{63}{5}$. 3. **Problem 3:** Calculate $\frac{3}{5} - \frac{15}{2}$. Step 1: Find common denominator: $10$. Step 2: Convert fractions: $$\frac{3}{5} = \frac{6}{10}, \quad \frac{15}{2} = \frac{75}{10}$$ Step 3: Subtract: $$\frac{6}{10} - \frac{75}{10} = -\frac{69}{10}$$ **Answer:** $-\frac{69}{10}$. 4. **Problem 4:** Calculate $\frac{7}{8} - \frac{3}{5}$. Step 1: Find common denominator: $40$. Step 2: Convert fractions: $$\frac{7}{8} = \frac{35}{40}, \quad \frac{3}{5} = \frac{24}{40}$$ Step 3: Subtract: $$\frac{35}{40} - \frac{24}{40} = \frac{11}{40}$$ **Answer:** $\frac{11}{40}$. 5. **Problem 5:** Calculate $\frac{24}{3} \div \frac{4}{3}$. Step 1: Division of fractions: multiply by reciprocal. $$\frac{24}{3} \div \frac{4}{3} = \frac{24}{3} \times \frac{3}{4}$$ Step 2: Multiply numerators and denominators: $$\frac{24 \times 3}{3 \times 4} = \frac{72}{12}$$ Step 3: Simplify: $$\frac{\cancel{72}^{6}}{\cancel{12}^{1}} = 6$$ **Answer:** $6$. 6. **Problem 6:** Calculate $\frac{20}{5} + \frac{14}{17}$. Step 1: Simplify $\frac{20}{5} = 4$. Step 2: Add $4 + \frac{14}{17} = \frac{68}{17} + \frac{14}{17} = \frac{82}{17}$. Step 3: Simplify if possible. $\frac{82}{17}$ is simplest. **Answer:** $\frac{82}{17}$. 7. **Problem 7:** Calculate $-\frac{12}{6} + \frac{1}{2}$. Step 1: Simplify $-\frac{12}{6} = -2$. Step 2: Convert $-2$ to fraction with denominator 2: $-\frac{4}{2}$. Step 3: Add: $$-\frac{4}{2} + \frac{1}{2} = -\frac{3}{2}$$ **Answer:** $-\frac{3}{2}$. 8. **Problem 8:** Calculate $\frac{20}{6} \times \frac{1}{3}$. Step 1: Multiply numerators and denominators: $$\frac{20 \times 1}{6 \times 3} = \frac{20}{18}$$ Step 2: Simplify by dividing numerator and denominator by 2: $$\frac{\cancel{20}^{10}}{\cancel{18}^{9}} = \frac{10}{9}$$ **Answer:** $\frac{10}{9}$. 9. **Problem 9:** Calculate $-\frac{13}{2} \div 3$. Step 1: Division by integer is multiplication by reciprocal: $$-\frac{13}{2} \div 3 = -\frac{13}{2} \times \frac{1}{3} = -\frac{13}{6}$$ **Answer:** $-\frac{13}{6}$.