## What Is Division of Fractions? To **divide fractions**, you use the "invert and multiply" rule: $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$ In other words, flip the second fraction and then multiply. Division is just multiplication by the reciprocal. ## Step-by-Step: How to Divide Fractions Example: $\frac{3}{4} \div \frac{2}{5}$ ### Step 1: Flip the second fraction $\frac{2}{5} \; \rightarrow \; \frac{5}{2}$ ### Step 2: Multiply $\frac{3}{4} \times \frac{5}{2} = \frac{15}{8}$ ### Step 3: Convert to a mixed number if needed $\frac{15}{8} = 1 \tfrac{7}{8}$ **Final Answer:** $\frac{3}{4} \div \frac{2}{5} = \frac{15}{8}$ ## Real-World Example: Current Division In a parallel circuit, current divides based on resistance. The formula is: $I_1 = I_T \times \frac{R_T}{R_1}$ Suppose: - $I_T = 6 \, A$ - $R_T = \tfrac{3}{4} \, \Omega$ - $R_1 = \tfrac{1}{2} \, \Omega$ ### Step 1: Divide the resistances $\frac{R_T}{R_1} = \frac{3}{4} \div \frac{1}{2} = \frac{3}{4} \times \frac{2}{1} = \frac{6}{4} = \frac{3}{2}$ ### Step 2: Multiply by total current $I_1 = 6 \times \frac{3}{2} = 9 \, A$ The resistor with lower resistance receives more current. Dividing fractions made it possible to calculate this directly. ## Try It Yourself 1. $\frac{5}{6} \div \frac{2}{3}$ 2. You have a 60 V source divided evenly among resistors. Each gets $\tfrac{1}{4}$ of the total voltage. How many resistors are there? 3. A circuit section receives only $\tfrac{1}{2}$ of the available power. Another section receives $\tfrac{1}{3}$ of that. What fraction of the original power does the second section get?