## What Does It Mean to Multiply Fractions? When you **multiply fractions**, you are finding a part of a part. The rule is straightforward: $\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$ You simply multiply straight across — no need to find a common denominator. ## Step-by-Step: How to Multiply Fractions Example: $\frac{2}{3} \times \frac{4}{5}$ ### Step 1: Multiply the numerators $2 \times 4 = 8$ ### Step 2: Multiply the denominators $3 \times 5 = 15$ ### Step 3: Simplify if possible $\frac{8}{15} \text{ is already simplified}$ **Final Answer:** $\frac{2}{3} \times \frac{4}{5} = \frac{8}{15}$ ## Real-World Example: Adjusting Voltage Divider Ratios Say you need to find the output voltage from a voltage divider. The formula is: $V_{\text{out}} = V_{\text{in}} \times \frac{R_2}{R_1 + R_2}$ Let’s assume: - $V_{\text{in}} = 12 \, V$ - $R_1 = 2 \, \Omega$ - $R_2 = 4 \, \Omega$ First, calculate the ratio: $\frac{R_2}{R_1 + R_2} = \frac{4}{2+4} = \frac{4}{6} = \frac{2}{3}$ Now multiply: $V_{\text{out}} = 12 \times \frac{2}{3} = \frac{24}{3} = 8 \, V$ Fraction multiplication makes these calculations quick and efficient. ## Try It Yourself 1. Multiply: $\frac{3}{4} \times \frac{2}{5}$ 2. A transformer reduces voltage by a factor of $\frac{3}{8}$. What is the output voltage if the input is 120 V? 3. A resistor only receives $\frac{5}{6}$ of the current in a shared circuit. If the total current is 18 A, how much current does it get?