4.2 Calculate the value of \( a \) if: \[ a: 0,4=3: 6 \]

To solve the proportion \( \frac{a}{0.4} = \frac{3}{6} \), we can cross-multiply to find the value of \( a \). 1. **Set up the equation**: \[ a \cdot 6 = 0.4 \cdot 3 \] 2. **Calculate the right side**: \[ 0.4 \cdot 3 = 1.2 \] 3. **Now the equation is**: \[ 6a = 1.2 \] 4. **Solve for \( a \)**: \[ a = \frac{1.2}{6} \] Now, let's calculate \( a \). Calculate the value by following steps: - step0: Calculate: \(\frac{1.2}{6}\) - step1: Convert the expressions: \(\frac{\frac{6}{5}}{6}\) - step2: Multiply by the reciprocal: \(\frac{6}{5}\times \frac{1}{6}\) - step3: Reduce the numbers: \(\frac{1}{5}\times 1\) - step4: Multiply: \(\frac{1}{5}\) Calculating \( a \) gives us: \[ a = \frac{1.2}{6} = 0.2 \] Thus, the value of \( a \) is \( 0.2 \).