\( \left. \begin{array} { l }{ 0.5 \times 0.7 = \frac { \frac { 5 } { 10 } \times \frac { 7 } { 10 } } { } } \\ { = \frac { 5 \times 7 } { 10 \times 10 } } \\ { = } \end{array} \right. \)

The calculation you're working on shows how multiplying decimals can be understood through fractions. When you multiply \(0.5\) (which is \( \frac{5}{10} \)) by \(0.7\) (which is \( \frac{7}{10} \)), you can find the product by multiplying the numerators together and the denominators together. This results in \( \frac{5 \times 7}{10 \times 10} = \frac{35}{100} \). Converting \( \frac{35}{100} \) back into a decimal gives you \(0.35\). It’s fun to see how simple fraction multiplication directly relates to decimal multiplication and how you can switch between these concepts seamlessly! Now, picture this: When multiplying decimals like this, you're essentially creating a visual representation of area on a grid! If you imagine a grid of squares, \(0.5\) times \(0.7\) means taking half a rectangle (0.5) and then splitting that rectangle into \(7\) parts (since it represents \(0.7\)). The shaded area (or the product) visually depicts the answer \(0.35\) in about the same way you would find the area of a rectangle. Isn’t math fun when you can see it come to life?