Bill could choose the fraction \( \frac{1}{2} \) and the decimal \( 0.5 \).
Here's the reasoning:
1. Understanding equivalent values:
- Fractions and decimals are different representations of the same value. For instance, some common fractions and their decimal equivalents include:
- \( \frac{1}{4} = 0.25 \)
- \( \frac{1}{2} = 0.5 \)
- \( \frac{3}{4} = 0.75 \)
- \( \frac{1}{3} \approx 0.333\ldots \)
2. Matching chosen cards:
- Bill needs to choose one fraction card and one decimal card such that both representations are numerically equal.
3. Selection:
- One common fraction and its equivalent decimal value is \( \frac{1}{2} \) which is equal to 0.5.
Therefore, Bill could choose the fraction [tex]\( \frac{1}{2} \)[/tex] and the decimal [tex]\( 0.5 \)[/tex].
