To represent the need to gain 4 yards to score in terms of rational numbers, we would use the integer 4. The integer 4 can be written as the rational number \( \frac{4}{1} \). Since the football team needs to gain those yards and is progressing positively, we can simply represent it as \( +4 \).
So, the rational number that represents the need to gain 4 yards is \( +4 \) or \( \frac{4}{1} \).