Question

In a basketball game, you made 4 baskets out of 12 attempts. Your teammate made 3 baskets out of 8 attempts. a. What fraction of your attempted shots did you make? b. What fraction of your teammate’s attempted shots did she make? c. Who was the more accurate shooter?

Short answer

Answer: You were the more accurate shooter, as your successful shot fraction (1/3) was larger than your teammate's shot fraction (3/8).

Step-by-step solution

a. Your attempted shot fraction

To find the fraction of your successful shots, divide the number of successful shots by the total attempts: \(\frac{4}{12}\). In order to simplify this fraction, find the greatest common divisor (GCD) of the numerator (4) and the denominator (12). In this case, the GCD is 4, so divide both the numerator and the denominator by this number: \(\frac{4}{12} = \frac{4\div4}{12\div4} = \frac{1}{3}\). So the fraction of your attempted shots that you made is 1/3.

b. Your teammate's attempted shot fraction

To find the fraction of your teammate's successful attempts, divide her number of successful shots by her total attempts: \(\frac{3}{8}\). This fraction is already in its simplest form, so we can conclude that your teammate made 3/8 of her attempted shots.

c. Comparing shooting accuracy

In order to determine who was the more accurate shooter, we need to compare your shot fraction (1/3) with your teammate's shot fraction (3/8). One way to do this is to cross-multiply the fractions: \(\frac{1}{3} \cdot \frac{8}{1} = \frac{8}{3}\) and \(\frac{3}{8} \cdot \frac{3}{1} = \frac{9}{8}\). Since \(\frac{8}{3} > \frac{9}{8}\), your shot fraction (1/3) is larger than your teammate's shot fraction (3/8), which makes you the more accurate shooter in this game.