Answer :
To determine the fraction and the percentage of free throws made by the basketball player, we can proceed step-by-step.
1. Determine the total number of free throws attempted:
- The problem states that the player attempted 100 free throws in total.
2. Determine the number of free throws missed:
- The player missed 23 out of these 100 free throws.
3. Calculate the number of free throws made:
- Since the player missed 23 free throws, the number of free throws made is:
[tex]\[ \text{Number of free throws made} = \text{Total free throws} - \text{Missed free throws} = 100 - 23 = 77 \][/tex]
4. Calculate the fraction of free throws made:
- To find the fraction of free throws made, we divide the number of made free throws by the total number of free throws attempted:
[tex]\[ \text{Fraction of free throws made} = \frac{\text{Number of free throws made}}{\text{Total free throws}} = \frac{77}{100} \][/tex]
5. Calculate the percentage of free throws made:
- To convert the fraction to a percentage, we multiply the fraction by 100:
[tex]\[ \text{Percentage of free throws made} = \left(\frac{77}{100}\right) \times 100 = 77\% \][/tex]
Thus, the fraction of free throws made is \(\frac{77}{100}\) and the percentage of free throws made is \(77\%\).
Hence, the correct answers are:
- Fraction: B. \(\frac{77}{100}\)
- Percentage: D. [tex]\(77\%\)[/tex]
1. Determine the total number of free throws attempted:
- The problem states that the player attempted 100 free throws in total.
2. Determine the number of free throws missed:
- The player missed 23 out of these 100 free throws.
3. Calculate the number of free throws made:
- Since the player missed 23 free throws, the number of free throws made is:
[tex]\[ \text{Number of free throws made} = \text{Total free throws} - \text{Missed free throws} = 100 - 23 = 77 \][/tex]
4. Calculate the fraction of free throws made:
- To find the fraction of free throws made, we divide the number of made free throws by the total number of free throws attempted:
[tex]\[ \text{Fraction of free throws made} = \frac{\text{Number of free throws made}}{\text{Total free throws}} = \frac{77}{100} \][/tex]
5. Calculate the percentage of free throws made:
- To convert the fraction to a percentage, we multiply the fraction by 100:
[tex]\[ \text{Percentage of free throws made} = \left(\frac{77}{100}\right) \times 100 = 77\% \][/tex]
Thus, the fraction of free throws made is \(\frac{77}{100}\) and the percentage of free throws made is \(77\%\).
Hence, the correct answers are:
- Fraction: B. \(\frac{77}{100}\)
- Percentage: D. [tex]\(77\%\)[/tex]
