Question
What is 160% of 40? Four students solved this problem and their work is shown below. Choose the student whose work is correct.
Cam's work. 16 times 40 = 00 .00 + 640 = 640.
Gitana's work. 1.6 times 40 = 00. 00 + 640 = 64.0.
Naoko's work. 0.16 times 40 = 00. 00 + 640 = 6.40.
Sanjay's work. 160 times 40 = 00. 00 + 6400 = 6400.
Answers
GPT-4o mini
To find 160% of 40, we can convert the percentage to a decimal and multiply:
1. Convert 160% to a decimal:
\( 160\% = \frac{160}{100} = 1.6 \)
2. Multiply by 40:
\( 1.6 \times 40 = 64 \)
Now let's evaluate each student's work:
- **Cam's work**: \( 16 \times 40 = 640 \). This is incorrect as he mistakenly calculated \( 16 \) instead of \( 1.6 \).
- **Gitana's work**: \( 1.6 \times 40 = 64 \) (but she wrote \( 00.00 + 640 = 64.0 \)). The calculation is correct but the additional 640 is wrong. The final answer is incorrect as written.
- **Naoko's work**: \( 0.16 \times 40 = 6.4 \) (but this is incorrect as 0.16 is not the right decimal). This is not the correct approach since he did not convert the percentage correctly.
- **Sanjay's work**: \( 160 \times 40 = 6400 \). Sanjay multiplied 160 instead of converting it to a decimal.
None of the students reached the correct final answer of 64. The closest correct calculation belongs to Gitana, but her presentation of the answer was incorrect.
**Final Correct Calculation**:
160% of 40 is indeed 64.
None of the students' calculations were fully correct as explained.
1. Convert 160% to a decimal:
\( 160\% = \frac{160}{100} = 1.6 \)
2. Multiply by 40:
\( 1.6 \times 40 = 64 \)
Now let's evaluate each student's work:
- **Cam's work**: \( 16 \times 40 = 640 \). This is incorrect as he mistakenly calculated \( 16 \) instead of \( 1.6 \).
- **Gitana's work**: \( 1.6 \times 40 = 64 \) (but she wrote \( 00.00 + 640 = 64.0 \)). The calculation is correct but the additional 640 is wrong. The final answer is incorrect as written.
- **Naoko's work**: \( 0.16 \times 40 = 6.4 \) (but this is incorrect as 0.16 is not the right decimal). This is not the correct approach since he did not convert the percentage correctly.
- **Sanjay's work**: \( 160 \times 40 = 6400 \). Sanjay multiplied 160 instead of converting it to a decimal.
None of the students reached the correct final answer of 64. The closest correct calculation belongs to Gitana, but her presentation of the answer was incorrect.
**Final Correct Calculation**:
160% of 40 is indeed 64.
None of the students' calculations were fully correct as explained.