Question
86 2/3% as a fraction
Answers
GPT-4o
To convert 86 2/3% to a fraction, follow these steps:
1. **Convert the mixed number to an improper fraction.**
- 2/3 as a fraction is already in its simplest form.
- To combine it with 86, we convert 86 and 2/3 to an improper fraction:
\( 86 \frac{2}{3} = \frac{86 \times 3 + 2}{3} = \frac{258 + 2}{3} = \frac{260}{3} \)
2. **Convert the percentage to a fraction.**
- Since 86 2/3% is a percent, it means \( \frac{86 \frac{2}{3}}{100} \).
\( 86 \frac{2}{3}\% = \frac{\frac{260}{3}}{100} \)
3. **Simplify the complex fraction.**
- To divide by 100, multiply by the reciprocal of 100, which is \( \frac{1}{100} \):
\( \frac{\frac{260}{3}}{100} = \frac{260}{3} \times \frac{1}{100} = \frac{260}{300} \)
4. **Simplify the resulting fraction.**
- Both the numerator (260) and the denominator (300) can be divided by 20:
\( \frac{260 \div 20}{300 \div 20} = \frac{13}{15} \)
Therefore, 86 2/3% as a fraction is \( \frac{13}{15} \).
1. **Convert the mixed number to an improper fraction.**
- 2/3 as a fraction is already in its simplest form.
- To combine it with 86, we convert 86 and 2/3 to an improper fraction:
\( 86 \frac{2}{3} = \frac{86 \times 3 + 2}{3} = \frac{258 + 2}{3} = \frac{260}{3} \)
2. **Convert the percentage to a fraction.**
- Since 86 2/3% is a percent, it means \( \frac{86 \frac{2}{3}}{100} \).
\( 86 \frac{2}{3}\% = \frac{\frac{260}{3}}{100} \)
3. **Simplify the complex fraction.**
- To divide by 100, multiply by the reciprocal of 100, which is \( \frac{1}{100} \):
\( \frac{\frac{260}{3}}{100} = \frac{260}{3} \times \frac{1}{100} = \frac{260}{300} \)
4. **Simplify the resulting fraction.**
- Both the numerator (260) and the denominator (300) can be divided by 20:
\( \frac{260 \div 20}{300 \div 20} = \frac{13}{15} \)
Therefore, 86 2/3% as a fraction is \( \frac{13}{15} \).