What is the fraction form of $87\frac{1}{2}$ %?
$\frac{7}{8}$
To find the fraction form of the percentage $87\frac{1}{2}$%, we first need to convert this percentage into a numerical fraction. The step-by-step solution is as follows:
- Understand what $87\frac{1}{2}$% means in fraction form. The percentage means per hundred, so we have: \(87\frac{1}{2} \% = 87.5 \% = \frac{87.5}{100}\).
- Convert the decimal to a fraction: \(87.5 = \frac{175}{2}\) because dividing 87.5 by 1 gives us 87 and 0.5, which is expressed as \(\frac{1}{2}\). Multiplying both numerator and denominator by 10 to eliminate the decimal gives: \(\frac{875}{10} = \frac{175}{2}\).
- Use the fraction of \(\frac{875}{10} = \frac{175}{2}\) and convert it over 100 for percentage conversion: \(\frac{175}{2} \times \frac{1}{100} = \frac{175}{200}.\)
- Simplify the fraction \(\frac{175}{200}\):
The greatest common divisor (GCD) of 175 and 200 is 25. Therefore, divide both numerator and denominator by 25: \(\frac{175}{25} = 7\) and \(\frac{200}{25} = 8\), so \(\frac{175}{200} = \frac{7}{8}\).
Thus, the fraction form of $87\frac{1}{2}$% is \(\frac{7}{8}\). This matches our given correct answer option, \(\frac{7}{8}\).
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