Question

write as a fraction or as a mixed number.
$2\frac{1}{2}\\%$
$2\frac{1}{2}\\% = \square$
(type an integer, a fraction, or a mixed number. simplify your answer.)

Explanation:

Step1: Convert mixed number to improper fraction

First, convert the mixed number \( 2\frac{1}{2} \) to an improper fraction. The formula for converting a mixed number \( a\frac{b}{c} \) to an improper fraction is \( \frac{a\times c + b}{c} \). So for \( 2\frac{1}{2} \), we have \( a = 2 \), \( b = 1 \), \( c = 2 \). Then \( \frac{2\times2 + 1}{2}=\frac{4 + 1}{2}=\frac{5}{2} \). So \( 2\frac{1}{2}\%=\frac{5}{2}\% \).

Step2: Convert percentage to fraction

To convert a percentage to a fraction, we divide by 100. So \( \frac{5}{2}\%=\frac{5}{2}\div100 \). Dividing by 100 is the same as multiplying by \( \frac{1}{100} \), so \( \frac{5}{2}\times\frac{1}{100}=\frac{5}{200} \).

Step3: Simplify the fraction

Simplify \( \frac{5}{200} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 5. So \( \frac{5\div5}{200\div5}=\frac{1}{40} \).

Answer:

\( \frac{1}{40} \)