To convert the percentage [tex]\(61 \frac{1}{2}\% \)[/tex] to a fraction and reduce it to its lowest terms, follow these steps:
1. Convert the mixed number percentage to an improper fraction:
[tex]\(61 \frac{1}{2}\%\)[/tex] can be written as [tex]\(61.5\%\)[/tex] in decimal form.
2. Convert the decimal percentage to a decimal:
Divide the percentage by 100 to convert it to a decimal.
[tex]\[
61.5\% = \frac{61.5}{100} = 0.615
\][/tex]
3. Convert the decimal to a fraction:
Now, express [tex]\(0.615\)[/tex] as a fraction. This is done by recognizing the place value.
[tex]\[
0.615 = \frac{615}{1000}
\][/tex]
4. Reduce the fraction to its lowest terms:
To simplify [tex]\(\frac{615}{1000}\)[/tex], find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 615 and 1000 is 5.
Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{615 \div 5}{1000 \div 5} = \frac{123}{200}
\][/tex]
So, [tex]\(61 \frac{1}{2}\% = 0.615 = \frac{123}{200}\)[/tex] when converted to a fraction and reduced to its lowest terms.
