Question

a fraction in simplest form. (example 5)

1. $15\frac{3}{5}\\% =$

12.

Explanation:

Step1: Convert mixed number to improper fraction

First, convert \(15\frac{3}{5}\) 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 \(15\frac{3}{5}\), we have \(a = 15\), \(b = 3\), \(c = 5\). Then \(15\times5+3=75 + 3=78\), so \(15\frac{3}{5}=\frac{78}{5}\). But since it's a percentage, we also have to divide by 100, so we get \(\frac{78}{5}\%\) which is equivalent to \(\frac{78}{5}\div100\).

Step2: Divide by 100 (multiply by reciprocal)

Dividing by 100 is the same as multiplying by \(\frac{1}{100}\). So \(\frac{78}{5}\div100=\frac{78}{5}\times\frac{1}{100}\).

Step3: Multiply the fractions

Multiply the numerators and denominators: \(78\times1 = 78\) and \(5\times100 = 500\), so we have \(\frac{78}{500}\).

Step4: Simplify the fraction

Find the greatest common divisor (GCD) of 78 and 500. The factors of 78 are \(2\times3\times13\) and the factors of 500 are \(2\times2\times5\times5\times5\). The GCD is 2. Divide both the numerator and denominator by 2: \(\frac{78\div2}{500\div2}=\frac{39}{250}\).

Answer:

\(\frac{39}{250}\)