To display a percentage as a fraction, divide the number of percent by 100 to give you \(\displaystyle \frac{40}{100}\). Then simplify the fraction by dividing each number by 20, yielding  \(\displaystyle \frac{2}{5}\).

\(\displaystyle 40\%=\frac{40}{100}=\frac{\frac{40}{20}}{\frac{100}{20}}=\frac{2}{5}\)

This is just a simple problem of translation.   We know that \(\displaystyle 135\% = 1.35\) and can translate the rest of the problem into this form: \(\displaystyle 1.35 * 45 = x\).  Merely multiply and get the answer, namely \(\displaystyle 60.75\).

\(\displaystyle \frac{12.5}{100}\) is easier to simplify if you multiply top and bottom by 2.

Then it becomes \(\displaystyle \frac{25}{200}\).

Divide the numerator and denominator by 25 and you get \(\displaystyle \frac{1}{8}\).

To display a percentage as a fraction, divide the number of percent by 100 to give you \(\displaystyle \frac{71}{100}\).

\(\displaystyle \textup{Percent simply means out of one hundred parts. Therefore:}\)

\(\displaystyle 65\%=\frac{65}{100}=\frac{13}{20}\)

The reduction of the value of a car by 10% is the same as the car retaining 90%, or \(\displaystyle \frac{9}{10}\), of its value.

If a car is worth \(\displaystyle x\) when new, then it is worth \(\displaystyle \frac{9}{10}x\) after one year. Its value after two years will be \(\displaystyle \frac{9}{10}\) times its value after one year, or \(\displaystyle \frac{9}{10}* \left (\frac{9}{10}x \right )\). After three years, it will be \(\displaystyle \frac{9}{10}\) times its value after two years, or \(\displaystyle \frac{9}{10}*\left (\frac{9}{10}*( \frac{9}{10}x) \right )\).

\(\displaystyle \frac{9}{10}*\left (\frac{9}{10}*( \frac{9}{10}x) \right )=(\frac{9*9*9}{10*10*10})x=\frac{729}{1000}x\)

To convert a percentage into a fraction, remove the percentage sign and divide the number by 100.

\(\displaystyle 0.2\%= \frac{0.2}{100}= \frac{\frac{1}{5}}{100}= \frac{1}{5}\div 100= \frac{1}{5}\times \frac{1}{100}= \frac{1}{500}\)

When finding the fraction from a percent, express that value over \(\displaystyle 100\).

We now have 

\(\displaystyle \frac{45}{100}\).

We simplify it by dividing top and bottom by \(\displaystyle 5\).

\(\displaystyle \frac{45}{100}=\frac{9\cdot 5}{20 \cdot 5}\)

Final answer is \(\displaystyle \frac{9}{20}\). 

First, we take that value and divide over \(\displaystyle 100\).

We have 

\(\displaystyle \frac{26.5}{100}\).

Next, since there is a decimal present, we shift that decimal one place so we have a whole number. Since we did that to the top, we add one zero to the bottom since we shifted one place. We have 

\(\displaystyle \frac{265}{1000}\).

To reduce, we divide top and bottom by \(\displaystyle 5\) 

\(\displaystyle \frac{265}{1000}=\frac{53\cdot 5}{200\cdot 5}\)

to get \(\displaystyle \frac{53}{200}\) as the final answer. 

We take that value and divide that over \(\displaystyle 100\).

We get 

\(\displaystyle \frac{150}{100}\).

Next we can reduce by taking one zero from top and bottom and also divide top and bottom by \(\displaystyle 5\).

\(\displaystyle \frac{150}{100}=\frac{15}{10}=\frac{3\cdot 5}{2\cdot 5}=\frac{3}{2}\)

This gives us an answer of \(\displaystyle \frac{3}{2}\).