Expressing a Fraction as a Percentage and Vice Versa

1. Determine the number by which to multiply or divide the denominator to obtain |100.|

2. Multiply or divide the numerator and denominator of the fraction by this number.

3. Write the numerator of the fraction obtained in step 2 and add the % symbol to the right of it.

Express the fraction |\displaystyle \frac{6}{25}| as a percentage.

1. Determine the number by which to multiply or divide the denominator to obtain |100|
   It is possible to multiply the denominator of the fraction by |\color{green}{4}| to obtain |100|.||25\times \color{green}{4}=100||

2. Multiply or divide the numerator and denominator of the fraction by this  number.||\displaystyle \frac{6\times \color{green}{4}}{25\times \color{green}{4}}=\frac{24}{100}||

3. Write the numerator of the fraction obtained in step 2 and add the % symbol  to the right of it
   The answer is then |24\ \%.|

Express the fraction |\dfrac{163}{200}| as a percentage.

1. Determine the number by which to multiply or divide the denominator to obtain |100|
   It is possible to divide the denominator of the fraction by |\color{green}{2}| to obtain |100|.||200\div \color{green}{2}=100||

2. Multiply or divide the numerator and denominator of the fraction by this number ||\displaystyle \frac{163\div \color{green}{2}}{200\div \color{green}{2}}=\frac{81{.}5}{100}||

3. Write the numerator of the fraction obtained in step 2 and add the % symbol to the right of it
   The answer is then |81{.}5\ \%.|

1. Divide the numerator by the denominator.

2. Multiply the quotient by |100.| 

3. Add the % symbol to the right of the result.

Write the fraction |\dfrac{5}{8}| as a percentage.

1. Divide the numerator by the denominator

2. Multiply the quotient by |100| ||0{.}625\times 100=62{.}5||

3. Add the % symbol to the right of the result
   |\dfrac{5}{8}| equals |62{.}5\ \%.|

1. Express the percentage as a fraction whose denominator is |100.| 

2. If the numerator is not a whole number, convert it into a whole number by multiplying the numerator and the denominator by an appropriate power of |10|.

3.  If necessary, simplify the fraction to obtain an irreducible fraction.

Express |28\ \%| in the form of an irreducible fraction.

1.  Express the percentage as a fraction whose denominator is |100|||\dfrac{28}{100}||

2. If the numerator is not a whole number, convert it into a whole number by multiplying the numerator and the denominator by an appropriate power of |10|
   Since the numerator is a whole number, we can go directly to step 3.

3. If necessary, simplify the fraction to obtain an irreducible fraction ||\dfrac{28\color{green}{\div 4}}{100\color{green}{\div 4}}=\dfrac{7}{25}||
   
   |28\ \%| is equivalent to the irreducible fraction |\dfrac{7}{25}.|

Express |72{.}4\ \%| in the form of an irreducible fraction.

1. Express the percentage as a fraction whose denominator is |100| ||72{.}4\ \%=\displaystyle \frac{72{.}4}{100}||

2. If the numerator is not a whole number, convert it into a whole number by multiplying the numerator and the denominator by an appropriate power of |10|
   Since the numerator has a number after the decimal point, we will have to multiply the numerator and the denominator by |10.| ||\dfrac{72{.}4\color{green}{\times 10}}{100\color{green}{\times 10}}=\dfrac{724}{1\ 000}||

3. If necessary, simplify the fraction to obtain an irreducible fraction
   Simplify the fraction.||\dfrac{724\color{green}{\div 4}}{1\ 000\color{green}{\div 4}}=\dfrac{181}{250}||
   |72{.}4\ \%| is equivalent to the irreducible fraction |\dfrac{181}{250}.|