Learning Materials

Structured explanations, one concept at a time.

Expressing One Number as a Fraction or Percentage of Another

To express one number as a fraction of another, write the first number (the part) over the second number (the whole), then simplify if possible.

$$
\text{fraction} = \frac{\text{part}}{\text{whole}}
$$

 

For example, expressing \(12\) as a fraction of \(20\):

$$
\frac{12}{20} = \frac{3}{5}
$$

 

To express one number as a percentage of another, first form the fraction, then convert it into a percentage by multiplying by \(100\).

$$
\text{percentage} = \frac{\text{part}}{\text{whole}} \times 100
$$

 

For example, expressing \(15\) as a percentage of \(60\):

$$
\frac{15}{60} = \frac{1}{4}
$$

$$
\frac{1}{4} = 25%
$$

 

You can also calculate the percentage directly using division:

$$
15 \div 60 = 0.25
$$

$$
0.25 = 25%
$$

 

Always identify the correct whole before forming the fraction or percentage. Reversing the numbers will give the wrong answer, even though the calculation method is correct.