## Percentages, Fractions, and Decimals

Percentages, Fractions and Decimals are connected with each other.

We often see the phrases like

- up to 75% off on all items
- 90% housing loan with low-interest rates
- 10% to 50% discount advertisements

These are some examples of percentages.

Suppose, there are 200 students in a college. Let 80 students remain in college to participate in college extra-curricular activities (ECA). The fraction of students participated in college ECA can be written as $\frac{80}{100}$, or $\frac{40}{100}$, or $\frac{2}{5}$. We can read it as 80 out of 200 students participated in ECA (or 2 out of 5 participated in ECA). Multiplying this fraction with 100 will convert the fraction to percentages. Therefore, 40% of the students participated in ECA.

**By percent means that for every hundred or out of every hundred.**

Therefore, a percentage is a fraction whose denominator is always 100. Therefore, a percentage can be converted to a fraction by dividing it by 100. Alternatively, one can change a fraction or a decimal to a percentage by multiplying it by 100. The following figure is about the conversion cycle of percentage to fraction or decimal and vise versa.

**Real-life Example of Percentages, Fractions, and Decimals**

Suppose, you are told that 70% of the students in a class of 50 passed a Mathematics test. How many of them failed?

Number of Students passed the Mathematics test = 70% of 50 = $\frac{70}{100}\times 50 = 35$

Number of students who failed the Mathematics test = $50 – 35 = 15$.

Number of students who failed can be found in an alternative way

\[(100-70)\%\times 50 = \frac{30}{100}\times 50 = 15\]