Percentage - Concept of Percentage

Definition of Percentage: The word 'percent' comes from the Latin 'per centum', which means 'per hundred'. It is a way of expressing a part of a whole where the whole is always $100$. Imagine a large square grid divided into $100$ equal smaller squares; if you shade $35$ of those squares, you have shaded $35\%$ of the grid.

The Percentage Symbol: We use the symbol $\%$ to denote percentage. For example, $25\%$ is read as 'twenty-five percent' and represents the fraction $\frac{25}{100}$. Visually, this means $25$ parts out of every $100$ equal parts.

Converting Fractions to Percentages: To convert any fraction into a percentage, multiply the fraction by $100$ and add the $\%$ sign. For example, to convert $\frac{4}{5}$ to a percentage, calculate $\frac{4}{5} \times 100 = 80\%$.

Converting Percentages to Fractions: To convert a percentage back into a fraction, remove the $\%$ sign, place the number over a denominator of $100$, and simplify to the lowest terms. For instance, $60\% = \frac{60}{100}$, which simplifies to $\frac{3}{5}$.

Converting Decimals to Percentages: To change a decimal into a percentage, multiply the decimal by $100$. This effectively moves the decimal point two places to the right. For example, $0.75$ becomes $0.75 \times 100 = 75\%$.

Finding Percentage of a Quantity: To find a specific percentage of a given number, convert the percentage into a fraction (by dividing by $100$) and then multiply it by the number. For example, $20\%$ of $50$ is calculated as $\frac{20}{100} \times 50 = 10$.

The Concept of $100\%$: In any situation, the entire quantity or the whole is always represented as $100\%$. If a tank is half full, it is $50\%$ full; if it is completely full, it is $100\%$ full.

Expressing One Quantity as a Percentage of Another: To find what percent $x$ is of $y$, we use the fraction $\frac{x}{y}$ and multiply by $100$. If a student scores $45$ out of $50$ marks, the percentage is $\frac{45}{50} \times 100 = 90\%$.