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Let us talk about percentages and how they are useful to us. First of all, they help us find the proportion or ratio of an amount and for that a percentage equation is used. Percentages are frequently used in other aspects of our everyday life as well and not just in math. It is very useful when we go out shopping and also for sales. The part, the percent and the whole are the three parts of a percentage equation. This will be covered in greater depth later in this article....Read MoreRead Less

The percent symbol represents a fraction of a hundred. Since cent is the French word for 100, the word percent actually means “per 100.” When expressing the demographics of a population, percentages help us understand different aspects about their lives. Consider this for example; if someone claims that 75% of the population commutes to work, they are referring to 75 people out of every 100.

Depending on the given information, only one formula is used for the percent equation.

\( a=p\%\times w \) is the percent equations formula.

There are three variables in the percent equation formula: percent (p), part of the whole that has been chosen for comparison (a) and the whole (w). When any two out of the three are known, the third quantity can be calculated.

The basic form of the percent equation is “p percent of w is a.” Algebraically, this is written as:

\( a=p\%\times w \), which is the **percent equation**.

Where,

- p is the percent.
- a is the part of the whole.
- w is the whole number.

**Example 1:** What number is 15% of 300?

**Solution:**

\( a = p\% \times w \) Write the percent equation

Where ‘a’ is the part of the whole, ‘w’ is the whole (total) amount, and ‘p’ is the percentage.

\( a=\frac{15}{100}\times 300 \) Substitute \( \frac{15}{100} \) for p% and 300 for w.

\( a = 45 \) Simplify.

So, 45 is 15% of 300.

**Example 2:** What number is 20% of 600?

**Solution:**

\( a = p\% \times w \) Write the percent equation

Where ‘a’ is the part of the whole, ‘w’ is the whole (total) amount, and ‘p’ is the percentage.

\( a=\frac{20}{100}\times 600 \) Substitute \( \frac{20}{100} \) for p% and 600 for w.

\( a = 120 \) Simplify.

So, 120 is 20% of 600.

**Example 3:** What percent of 80 is 20?

**Solution:**

\( a = p\% \times w \) Write the percent equation

Where ‘a’ is the part of the whole, ‘w’ is the whole (total) amount, and ‘p’ is the percentage.

\( 20=\frac{p}{100}\times 80 \) Substitute 20 for a, 80for w and \( \frac{p}{100} \) for p%.

\( p=100\times \frac{20}{80} \) Simplify.

\( p=25\% \)

So, 25% of 80 is 20.

**Example 4:** 30 is 25% of what number?

**Solution:**

\( a = p\% \times w \) Write the percent equation

\( 30=0.25\times w \) Substitute 30 for a and 0.25 for p %.

\( \frac{30}{0.25}=\frac{0.25\times w}{0.25} \) Division Property of Equality

\( w=120 \) Simplify.

So, 30 is 25% of 120.

**Example 5: **Copper makes up 24% of an alloy’s composition. To obtain “240” g of copper, how much alloy is required?

**Solution:**

\( a = p\% \times w \) Write the percent equation

Where ‘a’ is the part of the whole,‘w’ is the whole (total) amount, and ‘p’ is the percentage.

\( 240=\frac{24}{100}\times w \) Substitute \( \frac{24}{100} \) for p% and 240 for a.

\( w=1000 \) Simplify.

Hence, 1,000 g alloy is required.

**Example 6:**Aluminium makes up 28% of an alloy’s composition. If 560 g of alloy was taken, how much aluminium can be extracted from it?

**Solution:**

\( a = p\% \times w \) Write the percent equation

Where ‘a’ is the part of the whole, ‘w’ is the whole (total) amount, and ‘p’ is the percentage.

\( a=\frac{28}{100}\times 560 \) Substitute \( \frac{28}{100} \) for p% and 560 for w.

\( a=156.8 \) grams Simplify.

Hence, 156.8 grams of aluminium were extracted.

Frequently Asked Questions on Percent Equation Formula

The part (a), the percent (p), and the whole number (w) are the three variables in the percent equation formula. The formula used is

\( a=p \% \times w \).

Before using percentages in equations, they must be converted to decimals. This can be achieved by dividing them by 100.

A percentage is a ratio or fraction with a constant denominator of 100, while a proportion is the relationship or equality between two ratios or fractions. Hence they are different but both proportion and percentage can be expressed as fractions.

The symbol % basically denotes that the quantity is a fraction and 100 is in the denominator.

A number’s percentage is its value out of 100. For example; let us consider that there are 26 girls and 24 boys in a class.

As a result, the percentage of females in the class is 52% , which signifies that if there were a total of 100 students in the class, 52 out of them would be girls.

Yes, when we have a value that is greater than the total value, the percentage can be greater than 100.

To calculate a percentage, divide the chosen value by the total value and multiply the result by 100. \( \frac{\text{Value}}{\text{Total value}}\times 100\% \) is the formula for calculating percentages.