## How to Calculate Percentage

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How many of you are aware that the word percent is derived from the Latin word "**per centum**"? It is also clear that if you break down the word "percent" into the two words "per" and "cent," the meaning becomes pretty clear: it means by a hundred percent. In this case, we can conclude that percentages are nothing more than **fractions **with denominators equal to \(100\)** **in all instances.

### Calculation of Percentage

Now that we know what is percentage, let’s find out how to calculate it with ease. In percentage problems, we basically have to find the part/share of a whole in terms of \(100\). This we can do in the following 2 ways:

- Firstly, we can apply the
**unitary**method. - Secondly, we take the fraction in consideration and
**change**its**denominator**to \(100\).

A thing to note is that the **second method **can only be effectively used when the denominator of the fraction is a **factor **of \(100\). If this isn’t the case, we will always resort to the first method.

**Example 1**: \(6\) is what percentage of \(24\)?

So, for this question, we first make the fraction as \(\frac{6}{24}\) , and then since the fraction can be simplified, we **simplify **it to \(\frac{1}{4}\) .

Next, we will **multiply **it by \(100\) to get the percentage as \(\frac{1}{4} \times 100 \ = \ 25%\)

**Example 2**: \(9\) is what percentage of \(63\)?

So, for this question, we first make the fraction as \(\frac{9}{63}\) , and then since the fraction can be simplified, we **simplify **it to \(\frac{1}{7}\) .

Next, we will **multiply **it by \(100\) to get the percentage as \(\frac{1}{7} \times 100 \ = \ 14.28%\)

**Example 3**: \(27\) is what percentage of \(81\)?

So, for this question, we first make the fraction as \(\frac{27}{81}\) , and then since the fraction can be simplified, we **simplify **it to \(\frac{1}{3}\) .

Next, we will **multiply **it by \(100\) to get the percentage as \(\frac{1}{3} \times 100 \ = \ 33.34%\)

### Exercises for Percentage Calculations

**1)** \(4.2\) is what percentage of \( 12? \)\( \ \Rightarrow \ \)

**2) **\(9.45\) is what percentage of \( 27? \)\( \ \Rightarrow \ \)

**3) **\(0.95\) is what percentage of \( 19? \)\( \ \Rightarrow \ \)

**4) **\(24.6\) is what percentage of \( 41? \)\( \ \Rightarrow \ \)

**5) **\(15.3\) is what percentage of \( 34? \)\( \ \Rightarrow \ \)

**6) **\(16.8\) is what percentage of \( 56? \)\( \ \Rightarrow \ \)

**7) **\(53.55\) is what percentage of \( 63? \)\( \ \Rightarrow \ \)

**8) **\(74.1\) is what percentage of \( 78? \)\( \ \Rightarrow \ \)

**9) **\(63.75\) is what percentage of \( 85? \)\( \ \Rightarrow \ \)

**10) **\(80\) is what percentage of \( 100? \)\( \ \Rightarrow \ \)