# Percentages and fractions

**What are fractions and percentages?**

**Fractions**

A fraction is a numerical value which is used to define part of a whole. There are two parts in a fraction: Numerator and Denominator. Numerator and denominator are separated by a horizontal line. The upper part of the fraction is the numerator and the lower part of the fraction is the denominator. Some examples of fractions are: $$\frac{27}{40}$$, $$\frac{26}{58}$$, $$\frac{65}{22}$$.

**Percentages**

Percentage can be defined as a fraction that has a denominator equal to $$100$$. For example: $$52%$$ can be written as $$\frac{52}{100}$$, and $$45%$$ can be written as $$\frac{45}{100}$$. The $$%$$ symbol describes the percentage. Discounts in shops, bank loan costs, paces of expansion, and numerous measurements in the media are in the form of percentages.

**E1.5A:** **Use the language and notation of simple vulgar fractions and percentages in appropriate contexts. **

In other words, the term 'percent' signifies 'out of $$100$$'. In arithmetic, the percentage is utilized like divisions and decimals, as approaches to depicting portions of a whole. When a person utilizes percentages, the whole is viewed as a combination of $$100$$ equivalent parts.

Let's look at an example. Suppose a square has $$100$$ smaller squares in it.

Each small square is $$1%$$ of the big square, which means the light blue is $$1%$$. Two small squares are equal to $$2%$$, which means purple squares are $$2%$$. Five small squares are equal to $$5%$$, which means pink squares are $$5%$$. Twenty-five cells are equal to $$25%$$ of the whole or one-fourth of the big square which means green squares are $$25%$$. Fifty small squares equal $$50%$$ of the whole of half that means brown squares are $$50%$$. Thus, the unshaded squares are $$17$$ of them. So, these are said to be $$17%$$ of the whole.

**Worked example**

**Example 1:** Find what percent of $$200$$ is $$36$$.

**Step 1: Change the whole to $$100$$ by dividing it by $$2$$**

$$200\div 2=100$$

**Step 2: Also divide the number by $$2$$ whose percentage has to be calculated**

$$36\div 2=18$$

**Step 3: Write the final answer**

$$36$$ is $$18%$$ of $$200$$.

**Example 2: **Find what percent of $$50$$ is $$45$$.

**Step 1: Change the whole to $$100$$ by multiplying it with $$2$$**

$$50\times 2=100$$

**Step 2: Also multiply the number with $$2$$ whose percentage has to be calculated**

$$45\times 2=90$$

**Step 3: Write the final answer**

$$45$$ is $$90%$$ of $$50$$.

**E1.5B: Recognize equivalence and convert between these forms**

Decimals, fractions, and percentages are various methods of showing a similar value of the same number. As discussed above that the percentage is a fraction having the denominator $$100$$. So, from the statement it can be concluded that $$1%= \frac{1}{100}$$. Keep in mind that to change the value of percentage in fraction. For example, $$28%$$ means $$\frac{28}{100}$$.

**Worked examples**

**Example 1: **Change $$75%$$ to fraction.

**Step 1: Change $$%$$ into $$\frac{1}{100}$$.**

$$1%=\frac{1}{100}$$

**Step 2: Multiply the given percentage with $$\frac{1}{100}$$**

$$75\times \frac{1}{100}=\frac{75}{100}$$

**Step 3: Simplify the resultant fraction**

$$\frac{75}{100}=\frac{3}{4}$$

**Example 2:** Change $$\frac{3}{5}$$ into percentage.

**Step 1: Change the denominator to $$100$$ by multiplying it with required number**

$$5\times 20=100$$

**Step 2: Change numerator by multiplying it with the same number**

$$3\times 20=60$$

**Step 3: Form a new fraction using a new numerator and a new denominator**

$$\frac{60}{100}$$

**Step 4: Multiply the fraction with $$100$$ to find the final answer.**

$$\frac{60}{100}\times 100=60$$

**Step 5: Simplify accordingly.**

$$\frac{60 \div 20}{100 \div 20}$$

$$\frac{3}{5}=60\%$$