The **percentage** is a way of representing a fraction in which a total is divided into one hundred parts. For example, saying that an object contains 30% fat, means that if we divided it into 100 parts, 30 of them would be fat.

The **% symbol** It is equivalent in mathematics to the fact 0.01 that is to say that 1% is equal to 0.01.

A **fraction** is a relationship between two quantities. The percentage allows you to compare different amounts with respect to a total.

To find out the percentage of the total **(Y)** which represents a quantity **X**, we must divide X by Y, and then multiply it by 100.

For example, if the total of a food is 40 grams and it contains 15 grams of fat:

- 15/40 x 100 = 37.5%. That is, the food contains 37.5% fat.

To find out what a real quantity represents a percentage P of a total Y, multiply P by the total Y, and then divide it by 100. For example, if you want to know how much 30% of 120 is:

- 30 x 120/100 = 36. That is, 30% of 120 is 36.

A high percentage may indicate a **real small amount**. For example, if 90% of a tablespoon is sugar, it may be only 1.8 grams of sugar. While 15% of a packet of sugar can be 150 grams. Therefore, to know the actual quantity it is necessary to know with respect to what total quantity the percentage is measured.

### Examples of percentages

- A fraction of 1/1 is 100%
- A fraction of 9/10 is 90%
- A fraction of 4/5 is 80%
- A fraction of ¾ is 75%
- A fraction of 7/10 is 70%
- A fraction of 3/5 is 60%
- A fraction of 1/2 is 50%
- A fraction of 2/5 is 40%
- A fraction of 3/10 is 30%
- A fraction of 1/4 is 25%
- A fraction of 3/20 is 15%
- A fraction of 1/8 is 12.5%
- A fraction of 1/10 is 10%
- A fraction of 1/20 is 5%
- A fraction of 1/50 is 2%
- A fraction of 1/100 is 1%
- A fraction of 1/200 is 0.5%
- In a group of 30 students, 12 are boys. 12/30 x 100 = 40. That is, 40% of the students are male.
- Veal is 20% fat, and a 300-gram serving is served at one meal. 20 x 300/100 = 60. This means that the food has 60 grams of fat.
- In a town there are 1,462 houses, of which 1,200 are connected to the gas network: 1,200 / 1,462 x 100 = 82.079 In other words, 82% of the houses are connected to the gas network.
- A water tank with a capacity of 80 liters has 28 liters. 28/80 x 100 = 35. This means that the tank is 35% full.
- In a botanical garden, out of 230 species, 140 are indigenous. 140/230 x 100 = 60.869. In other words, 60.8% of the species are autochthonous.
- Of a $ 100,000 prize, the winner must pay 20% in taxes. 20 x 100,000 / 100 = 20,000. In other words, the taxes are $ 20,000.
- A trouser that costs 300 pesos has a 25% discount. 25 x 300/100 = 75. In other words, the discount is 75 pesos and the final price is 225 pesos.
- 100 grams of rice contain 7 grams of protein. Since the total is 100, you don’t need to do the math: rice contains 7% protein.