## Calculation of percentages. Calculator, tasks

Mathematics is called the queen of sciences, but sometimes it is a real challenge for the student. One problem may be calculating percentages. However, it is not too complicated. It is enough that we know the basic dependencies. So how do you calculate the percentage of a number?

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## 1. Percentages - what is it?

The word "percent" has been in use in the Polish language since the mid-nineteenth century. It was borrowed from the German "prozent", which means "for a hundred" (thus the sum due for every 100 sum borrowed).

By means of percentages we write a dimensionless ratio of two values in which one number is expressed as a fraction with a denominator of 100 and corresponds to a hundredth of this value. We mark percentages with the symbol%.

For example, 1% (1 percent) is 1/100, or 0.01;

50% - we read "50 percent" and we can write 0.5 or 50/100.

## 2. Percentage calculator - how to calculate the% of a given number?

How do I calculate the percentage of a given number?

First, you need to convert the percentage into a fraction, and then multiply the numerical value of the given% by the reciprocal of the obtained fraction.

We know that:

- 100 percent is whole;

- 50 percent is half;

- 25 percent is a quarter;

- 10 percent is one tenth;

- 20 percent is one fifth.

Example:

Find a number whose 50% equals 16.

We know 50% is half, let's immediately convert it to a fraction - 1/2. Or:

50 ⋅ * x = 16 (so ½ ⋅ x = 16)

x = 32.

What percentage of x is y? Works

And now let's try to calculate what percentage of one number is the second number.

What percentage of x is y? First, we have to write our expression as a fraction: x / y.

Task: There are 12 cars in the parking lot, 3 red cars and 9 green cars.

Calculate how many percent of all cars are red cars.

Calculations:

3 + 9 = 12

3/12 ⋅ 100% = 25%

Find 5% of 70

We start with a simple calculation: 5% ⋅ 70 = 5/100 ⋅ 70 = 35/10 = 3.5.

Solution: 5% of the number 70 is 3.5.

Task: The price of one book was PLN 32 and increased by 1.5%. How much are 100 such books now?

PLN 32 - the price of one book

1.5% ⋅ 32 = 1.5 / 100 ⋅ 32 = 0.015 ⋅ 32 = 0.48 - this is how much more expensive 1 book

32 + 0.48 = PLN 32.48 - the price of the book after the increase

32.48 ⋅ 100 = PLN 3248 - this is how much 100 books will cost after the raise.

Task: The price of the goods increased by PLN 6, which is 20% of its value. How much is this product currently costing?

Reply:

x - the initial price of the goods

PLN 6, i.e. 20% ⋅ x - the price of the goods increased by this amount

So: 20% ⋅ x = 6

0.2 ⋅ x = 6

x = 6: 0.2

x - 60 ⋅ 2 = 30

30 + 6 = PLN 36

Answer: The product now costs PLN 36.

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