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How to define percents?

percents

In this lesson we’ll be learning about percentages or percents. The word “percentage” comes from a Latin “per centrum” or one one-hundredth part. Basically the percentage is number of hundredth parts in the whole.

Let’s start with the basics.
% is a sign for percentage. Percentage is one-hundredth part of the whole. That means that

what is percentageExample 1: You’re on a party with 24 other people. Let’s say you have a cake that has been divided in 25 equal parts. You notice that on only 15 of those parts have strawberries. You want to calculate what percentage of people will get the strawberries.

How would you do that? You know to present this in a ratio. So let’s do that. 15 of 25 have strawberries.

strawberries example

You know this, and you know that \frac{1}{100} = 1%.

So what can you do? You can expand that first fraction so that denominators match, and you numerator will be that percentage you are looking for. Let’s do that.

expanding a fractionThe numerator of expanded fraction is equal to 60, that means that percentage of pieces of cake with strawberries is 60%.

Percentage can be calculated like this:

calculation of percentsExplaining the formula : % means \frac{1}{100} and “from” represents multiplying.

Example 2: what is \ 60% from 120?

x = 60, b = 120:
60 % from 120 = c => \frac{60}{100} * 120 = c => c = 6 * 12 = 72

Example 3: 50 is what percent of 400?

c = 400, x = 50:

x % from b = c => \frac{x}{100} * b = c => \frac{x}{100} * 400 = 50

4x = 50

x = 12.5
 

Example 4: You bought a new bag of chips and you know that in it there are 70 chips, you ate 50% of it, and then you left it. You came back after a while and ate another 50% of it. How much chips do you have now?

The point of this example is that you have to be careful with addition of percentages. You may think that first you ate 50% and then another 50% and that is 100% and you have no chips left at all. But that is not true. Here is what is happening:

First you ate \ 50% from 70, and that is \frac{50}{100} * 70 = 35
Since you ate 35, you are left with \ 70 - 35 = 35 chips.
You left, and came back to get another 50%. But now you have 35 chips so 50% from 35 is \frac{50}{100} * 35 = 17.5

In the end you are left with 17.5 chips.

Example 5: You want to start saving for your future. You go to bank and say you want to put 1000 dollars in your saving account. The bank tells you that every year they will add 0,2% of your total on your account. How much money will you have after 3 years?

We’ll break it down in parts.
Let’s say a year has passed.
How much money will you have?

You’ll have your money you put there a year ago+ the part that the bank added.
The money you put a year ago = 1000 dollars
the money that a bank added: 0.2% from 1000 is

\frac{0.2}{100} * 1000 = x dollars
0.2 * 10 = x dollars
x = 2 dollars
It’s year one and now you have \ 1000 + 2 = 1002 dollars.

On second year, you have what you had last year (1002 dollars) + the money that bank added (0.2% from 1002 dollars).
The money that bank added: \frac{0.2}{100} * 1002 = x_2 => \frac{(2*1002)}{1000} = x_2 => x_2 = 2.004 dollars
It’s year two and now you have 1002 + 2.004=1004.004 dollars

Finally we come to year three.
On third year, you have what you had last year (1004.004 dollars) + the money that bank added (0.2% from 1004.004 dollars).
The money that bank added: \frac{0.2}{100} * 1004.004 = x_3 => \frac{(2 * 1004.004)}{1000} = x_3 -> x3 = 2.008008 dollars.

In the end of year three you have : 1004,004 + 2,008008 = 1006,01 dollars

 

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