Two quarters three pennies is what percentage
Percentage calculator online
What does 100% actually mean?
You have probably heard the sentence: "We have to give 100% now!" This means that everyone should give everything and try hard. This perfectly reflects the mathematical meaning of 100%. 100% is "everything"!
If you have a cake that hasn't been taken away, you have 100% cake. And if you receive your pocket money at the beginning of the month and have not bought any of it yet, you still have 100% pocket money. As soon as you take something away from this, you have less. With the percentage calculation you can calculate this “less” very precisely.
The word "percent" and its meaning
The term “percent” comes from the Latin “per centum”, which translates as “from a hundred”. Whatever you are investigating with the percentage calculation, just imagine that you are dividing this object into 100 pieces. This is easy to imagine with a cake that you cut into 100 small pieces. Or you get € 25 pocket money a month. Then you can also divide this into 100 equal pieces that are worth 25 cents. After all, 100 * 25 cents = 25 euros.
What do percentages have to do with fractions?
Whenever you calculate with percentages, you can also calculate with fractions. You don't like fractions? Don't worry, it's easier than it looks. Each of the pieces described above is one hundredth of the cake. Each of these pieces therefore represents 1%. If you take three of the 100 pieces of cake, you have 3% of the cake. And if you take all 100 pieces, you have the entire cake again and thus 100%.
Half, third, quarter in percent
There are some important fractions that you should keep in mind with their percentages. To do this, imagine the cake again. Imagine cutting a cake in half. Each of these halves consists of 50 small individual pieces if you had cut it into a total of 100 pieces as described above. Half are therefore 50% of the cake. Half is expressed as a fraction by 1/2, so you can also do arithmetic.
(The entire cake (100%) is divided by two (multiplied by 1/2) and you get 50).
You can do this with other fractions as well, if you cut the cake into three, four or five equal-sized pieces:
So a fifth of the cake is 20% of the cake, a quarter of the cake is 25%. And how much is a tenth of the cake? Exactly: 10%.
Some theory: the basic mathematical terms
So that you can use the percentage calculation correctly, we are now introducing the three most important mathematical terms. You can easily understand this if you always imagine the cake. Nevertheless, make a careful note of these three terms for homework and class work.
Base value (G)
The basic value or starting value is the number you start with. For example, this can be 1.0 cake. Or the 25 euros from our example with pocket money.
The percentage is the number that comes before the percent sign (%). If you have two cakes and want to know how much 25% of 1.0 cakes is, then 25 is the percentage and 1.0 is the base value.
The percentage value is the result that you get when calculating a percentage from a base value. You already know that 25% * 1.0 = 0.25 (or a quarter). That result, the 0.25, is the percentage.
This is how the percentage formula works
So far we have always expected a cake and 100%. But what if you start with a different basic value, like 25 euros pocket money? In this case, we have to mathematically divide the 25 euros into 100 equal parts, each worth 1.0 percent. We have already shown you above that the 25 euros can be divided into 100 parts of 25 cents each. Mathematically, we use the only formula that you have to remember around the percentage calculation:
Just remember the formula like this: “If you speak 100 words, you need a long break afterwards (to breathe)”.
If you divide both sides of this equation by 100, you get the exact formula for the percentage (W):
We test you once with the question “How much is 40% of your monthly pocket money of 25 euros?”. The base value G is 25 euros, the percentage P is 40. Therefore the formula is:
It follows from this:
Now you know that 40 percent of 25 euros is 10 euros.
This is how you calculate with the percentage formula
It is not always the percentage that is asked, but the percentage. In our pocket money example, you are given two euro amounts and you should say what percentage of the one amount is from the other. This is not a problem at all if you use the formula 100 * W = G * P and solve for P. To do this, you have to divide both sides of the equations by G and you get the formula:
We will also test this formula with an example. Our question is: “If you still have 20.00 euros of your 25.00 euros pocket money, what percentage do you still have?”. Inserted into the formula this means:
In this case you have the fraction 20/25 at the back, which can be shortened to 4/5. So the calculation is:
Now you know: 20.00 euros are 80% of 25.00 euros.
Percentage calculation - some examples for you
Example 1: What is 40 percent of 120?
We look for the percentage value (W) and calculate W = G * P / 100
Example 2: How much is 50 out of 300 in percent?
For this we are looking for the percentage P = 100 * W / G
So the percentage is 16.666%. Incidentally, as a fraction, this is a sixth, as you can see when doing the calculation.
Example 3: How much is 200 euros plus or minus 15 percent?
For this task, of course, we first have to know what 15% of 200 is. We can then offset the result by addition or subtraction. We use the formula from example 1:
Now we know that 15% is worth 30 euros. To solve the problem, we only have to add it up to our basic value or subtract it from it. Concrete:
Adding up: 200 euros + 30 euros = 230 euros. Deduction: 200 euros - 30 euros = 170 euros. A small donkey bridge for everyday life
We have another little trick for you, how you can quickly and easily calculate the percentage value if you have mastered the multiplication tables well. As you may have noticed, the formula for calculating percentages only uses points, i.e. multiplication and division. We can therefore offset the factors in any order when calculating.
Specifically, this means: You don't have to first GCalculate P and then divide by 100. You can use the fraction GP / 100 also split into G / 10 * P / 10. In this case you are calculating with significantly smaller numbers.
Here are a few examples:
What is 80% of 20? Just divide both values by 10 and take them together. 8 * 2 = 16.
What is 20% of 80? Exactly the same thing happens here, you calculate 2 * 8 = 16.
What is 35% of 50? This is a little more difficult because when dividing by 10 you now have to calculate 3.5 * 5. You can still get the result quickly: 17.5.
The hardest thing at the end: calculate the starting value!
In most cases you will need to calculate either the percentage or the percentage. Of course, it is also possible to calculate the basic value (G) with our formula. A question for this would be, for example: "If 25% of your pocket money is 5.0 euros, how much is your total pocket money (the full 100%)?"
To calculate this, we convert our well-known formula 100 * W = G * P to G. As a formula for the basic value, this means:
Specifically in our example this means:
If 25% of your pocket money is 5.0 euros, 20.0 euros is your total pocket money. Perhaps you have already recognized that the quarter of your pocket money was asked at 25%. To infer the whole from a quarter, you simply have to take four. And also 5 euros * 4 = 20 euros would have brought you to the result.
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