# How do you calculate the percentage won

## Express and compare proportions in percent

Wolfgang and Andres play table football together every lunch break. They always play several rounds, but never the same number of rounds. It always depends on how much time you have. In order to still be able to compare their victories with one another, they have to express and compare shares in percent. On Monday they played a total of 6 games. Wolfgang won 3 of these games, so Andres won 3 too. So everyone won exactly half of the games, i.e. 50%. We can also calculate the 50 percent by writing the percentage of wins in all games as a fraction. The numerator then shows the number we are looking at: the three victories. The denominator is the total number of games, so 6. So that's three sixths ... and shortened a half. As a decimal fraction we get 0.5, i.e. also 50%. We call this percentage p%. The total number, in our example the 6 games, we call the base value G in the percentage calculation. And the proportion of this total number, in our example the victories, we call the percentage value W. Let's take a look at the games on the next day failed. On that day they played 8 games. Wolfgang only won 2 of them, Andres won 6. So this time we have 8 as the base value, as this is the total number of games. If we want to calculate the proportion of games that Wolfgang has won, the percentage is 2. We can again write the proportion as a fraction and get two eighths. To find out the percentage, let's convert that to a decimal fraction and convert it to percent. Wolfgang only won 25% of the games, which is definitely less than the day before. If we want to find out what percentage corresponds to Andre's victories, we have the percentage value 6, because now we consider 6 wins in 8 games. So the basic value remains the same. If we again calculate W divided by G, i.e. 6 divided by 8 and then convert this to a percentage, we see that Andres won 75% of the games. If we now take a closer look at the two percentages, we can see that they add up to 100%. If you add the percentage of Wolfgang's victories, i.e. 2, and Andre's victories, i.e. 6, together, we get 8, exactly the number of games, i.e. 100%. Did Wolfgang improve the next day? Since they managed to play 4 games, Wolfgang won 3 of them and therefore Andres won 1 game. What percentage correspond to Wolfgang's victories? 3 is the percentage and 4 is the basic value. So we get three quarters and that's 75%. Wolfgang won 75% of the games. Since we only have two shares again, this time we can simply calculate 100% minus 75% for the calculation of the percentage of Andres wins. Andres won 25% of the games. How was it the next day? You played 9 games and Wolfgang actually won 9 times. Oh, we don't even need to calculate that. Since he has won all games, this is 100%. How did Wolfgang manage to improve so? Before we see that, let's summarize again. We can express proportions in percent by first writing them as a fraction and then converting them to percent. The numerator then shows the number that we are looking at. We also call this the percentage value W. The denominator is the total number we are looking at. We also call this the basic value G. This means that proportions can also be compared with one another if different total numbers are assumed. And how did Wolfgang manage to become so strong? Hm, he trained well there!