A brief explanation of how fractions, decimals, and percentages work.
These three different mathematical functions are very closely associated with each other; you can’t have one without the other. Fractions are best described by comparing them to a pie. This is where percentages and decimals come into the picture. A whole pie is 100% of the pie; or as a decimal it is 1.00, and as a fraction it is 1/1. In fractions anything smaller than one is written as 1/n. Any positive integer is denoted with an “n”. Any number above zero is a positive integer. Any number below zero is a negative integer. In all fractions the number at the top is called the numerator and the number at the bottom is called the Denominator.
Going back to the pie simile if we were consider a whole pie as 1/1 = 1.00 as expressed in decimals and 100% is found by dropping the decimal point in 1.00 = 100%
If we take half the pie we get a fraction of 1/2 or 0.50 which is the decimal equivalent of 1/2 or by dropping the decimal point and the zero to the left of the decimal we are left with 50%.
If we take one half of the pie and divide it into two pieces; each of the new pieces are a quarter of the pie or 1/4 or 0.25 or 25%. If we take one of the quarter pieces and subdivided again in two to we are left with 1/8 or 0.125 or 12.5%.
On the other hand if we took 1/2 and 1/4 of the pie we would now have three quarters of the pie. This would be 0.75 or 75% of the pie. No matter how you divide the pie it will always come out with a fraction that is equal to x/n, where “x” is the numerator; and “n” is the denominator.
From this we learn that there are three different names for essentially the same mathematical function, but they are expressed in different terms. This looks essentially like this: ¾ = 300/4 = .75 = 75%. This is how you can break a fraction down into decimals and percentages.
We have also in this brief lesson learned some of the smallest fundamentals of algebra. You can find that in the part about x/n. In algebra all that you do is substitute letters or numbers.