Convert 14.75% To A Fraction: Easy Steps

Hey guys! Have you ever wondered how to turn a percentage like 14.75% into a fraction? It might seem a bit tricky at first, but trust me, it's super manageable once you get the hang of it. In this guide, we'll break down the process step-by-step, so you can confidently convert percentages to fractions. Let's dive in!

Understanding Percentages

Before we get started, it's important to understand what a percentage actually represents. The word "percent" comes from the Latin "per centum," which means "out of one hundred." So, when we say 14.75%, we really mean 14.75 out of 100. This understanding is crucial because it forms the foundation for converting percentages to fractions. Percentages are a way of expressing a number as a fraction of 100. Think of it like this: if you have a pie and you cut it into 100 slices, a percentage tells you how many of those slices you have.

So, 14.75% simply means you have 14.75 slices out of that 100-slice pie. This is why the first step in converting a percentage to a fraction is to write it as a fraction with a denominator of 100. This initial fraction might not be in its simplest form, especially if the percentage includes a decimal, like our 14.75%. But don't worry, we'll take care of that in the following steps. Remember, the key idea is that a percentage is just a convenient way of expressing a fraction with a standard denominator, making it easier to compare different proportions. This makes understanding percentages key to unlocking the conversion process.

Step 1: Write the Percentage as a Fraction

The first thing we need to do is write 14.75% as a fraction. Since percent means "out of 100," we can directly write it as:

14. 75 / 100

This fraction represents exactly what the percentage means: 14.75 parts out of 100. However, this isn't the prettiest fraction, especially with that decimal in the numerator. Our next step will be to get rid of that decimal to make our fraction easier to work with. This initial step is straightforward, but it's crucial for setting up the rest of the conversion. You're essentially translating the percentage into its fractional form, which is the first step towards simplifying it. Remember, writing the percentage as a fraction is all about understanding that percent means "out of 100." Once you've got this down, the rest is just a matter of cleaning up the fraction to get it into its simplest form. This step provides the foundation for all subsequent calculations. It makes the process much clearer.

Step 2: Remove the Decimal

To get rid of the decimal in 14.75 / 100, we need to multiply both the numerator and the denominator by a power of 10. In this case, since there are two decimal places, we'll multiply by 100. This gives us:

(14. 75 * 100) / (100 * 100) = 1475 / 10000

Now we have a fraction with whole numbers in both the numerator and the denominator, which is much easier to work with. This step is all about cleaning up the fraction to make it easier to simplify. By multiplying both the top and bottom by the same number, we're not changing the value of the fraction, just its appearance. The key here is to choose the right power of 10 to completely eliminate the decimal. In our case, multiplying by 100 shifts the decimal point two places to the right, turning 14.75 into 1475. This makes the fraction much more manageable and sets us up for the final simplification step. Getting rid of the decimal is crucial for finding the simplest form of our desired fraction. Remember to multiply both the numerator and denominator.

Step 3: Simplify the Fraction

Now we need to simplify the fraction 1475 / 10000. To do this, we find the greatest common divisor (GCD) of 1475 and 10000 and divide both the numerator and the denominator by it.

The GCD of 1475 and 10000 is 25. So, we divide both by 25:

1475 / 25 = 59

10000 / 25 = 400

So, our simplified fraction is:

59 / 400

This is the simplest form of the fraction, as 59 is a prime number and doesn't share any common factors with 400 other than 1. Simplifying the fraction is essential to express it in its most concise form. Finding the greatest common divisor (GCD) can sometimes be a bit tricky, but it's worth the effort to get the fraction into its simplest form. In our case, dividing both the numerator and the denominator by 25 gives us the simplified fraction 59/400. This means that 14.75% is equivalent to 59/400. Simplifying fractions is not only useful for mathematical accuracy, but it also helps in understanding the true relationship between the numbers involved. It's the final touch that transforms the initial fraction into something much cleaner and easier to interpret. Finding and dividing by the GCD is the best way to simplify fractions.

Final Result

Therefore, 14.75% converted to a fraction in its simplest form is 59/400.

So there you have it! Converting percentages to fractions isn't so scary after all. Just remember to write the percentage as a fraction out of 100, remove the decimal by multiplying, and then simplify. You'll be a pro in no time!