# Simplify Fractions Calculator

By Wojciech Sas, PhD candidate
Last updated: Jul 24, 2020

Here it is - the simplify fraction calculator (also the reduce fraction calculator or fraction simplifier), a useful tool that helps you in reducing fractions.

Have you ever asked yourself "How do you simplify fractions?" or "How to reduce fractions to lowest terms?" and didn't know the answer? If so - this is a perfect place for you to start and learn something new!

## How to reduce fractions?

Before we get the answer of how to simplify fractions, let's start with the basics. What is a fraction?

A fraction is a ratio of two numbers, the numerator and the denominator. With this definition in mind, we can see that `1/2` is a fraction, `10/12` is a fraction, `3.3/6.2` is a fraction, and so on. Typically, we use whole numbers within fractions as it's more intuitive and simpler to use, especially when adding or subtracting fractions.

Additionally, you can turn any decimal value into a fraction.

Now, it's high time to ask yourself "How do you simplify fractions?" e.g., `4/8`. The solution is to find a common factor of both numbers and divide them by this value. `2` is one of the common factors, so:

1. `4` divided by `2` is `2`.
2. `8` divided by `2` is `4`.
3. As a result, we continue by reducing the fraction `4/8` to `2/4`.

In other words, we can say that `4/8` and `2/4` are equivalent fractions.

Although the outcome is correct, we usually want to reduce the fraction to its simplest form in these kinds of computations. The question is: What is the simplest form of a fraction?

## Reducing fractions to lowest terms

Reducing a fraction to its simplest form (or lowest term) is almost the same as the procedure explained in the previous section. The most significant difference is that we need to divide both the numerator and denominator by the greatest common factor (GCF). Let's take a look at the same example, `4/8`:

1. Find the GCF of `4` and `8`, which is `4`.
2. `4` divided by `4` is `1`.
3. `8` divided by `4` is `2`.
4. `4/8` in simplest form is `1/2`.
5. You can always convert a fraction to decimal, in this case `0.5`.

And what is the simplest form of a fraction with negative numbers, e.g., `-4/6`? That isn't difficult at all! The only thing you need to know is that the negative number factors are the same as the positive ones multiplied by `-1`.

As a result, we can reduce the fraction `-4/6` to `-2/3`.

By the way, did you know that there are other useful techniques used in real life, like converting inches to a fraction? If not - check it out!

## How to simplify improper fractions?

An improper fraction is a fraction where the numerator is higher than the denominator (or more precisely, their absolute values follow this rule). In general, they represent numbers greater than one. You can also write any improper fraction as a mixed number - a whole number with a regular fraction.

The good thing is that in our reduce fractions calculator, you can use either improper fractions or mixed numbers.

So, is there anything tricky when you are reducing improper fractions to their lowest terms? Take a look at the example of how to simplify improper fractions. The fraction we will be looking at is `117/52`:

1. Find all the factors of both numbers. We can use the prime factorization method:

• Factors of `117` are `3, 3, 13`; and
• Factors of `52` are `2, 2, 13`
2. The greatest common divisor of `117` and `52` is `13`.

3. Divide both numbers by `13`. `117/13 = 9`, and `52/13 = 4`.

4. `117/52` in simplest form is `9/4`.

5. We can also write it as a mixed number, which is `2 1/4`.

6. If you aren't satisfied yet, you can always convert the fraction to a percentage. In our case, `2 1/4` equals `225%`.

A piece of cake, wasn't it?

## How to use simplify fractions calculator? Fraction simplifier in practice

Imagine you are having a great time at a party with a couple of your friends. Suddenly, you decide to go crazy and order some pizzas. After a stormy discussion, you split into two teams: Hawaiian and Hot dog stuffed crust fans.

You buy two extra-large pizzas of the same size but different shapes. That's not all, the Hawaiian is divided into `16`, and Hot dog stuffed crust is cut into `24` pieces. In the end, the Hawaiian team ate fourteen, and Hot dog devoured fifteen portions.

So who is the winner? It isn't easy to estimate visually as the pieces are of different shapes and sizes. But let's try to find out the answer with our simplify fractions calculator:

• We can write team A score as a fraction `A = 14/16`.

• The same way for team B `B = 15/24`.

• To compare these results, we continue with reducing fractions to lowest terms.

• Team A score in simplest form is `A = 7/8`.

• Team B score in simplest form is `B = 5/8`.

As you can see, Hot dog stuffed crust team won this time with a slight advantage! Team Hawaiian - better luck next time (or just pick a real pizza topping).

Wojciech Sas, PhD candidate My fraction is in
standard form
Numerator (n)
Denominator (d)
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