Simplify Fractions Calculator

Created by Wojciech Sas, PhD
Reviewed by Bogna Szyk and Jack Bowater
Last updated: May 30, 2024

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!

What are fractions?

A fraction is a part of a whole. It is made up of a numerator and denominator. A fraction represents an object that has been divided into equal parts.

If you divide a cake into four equal parts, then give your friends two of the four pieces; the pieces you give away represent the fraction 2/4 or 1/2. The number at the top is the numerator, and the one at the bottom is the denominator.

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.

Unlike ratios, fractions need to have the same unit in the numerator and the denominator. Consult our ratio calculator for more details about this.

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.

🙋 You can quickly check if two fractions are equal with our equivalent fractions calculator!

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! You only need to know 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 other useful techniques are used in real life, like converting inches to a fraction? If not - check Omni's inches to fraction calculator!

What are improper fractions?

An improper fraction is a fraction where the numerator is greater than the denominator. An improper fraction represents a value that is greater than a whole. Improper fractions can also be written as mixed numbers. 3/2 is an example of an improper fraction. It is 11/2 when written as a mixed number.

Imagine that the objects we are dealing with are two cakes, each divided into two equal parts. This means that 3/2 is the same as one whole cake and half of the other.

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 having a great time with a couple of your friends at a party. Suddenly, you decide to go crazy and order some pizzas. After a stormy discussion, you split into two teams: Hawaiian and 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 the 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 the 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, the 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).

FAQ

What is the simple form of 6/9?

2/3 is the simplified version of 6/9. To arrive at this answer, we divide the numerator and denominator by the common factor 3.

How do you simplify the fraction 4/12?

To simplify a fraction, you need to divide the numerator and denominator by the same number. To simplify 4/12, follow these steps:

1. Find a number that can divide the numerator and denominator without leaving a remainder. In this instance, the numbers are 2 and 4.
2. Divide the numerator and denominator by the bigger number (4). Dividing by the bigger number will get us to the simplest form faster.

What fractions are equivalent to 4/12?

1/3 and 2/6 are equivalent to 4/12. To arrive at the first answer (1/3), you need to divide the numerator and denominator by 4. To arrive at the second answer (2/6), you need to divide the numerator and denominator by 2.

Wojciech Sas, PhD
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