 Fractions can be written in a variety of ways; however, you will often be asked to write fractions in their simplest form. In this lesson, learn about what it is and how to write fractions in simplest form. When you are done, assess your learning with a short quiz!

## What Is Simplest Form?

When you hear people talk about writing fractions in simplest form, it means that you are finding the smallest, easiest way to represent a fraction.

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When you are asked to simplify a fraction that is the same as writing it in simplest form.A fraction is a part of a whole. It is represented by two numbers: one on top of the other with a line in between.

The top number, or the numerator, represents how many pieces of the whole we are referring to, and the bottom number, or the denominator, represents how many pieces the whole has been broken into. Still a little confused? Let’s look at an example.

## Making a Fraction

It’s my birthday, and I have an amazing birthday cake. Right now, the whole birthday cake is in one piece. However, I want to feed all six of my guests plus myself. I want to be fair, so I want my cake split into eight equal pieces.

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The number 8 represents the number of pieces the whole is being separated into, the denominator. If one of my guests eats one of those pieces, we could represent that number using the fraction 1/8. The number 1 represents the piece of the whole that we are referring to in this problem; it is the numerator. Let’s take a look at some more fraction examples.

## Fraction Examples

You are having a party, and you order four pizzas. Each of those pizzas are cut into eight slices.

One pizza is cheese, one is supreme, one is sausage, and one is pepperoni. After the party, this is what has been eaten: • Six slices of the cheese pizza are eaten. That’s 6/8 of the pizza.
• Four slices of the supreme pizza are eaten. That’s 4/8 of the pizza.

• Two slices of the sausage pizza are eaten. That’s 2/8 of the pizza.
• Five slices of the pepperoni pizza are eaten. That’s 5/8 of the pizza.

In each of these examples, the numerator (the number on top) is the number of slices that were eaten. The denominator (the number on bottom) is the number of slices each whole pizza was sliced into.In the image above, you will notice that the supreme pizza looks as if exactly half was eaten. That’s correct! Exactly 1/2 or 4/8 of the pizza was eaten, but how can that be? How can half of the pizza be represented with two numbers? That is because the number 1/2 represents the simplest form of the fraction 4/8!

## Finding the Simplest Form

When writing fractions in simplest form, there are two rules to follow:

1. Ask if the numerator and denominator can be divided by the same number, which is called a common factor.
2. See if at least one number in the fraction is a prime number. A prime number is a number that is 1 or greater and cannot be divided by any number other than 1 and itself.

Let’s take a look at our pizza example.

Take the first fraction in the pizza example: 6/8.Now, ask yourself, can you divide this number by a common factor? Are there any prime numbers? Yes! You can divide both 6 and 8 by 2, and that gives you 3/4.Now, ask yourself again, can you divide this number by a common factor, and are there any prime numbers? This time, no, there are no other common factors, and yes, 3 is a prime number. Therefore, this fraction, 3/4, is the simplest form of 6/8.

We’re not full yet, so let’s move onto the second pizza: the supreme pizza. The fraction of eaten pieces is 4/8. Can you divide this number by a common factor? Yes, you can divide both 4 and 8 by 2, and that gives you 1/2. Now, are there any prime numbers? Yes, 1 and 2 are prime numbers. This fraction, 1/2, is the simplest form of 4/8.The third pizza, the sausage pizza, had two of the eight slices eaten, or 2/8.

Can you divide this number by a common factor, and are there any prime numbers? Yes, you can divide both 2 and 8 by 2, and that gives you 1/4. There are no other factors that this can be divided by, and 1 is a prime number. So, 1/4 is the simplest form of 2/8!Finally, we have the fourth pizza: 5/8 of the pepperoni pizza was eaten. Are there any common factors? How about prime numbers? In this case, too, there are no common factors, and 5 is a prime number. So, this fraction, 5/8, is already in its simplest form.Keep in mind that fractions can often be divided by 2 as a common factor.

However, while 2 is a great starting place for simplifying fractions, you will often have to use other numbers, such as 3 or even 30, to simplify.

## Lesson Summary

Fractions represent a part of a whole. That part can be represented with different fractions. A fraction contains a numerator, the top number, and a denominator ,the bottom number. The smallest, easiest way to represent that part is with a fraction in the simplest form. When writing fractions in simplest form remember to ask:

1. Can you divide this number by a common factor?
2. Are there any prime numbers?

Also remember that a common factor can be just about any number, but 2 is often the easiest to start with!

## Learning Outcomes

The video lesson might contribute to your ability to:

• Give the definitions of fractions, simplest form, numerator and denominator
• Create fractions and decipher examples
• Factor and write a fraction in its simplest form 