# What are the different types of fractions?

Various types of fractions can pop up all around you!

Whether you’re splitting a bill at a restaurant or trying to share a pizza with your friends, you’ll encounter situations where you need to understand fractional parts.

So, what are the types of fractions?

Whether you’re a student struggling with math or someone who wants to refresh their knowledge, this post will give you a solid foundation on the types of fractions.

Let’s dive in and explore the world of fractions together!

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## 5 Fraction Types

Here are five types of fractions, including the fraction definition of each:

Proper fractions: These represent a part that is less than one whole. They have a numerator smaller than the denominator. In all fractions, the numerator represents the part that’s being considered, and the denominator represents the number of parts in 1 whole object or collection. A horizontal bar separates the numerator from the denominator.

Improper fractions: Where the numerator is greater or equal to the denominator. These

Mixed fractions: These are a combination of a whole number and a proper fraction, representing a part of a whole that is greater than one whole.

Equivalent fractions: These represent the same part of a whole, but have different numerators and denominators.

Unit fractions: These have a numerator of 1 and a denominator that is a positive integer.

## Proper Fractions

A proper fraction always has a numerator smaller than the denominator and represents a part of a whole that is less than one whole.

Just Remember: Smaller numerator (smaller than the denominator) = Proper fraction

You can represent proper fractions as decimals or percentages too.

### Examples of Proper Fractions

1/2, which represents 1 part out of 2 parts

2/3, which represents two parts out of 3 parts

3/4, which represents three parts out of 4

### Real-World Connection for Proper Fractions:

Suppose you want to bake a cake and the recipe calls for 3/4 cup of flour.

In this case, the amount of flour needed is a proper fraction because it is less than 1 whole cup.

## Improper Fractions

An improper fraction has a numerator equal to or greater than the denominator and represents a part of a whole that is equal to or greater than one whole.

Just remember, anytime you see a fraction with a numerator greater than the denominator, it’s improper!

### Examples of Improper Fractions

5/3, which represents 5 parts, but it only takes 3 parts to make 1 whole.

7/2, which represents 7 parts, but it only takes 2 parts to make 1 whole.

9/4, which represents two wholes and one-quarter of another whole

### Real World Connection:

Imagine you are at a party and there are five different pizzas to choose from. Each pizza is cut into four slices. So, if you want to eat a whole pizza, you need to eat all four slices.

Let’s say you are really hungry and you eat two slices from the first pizza, one slice from the second pizza, and two slices from the third pizza. In total, you have eaten five slices of pizza.

This means that you have eaten more than one whole pizza because you have eaten five out of the 20 slices (5/4). That’s like eating one whole pizza and one extra slice!

Notice that the denominator is still 4. That’s because no matter how many slices you eat, there are still 4 slices in 1 whole.

## Converting Fractions

To convert an improper fraction to a proper fraction, divide the numerator by the denominator. Think of the fractional bar as a division sign.

The quotient will be the whole number, and the remainder will be the new numerator.

For example, if you have the improper fraction 7/4, divide 7 by 4 to get 1 with a remainder of 3. Therefore, 7/4 can be written as 1 3/4.

## Unit Fractions

Fractions where the numerator is 1 and the denominator represents the number of equal parts that make up the whole are called unit fractions.

In other words, a unit fraction is just 1 part of a whole, regardless of the number of parts that make up the whole. 1/4 is one because it represents 1 of 4 equal parts that make up a whole.

As a side note, when you see a numerator of 1, rest assured that it’s a fraction that’s in simplest form!

### The Building Blocks

Wholes are made up of the sum of their unit fractions. For example, if you have a whole that is divided into 5 equal parts, each part would be 1/5 of the whole. The whole can be represented as the sum of its unit fractions: 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 5/5 or 1 whole.

When you’re describing a whole by its unit fractions, each one will have the same denominators. In fact, all unit fractions have the same numerator too – 1!

### Real World Connection

Suppose you have a rectangular piece of cake that is cut into 12 equal pieces. Each piece represents 1/12 of the whole cake, which is a unit fraction.

If you eat 3 pieces of cake, you have consumed 3/12 of the whole cake because 1/12 + 1/12 + 1/12 = 3/12.

In this case, the unit fraction helps you understand how much cake you have eaten relative to the whole cake.

## Mixed Fractions

A mixed fraction consists of a whole number and a proper fraction. Many people called it a mixed number.

It represents a value that is greater than one whole. You can convert mixed fractions to improper fractions or decimals.

### Examples of Mixed Fractions

1 1/2, which represents one whole and one-half of another whole

2 3/4, which represents two wholes and three-quarters of another whole

3 2/5, which represents three wholes and two-fifths of another whole

### Converting Mixed Fractions to Improper Fractions

To convert mixed numbers to improper fractions, multiply the whole number by the denominator and add the numerator. The result will be the new numerator, and the denominator remains the same.

For example, if you have the mixed fraction 2 1/3, multiply 2 by 3 and add 1 to get 7. Therefore, 2 1/3 can be written as the improper fraction 7/3.

### Real World Connection

Imagine you want to buy a 5-foot shelf that comes in two pieces. The first piece is 4 feet long, and the second piece is 1 1/2 feet long.

In this case, the total length of the shelf is a mixed fraction because it represents one whole unit (the 4-foot piece) and one and a half units (the 1 1/2-foot piece).

## Equivalent Fractions

Equivalent fractions represent the same part of a whole, but have different numerators or different denominators. They are called equivalent fractions because they have the same value. They are equal!

Here’s an example of two fractions that are equivalent: 1/2 and 2/4.

If two fractions have the same numerator, but different denominators, they cannot be equal. Likewise, if they have the same denominator but different numerators, they cannot be equal.

You can create equivalent fractions by multiplying or dividing both the numerator and denominator of a fraction by the same number.

For example, let’s take 1/4 and multiply the numerator by 5 and the denominator by 5. We will have a second fraction, 5/20. So, 1/4 is equivalent to 5/20, even though they have unlike denominators and unlike numerators.

Equivalent fractions are useful when comparing and ordering fractions, or when adding and subtracting fractions with different denominators. By finding equivalent fractions with the same denominator, you can perform these operations easily.

### Examples of Equivalent Fractions

1/2 and 2/4, which represent the same part of a whole, but are written with different numerators and denominators. Even though they look different, both fractions represent the same value.

Another example is 3/6 and 5/10, which also represent the same part of a whole, but are written with different numerators and denominators.

In general, any fraction can have an infinite number of equivalent fractions.

### Can a fraction have more than one equivalent fraction?

A: Yes, a fraction can have an infinite number of equivalent fractions. To find equivalent fractions, multiply or divide both the numerator and denominator by the same number. For example, 1/2 is equivalent to 2/4, 3/6, 4/8, and so on.

### Real-World Connection for Equivalent Fractions:

Suppose you have a pizza that is cut into 8 slices, and you want to share it equally with a friend who prefers larger slices.

You could cut each slice in half, resulting in 16 smaller slices. In this case, the two halves of a larger slice represent the same part of the pizza as one whole smaller slice.

Therefore, 1/8 and 2/16 are equivalent fractions.

## Conclusion:

Understanding the different types of fractions is crucial for everyday life, whether you’re measuring ingredients for a recipe or splitting a pizza among friends.

Proper fractions, improper fractions, mixed fractions, unit fractions, and equivalent fractions all play a unique role in representing parts of a whole.

Keep practicing and exploring the world of fractions – with a little bit of effort, anyone can master them!

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