# Different Types of Fractions: An Overview of Proper, Improper, Mixed, and Like Fractions

## What is a Fraction?

Above picture is illustrating a whole Pizza which is being cut or divided into 6 equal slices. Therefore, each slice is represented as a Fraction of a Pizza. Therefore, when the whole is split or divided into equal parts, every part represents a Fraction.

I hope this made the concept of Fraction a little bit simpler.

If a Pizza is divided into six equal slices and each slice of pizza is given to a person then each person is supposed to have 1/6 of the pizza. So we read this one fraction of a pizza as ‘one-sixth’ or we also call it ‘ 1 by 6’.

Fractions make equal shares of a collection possible. On the other hand, Fraction can also be seen as Division. If we notice, all we are doing here is dividing a Pizza into equal numbers of parts so that every person can possibly get equal slices.

## Why Fractions are Important for Kids to Learn?

The fraction concept is mandatory for kids to understand as this is used in everyday life. Not only that it is one of the significant types of numbers in mathematics. Learning this concept facilitates the understanding of division and simplifies small or big numbers (Simplifying means reducing the value of any given number to the lowest form).  Kids grasp this concept better with the help of practical examples rather than theoretical knowledge.

For instance, How many portions of their favorite fruit or a dessert or a meal do they need?

If they love baking and cooking, then they can understand fractions more easily as baking involves questions such as how much of a certain ingredient is required to make a certain dish.

Apart from that, one of the most basic examples which can be shown is the use of fractions in telling time; each second is a fraction of a minute; each minute is a fraction of an hour.

## Fraction of a Set or Collection

This term is not confined to a whole but also represents parts of a set or collection. For example,

There are a total of 8 marbles.

3 out of 8 marbles are green. So, the fraction of green marbles is three-eighths (⅜).

And 5 out of 8 marbles are orange. So, the fraction of orange marbles is five-eighths (⅝).

## How to Represent a Fraction?

A Fraction consists of two numbers representing two parts of a whole. These two numbers are separated by a horizontal line “-” . The form in which a fraction is represented looks like this

The number on the top of the line is known as Numerator and the number which is below the line is known as Denominator. In the circle below, two parts (Numerator) out of total 5 parts (Denominator) are shaded.

### Numerator

This number represents how many equal parts of a whole or collection are taken and in some cases how many equal parts of a whole are left.

### Denominator

This number represents the total number of parts making up a whole or collection. Therefore, it shows the whole.

### Fraction Bar

The horizontal line helps in separating and comparing the numerator and denominator. Also, this line is referred to as the “Division Bar or Fraction Bar” as they have the same purpose of dividing. Moreover, in some countries this fraction bar is called by another name as “Vinculum”.

## Different Types Of Fractions

Fractions are solely based on the “Numerator and Denominator”, depending on them different types of fractions are classified. There are seven basic types of fractions, which we will be studying below.

### Unit Fractions

These fractions always have ‘1’ in the place of a numerator.

Example: ⅛ { Here the given fraction has ‘1’ as the numerator and ‘8’ as the denominator. We read this fraction as one-eighth.}

### Proper Fractions

Fractions where the Numerator is smaller or less than the denominator.

Example: { Here the given fraction has ‘2’ as the numerator which is less than the ‘5’ as the denominator and it can also be read as two-fifths.}

### Improper Fractions

Fractions in which the Numerator is bigger or more than the denominator.

Example: 7/6 { Here the given fraction has ‘7’ as the numerator which is more than the ‘6’ as the denominator and it can also be read as seven-sixths.}

### Mixed Fractions

As the name suggests, it is a mixture or a combination of a whole number and a proper fraction..

Example: 2 ¼ { Here ‘2’ represents a whole number, ‘1’ as a numerator and ‘4’ as a denominator and it can also be read as Two and one-fourths }

In the picture given above, there are three circles out of which 2 whole circles are completely shaded whereas the third circle has only one part shaded i.e. ¼ (one-fourths).

### Like Fractions

Fractions whose denominators are the same.

Example: and { Read as two-fifths and three-fifths.}

### Unlike Fractions

Fractions whose denominators are different.

Example: ⅖ and ¼ { Read as two-fifths and one-fourths.}

### Equivalent Fractions

As the name suggests, Equivalent means equal in value or amount. This type of Fraction can be found by multiplying or dividing both the numerator and denominator by the same number.

Example: ½ (Halves) is equal to 2/4 (two-fourths) is equal to 4/8 (four-eighths). Here in this example, we multiplied both the numerator and denominator of the fraction ½ with ‘2’.

## Conversion of Improper Fractions to Mixed Numbers

There is an easy method to convert Improper fractions into a mixed numbers by dividing the numerator by the denominator.

• Firstly, consider the numerator as the “dividend” and the denominator as the “divisor”.
• For instance, take a fraction of 9/4, where ‘9’ is a numerator and ‘4’ is a denominator.
• Secondly, we will start dividing the numerator with the denominator  (9➗4), the quotient will be the Whole Number, the remainder will be the numerator and the denominator always stays the same.
• Point to be noted- Improper fractions always yield remainder.
• Hence, ‘2’ is the Whole Number, ‘1’ is the numerator and ‘4’ is the denominator which doesn’t change.

## Conversion of Mixed Numbers to Improper Fractions

Turning mixed numbers into improper fractions can be very easy if one follows the steps given below,

• Firstly, we will consider a mixed number, for example: 1 ¾.
• Secondly, take the denominator (4) to multiply it with the whole number (1) and then add the product i.e. (4 X 1 = 4) obtained through multiplication with the given numerator (3).
• “4 + 3 = 7” , so ‘7’ becomes the new numerator and the denominator always stays the same as 4.
• 1 ¾  =  ((4X1) + 3 )  / 4 =   (4 + 3)/4   =  7 / 4

Hence, this method helps us in converting mixed number 1 ¾ to improper fraction 7/4.

## Conclusion

Fraction is a chapter that commonly becomes problematic if one does not comprehend the logic and reasoning behind it. The primary reason for Fractions’ existence was to break and share equal parts, portions, or segments of a whole. This term was originally derived from the Latin term “fractus”  which means broken. Describing how many parts make a complete whole exists.

Egyptians were the first civilizations who studied fractions and applied fractions to resolve their mathematical issues. As I mentioned before fractions concepts are needed for dividing or distributing food, money, supplies, etc.

Lastly, I would like to end by saying “ Fractions represent a portion of something that is larger.

Here at { igebra.ai }, the educators focus on relating math concepts with practical applications as this creates a greater understanding which retains in the memory of the kid for a longer period of time. If the foundation is better then the creation of stronger walls will be feasible.

On Key
The text passage provides an overview of fractions, including their definition, importance, representation, and different types. It also explains how to convert between improper fractions and mixed numbers. The passage does not contain any specific mathematical questions or answers to such questions.
no_question
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
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- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Different Types of Fractions: An Overview of Proper, Improper, Mixed, and Like Fractions

## What is a Fraction?

Above picture is illustrating a whole Pizza which is being cut or divided into 6 equal slices. Therefore, each slice is represented as a Fraction of a Pizza. Therefore, when the whole is split or divided into equal parts, every part represents a Fraction.

I hope this made the concept of Fraction a little bit simpler.

If a Pizza is divided into six equal slices and each slice of pizza is given to a person then each person is supposed to have 1/6 of the pizza. So we read this one fraction of a pizza as ‘one-sixth’ or we also call it ‘ 1 by 6’.

Fractions make equal shares of a collection possible. On the other hand, Fraction can also be seen as Division. If we notice, all we are doing here is dividing a Pizza into equal numbers of parts so that every person can possibly get equal slices.

## Why Fractions are Important for Kids to Learn?

The fraction concept is mandatory for kids to understand as this is used in everyday life. Not only that it is one of the significant types of numbers in mathematics. Learning this concept facilitates the understanding of division and simplifies small or big numbers (Simplifying means reducing the value of any given number to the lowest form).  Kids grasp this concept better with the help of practical examples rather than theoretical knowledge.

For instance, How many portions of their favorite fruit or a dessert or a meal do they need?

If they love baking and cooking, then they can understand fractions more easily as baking involves questions such as how much of a certain ingredient is required to make a certain dish.

Apart from that, one of the most basic examples which can be shown is the use of fractions in telling time; each second is a fraction of a minute; each minute is a fraction of an hour.

## Fraction of a Set or Collection

This term is not confined to a whole but also represents parts of a set or collection. For example,

There are a total of 8 marbles.

3 out of 8 marbles are green. So, the fraction of green marbles is three-eighths (⅜).

And 5 out of 8 marbles are orange. So, the fraction of orange marbles is five-eighths (⅝).

## How to Represent a Fraction?

A Fraction consists of two numbers representing two parts of a whole. These two numbers are separated by a horizontal line “-” . The form in which a fraction is represented looks like this

The number on the top of the line is known as Numerator and the number which is below the line is known as Denominator. In the circle below, two parts (Numerator) out of total 5 parts (Denominator) are shaded.

### Numerator

This number represents how many equal parts of a whole or collection are taken and in some cases how many equal parts of a whole are left.

### Denominator

This number represents the total number of parts making up a whole or collection. Therefore, it shows the whole.

### Fraction Bar

The horizontal line helps in separating and comparing the numerator and denominator. Also, this line is referred to as the “Division Bar or Fraction Bar” as they have the same purpose of dividing. Moreover, in some countries this fraction bar is called by another name as “Vinculum”.

## Different Types Of Fractions

Fractions are solely based on the “Numerator and Denominator”, depending on them different types of fractions are classified. There are seven basic types of fractions, which we will be studying below.

### Unit Fractions

These fractions always have ‘1’ in the place of a numerator.

Example: ⅛ { Here the given fraction has ‘1’ as the numerator and ‘8’ as the denominator. We read this fraction as one-eighth.}

### Proper Fractions

Fractions where the Numerator is smaller or less than the denominator.

Example: { Here the given fraction has ‘2’ as the numerator which is less than the ‘5’ as the denominator and it can also be read as two-fifths.}

### Improper Fractions

Fractions in which the Numerator is bigger or more than the denominator.

Example: 7/6 { Here the given fraction has ‘7’ as the numerator which is more than the ‘6’ as the denominator and it can also be read as seven-sixths.}

### Mixed Fractions

As the name suggests, it is a mixture or a combination of a whole number and a proper fraction..

Example: 2 ¼ { Here ‘2’ represents a whole number, ‘1’ as a numerator and ‘4’ as a denominator and it can also be read as Two and one-fourths }

In the picture given above, there are three circles out of which 2 whole circles are completely shaded whereas the third circle has only one part shaded i.e. ¼ (one-fourths).

### Like Fractions

Fractions whose denominators are the same.

Example: and { Read as two-fifths and three-fifths.}

### Unlike Fractions

Fractions whose denominators are different.

Example: ⅖ and ¼ { Read as two-fifths and one-fourths.}

### Equivalent Fractions

As the name suggests, Equivalent means equal in value or amount. This type of Fraction can be found by multiplying or dividing both the numerator and denominator by the same number.

Example: ½ (Halves) is equal to 2/4 (two-fourths) is equal to 4/8 (four-eighths). Here in this example, we multiplied both the numerator and denominator of the fraction ½ with ‘2’.

## Conversion of Improper Fractions to Mixed Numbers

There is an easy method to convert Improper fractions into a mixed numbers by dividing the numerator by the denominator.

• Firstly, consider the numerator as the “dividend” and the denominator as the “divisor”.
• For instance, take a fraction of 9/4, where ‘9’ is a numerator and ‘4’ is a denominator.
• Secondly, we will start dividing the numerator with the denominator  (9➗4), the quotient will be the Whole Number, the remainder will be the numerator and the denominator always stays the same.
• Point to be noted- Improper fractions always yield remainder.
• Hence, ‘2’ is the Whole Number, ‘1’ is the numerator and ‘4’ is the denominator which doesn’t change.

## Conversion of Mixed Numbers to Improper Fractions

Turning mixed numbers into improper fractions can be very easy if one follows the steps given below,

• Firstly, we will consider a mixed number, for example: 1 ¾.
• Secondly, take the denominator (4) to multiply it with the whole number (1) and then add the product i.e. (4 X 1 = 4) obtained through multiplication with the given numerator (3).
• “4 + 3 = 7” , so ‘7’ becomes the new numerator and the denominator always stays the same as 4.
• 1 ¾  =  ((4X1) + 3 )  / 4 =   (4 + 3)/4   =  7 / 4

Hence, this method helps us in converting mixed number 1 ¾ to improper fraction 7/4.

## Conclusion

Fraction is a chapter that commonly becomes problematic if one does not comprehend the logic and reasoning behind it. The primary reason for Fractions’ existence was to break and share equal parts, portions, or segments of a whole. This term was originally derived from the Latin term “fractus”  which means broken. Describing how many parts make a complete whole exists.

Egyptians were the first civilizations who studied fractions and applied fractions to resolve their mathematical issues. As I mentioned before fractions concepts are needed for dividing or distributing food, money, supplies, etc.

Lastly, I would like to end by saying “ Fractions represent a portion of something that is larger.

Here at { igebra.ai }, the educators focus on relating math concepts with practical applications as this creates a greater understanding which retains in the memory of the kid for a longer period of time. If the foundation is better then the creation of stronger walls will be feasible.

On Key
user
The text passage provides an overview of fractions, including their definition, importance, representation, and different types. It also explains how to convert between improper fractions and mixed numbers. The passage does not contain any specific mathematical questions or answers to such questions.

TYPE: NO_QUESTION