# Like and Unlike Fractions – Definition, Facts, Arithmetic Operations, and Examples

Wanna become perfect in fraction concepts? Here is the in-detail information regarding like and unlike fractions. Check the complete guide to know more about fractions and unlike fractions. Refer to various concepts like Examples, Conversions, etc. Follow the important points and steps to convert like fractions to, unlike fractions. Know who the various operations like addition, subtraction, multiplication, and division apply to various fractions. Go through the below sections to check details like solved questions, practice tests, definition, etc.

### Like Fractions and Unlike Fractions Definitions

A fraction is nothing but the number that is representing a part of a group of objects or a single whole object. The upper part of the fraction is called the numerator and the lower part of the fraction is called the denominator. Based on the similarities of the denominator, fractions are categorized into two types. They are:

1. Like or Similar Fractions
2. Unlike or Dissimilar Fractions

### Like Fractions

If two or more number of fractions or a group of fractions where the denominator is similar are said to be like fractions. Or we can also define as the fractions where the bottom number is the same.

Example: $$\frac { 4 }{ 4 }$$, $$\frac { 6 }{ 4 }$$, $$\frac { 8 }{ 4 }$$, $$\frac { 10 }{ 4 }$$

In the above example, the denominator is 4 in all cases. Therefore, they are all like factors.

#### Important Points for Like Fractions:

• Fraction values like $$\frac { 2 }{ 8 }$$, $$\frac { 25 }{ 20 }$$ , $$\frac { 9 }{ 12 }$$, $$\frac { 8 }{ 32 }$$ are also called fractions. Even though they possess different denominators, they are called like fractions because on further simplification, they will have the same denominators. i.e., $$\frac { 1 }{ 4 }$$, $$\frac { 5 }{ 4 }$$ , $$\frac { 3 }{ 4}$$, $$\frac { 1 }{ 4 }$$
• Fraction values like $$\frac { 4 }{ 10 }$$, $$\frac { 4 }{ 15 }$$, $$\frac { 4 }{ 20 }$$, $$\frac { 4 }{ 25 }$$ are not like fractions. Even they have the same numerators, they are not like factors as their denominators are not the same.
• All-natural numbers like 2,3,4,5 are considered to be the like fractions because they all have the same denominator value 1. They can be written as $$\frac { 2 }{ 1 }$$, $$\frac { 3}{1 }$$, $$\frac { 4 }{ 1 }$$, $$\frac { 5 }{ 1 }$$

### Arithmetic Operations on Like Fractions

Arithmetic operations like addition and subtraction can be easily done on like fractions. As they have the same denominators, addition and subtraction can be easily done.

#### Addition of Like or Similar Fractions

To add like fractions, we have to first consider the fractions. As both the denominators are the same, we directly add the numerators and write the value of it and then write the denominator value to it.

Example:

Add the like fractions – $$\frac { 2 }{ 3 }$$ and $$\frac { 4 }{ 3 }$$?

Solution:

As given in the question,

$$\frac { 2 }{ 3 }$$ and $$\frac { 4 }{ 3 }$$ are the like fractions

2 + $$\frac { 3 }{ 3}$$ = $$\frac { 5 }{ 3 }$$

Therefore, the final solution is $$\frac { 5 }{ 3 }$$.

#### Subtraction of Like or Similar Fractions

To add unlike or dissimilar fractions, we have to first consider the fractions. As both the denominators are the same, we directly subtract the numerators and write the value of it and then write the denominator value of it.

Example:

Subtract the fractions $$\frac { 1 }{ 2 }$$ from $$\frac { 11 }{ 2 }$$?

Solution:

As given in the question,

$$\frac { 1 }{ 2 }$$ and $$\frac { 11 }{ 2 }$$ are like fractions

To subtract the above fraction, we apply the rule of subtraction.

= $$\frac { (11-1) }{ 2 }$$

= $$\frac { 10 }{ 2 }$$

### Unlike Fractions

If two or more number of fractions or a group of fractions where the denominator is different are said to be like fractions. Or we can also define as the fractions where the bottom number is the same.

Example: $$\frac { 2 }{ 3 }$$, $$\frac { 4 }{ 5 }$$, $$\frac { 7 }{ 9 }$$, $$\frac { 9 }{ 11 }$$ etc.

In the above example, the denominator values are different, therefore they are unlike fractions.

#### Important Points for Unlike Fractions

• $$\frac { 2 }{ 4 }$$, $$\frac { 4 }{ 8 }$$, $$\frac { 1 }{ 2 }$$, etc. are unlike fractions, though after simplification they result in $$\frac { 1 }{ 2 }$$
• $$\frac { 6 }{ 16}$$ and $$\frac { 6 }{ 26 }$$ are unlike fractions. The numerators of the fractions are the same whereas the denominators are not.
• 2, 3, 4 are like or similar fractions since their denominators are considered as 1 because they all have the same denominator value 1. They can be written as $$\frac { 2 }{ 1 }$$, $$\frac { 3 }{ 1 }$$, $$\frac { 4 }{ 1 }$$. Hence, they are unlike fractions.

### Arithmetic Operation on Unlike Fractions

Arithmetic operations like addition and subtraction can be done on unlike fractions. As they have different denominators, addition and subtraction can be done.

To add unlike fractions, first, we have to convert unlike fractions to like fractions. Converting to like fraction means we have to make the denominators equal. There are 2 methods to make the denominator equal. They are:

1. LCM Method
2. Cross Multiplication Method

In the LCM Method of conversion, first, we have to take the LCM of denominators of the fractions. Using the result of LCM, make all the fractions as similar or like fractions. Then simplify the numerator to get the final result.

Example:

Simply the equation by adding $$\frac { 3 }{ 8 }$$ and $$\frac { 5 }{ 12 }$$?

Solution:

As given in the question, $$\frac { 3 }{ 8 }$$ + $$\frac { 5 }{ 12 }$$ are the fractions.

Now find the LCM of 8 and 12, we get

LCM of (8, 12) = 2 * 2 * 2 * 3 = 24

Now multiply the fractions to get the denominator values equal to 24, such that

= $$\frac { (3 * 3) }{ (8 * 3) }$$ + $$\frac { (5 * 2) }{(12 * 2) }$$

= $$\frac { 9 }{ 24 }$$ + $$\frac { 10 }{ 24 }$$

= $$\frac { 19 }{ 24 }$$

In the cross multiplication method, you have to multiply the numerator of the 1st fraction with the denominator of the second fraction. Then, multiply the numerator of the second fraction with the denominator of the first fraction. Now, multiply the denominators and consider it as a common denominator. Later we add the fraction values.

Example:

Simplify the equation by adding the fractions $$\frac { 1 }{ 3 }$$ and $$\frac { 3 }{ 4 }$$

Solution: $$\frac { 1 }{ 3}$$ + $$\frac { 3 }{ 4 }$$

By cross multiplication method, we get;

$$\frac { (1 x 4) + (3 x 3) }{ (3 x 4) }$$

= $$\frac {(4 + 9) }{ 12 }$$

= $$\frac {13 }{ 12 }$$

#### Subtraction of Unlike Fractions

To subtract, unlike fractions, first, we have to convert unlike fractions to like fractions. Converting to like fraction means we have to make the denominators equal. There are 2 methods to make the denominator equal. They are:

1. LCM Method
2. Cross Multiplication Method

In the LCM Method of conversion, first, we have to take the LCM of denominators of the fractions. Using the result of LCM, make all the fractions as similar or like fractions. Then simplify the numerator to get the final result.

Example:

Simplify the equation by subtracting $$\frac {1}{ 10 }$$ from $$\frac {2}{ 5 }$$?

Solution:

As given in question $$\frac { 2 }{ 5 }$$ – $$\frac { 1 }{ 10 }$$

Now find the L.C.M. of the denominators 10 and 5,

LCM of (10 & 5) is 10

Now multiply the fractions to get the denominator values equal to 10, such that

= $$\frac { 2 }{ 5 }$$ = $$\frac { (2 × 2) }{ (5 × 2) }$$ = $$\frac { 4 }{ 10 }$$ (because 10 ÷ 5 = 2)

= $$\frac { 1 }{ 10 }$$ = $$\frac { (1 × 1) }{ (10 × 1)) }$$ = $$\frac { 1 }{ 10 }$$ (because 10 ÷ 10 = 1)

Thus, $$\frac { 2 }{ 5 }$$ – $$\frac { 1 }{ 10 }$$

= $$\frac { 4 }{ 10 }$$ – $$\frac { 1 }{ 10 }$$

= $$\frac { (4 – 1) }{10 }$$

= $$\frac { 3 }{ 10 }$$

In the cross multiplication method, you have to multiply the numerator of the 1st fraction with the denominator of the second fraction. Then, multiply the numerator of the second fraction with the denominator of the first fraction. Now, multiply the denominators and consider it as a common denominator. Later we subtract the fraction values.

Example:

Simplify the equation by subtracting the fractions $$\frac { 3 }{ 4 }$$ and $$\frac { 1 }{ 3 }$$

Solution:

$$\frac { 3 }{ 4 }$$ – $$\frac { 1 }{ 3 }$$

By cross multiplication method, we get;

$$\frac { (3 x 3) – (1 x 4) }{ (3 x 4) }$$

= $$\frac { (9 – 4) }{ 12 }$$

= $$\frac { 5 }{ 12 }$$

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