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Like Fractions

Before moving to the like fraction, first we shall know what is fraction? A number in the form $\frac{a}{b}$ is called as fraction. It is also called as part of a whole representation.

The numbers between any two integers are represented in the form of fractions. But in the beginning fractions where defined only for reciprocals.

Fractions are mainly divided into two like fraction and unlike fraction. When the two fractions has same denominator then it is called as like fraction and when denominators are different it is unlike fractions.

Like and Unlike Fractions

Here we are going to learn about like fractions.

The fractions that are having the similar or common denominator called as like fractions.

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What are Like Fractions?

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Fractions that have same denominators are known as like fractions.

Like Fractions

Example:

$\frac{5}{4}$ and $\frac{3}{4}$ are two fractions

Numerator of $\frac{5}{4}$ = 5

Denominator of $\frac{5}{4}$ = 4

and

Numerator of $\frac{3}{4}$ = 3

Denominator of $\frac{3}{4}$ = 4

Denominator of $\frac{5}{4}$ = Denominator of $\frac{3}{4}$ = 4

So $\frac{5}{4}$ and $\frac{3}{4}$ are like fractions

Convert Unlike to Like Fractions

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Here we are going to learn the steps used to convert the unlike fractions into like fractions:

Step 1: Consider the given two fractions. Find the least common denominator for the given unlike fractions.

Step 2: Make the two denominators equal to the least common denominator of both fractions. Now we get the like fractions.

Let us see some problems related to like fractions.

Example 1 : Convert $\frac{1}{5}$ and $\frac{3}{2}$ into like fractions.

Solution:

Step 1: Find the LCD for the given fractions

LCD (5, 2) = 10

Convert the given fractions into equivalent fractions with denominator 10.

Multiply $\frac{1}{5}$ by 2 on both numerator and denominator

$\frac{1}{5}$ $\times$ $\frac{2}{2}$ = $\frac{2}{10}$

Multiply $\frac{3}{2}$ by 5 on both numerator and denominator

$\frac{3}{2}$ $\times$ $\frac{5}{5}$ = $\frac{15}{10}$

Hence $\frac{2}{10}$ and $\frac{15}{10}$ are like fractions.

Example 2: Convert $\frac{2}{15}$ and $\frac{3}{10}$ into like fractions.

Solution: To convert given fractions into like fractions, we find the LCM of 10 and 15.

LCM(10, 15) = 30

Convert the given fractions into equivalent fractions with denominator 30.

$\frac{2}{15}$ $\times$ $\frac{2}{2}$ = $\frac{4}{30}$

$\frac{3}{10}$ $\times$ $\frac{3}{3}$ = $\frac{9}{30}$

Thus required like fractions of $\frac{2}{15}$ and $\frac{3}{10}$ are $\frac{4}{30}$ and $\frac{9}{30}$.


Adding Like Fractions

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We are going to learn the steps used to adding the like fractions:
Steps for adding like Fractions:

Step 1: Add the numerator

Step 2: Place the addition over original denominator.

Step 3: Reduce the answer to lowest terms.

Example:

Add $\frac{9}{20}$ to $\frac{7}{20}$

Solution:


Given fractions are $\frac{9}{20}$ and $\frac{7}{20}$

The denominators of both the fractions are same, so fractions are like fractions

Step 1:
Add the numerators, 9 + 7 = 16

Step 2:
Place the addition, 16, over the original denominator, 20.

$\frac{9}{20}$ + $\frac{7}{20}$ = $\frac{9 + 7}{20}$ = $\frac{16}{20}$

Step 3:
Reduce the fraction $\frac{16}{20}$ to the lowest terms, $\frac{4}{5}$.


Subtracting Like Fractions

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We are going to learn the steps used to subtracting the like fractions:
Steps for Subtracting like Fractions:

Step 1: Subtract the numerator

Step 2: Place the difference over original denominator.

Step 3: Reduce the answer to lowest terms.

Example:

Subtract $\frac{5}{15}$ from $\frac{10}{15}$

Solution:


Given fractions are $\frac{10}{15}$ and $\frac{5}{15}$

The denominators of both the fractions are same, so fractions are like fractions

Step 1:
Subtract the numerators, 10 - 5 = 5

Step 2:
Place the difference, 5, over the original denominator, 15.

$\frac{10}{15}$ - $\frac{5}{15}$ = $\frac{10 - 5}{15}$ = $\frac{5}{15}$

Step 3:
Reduce the fraction $\frac{5}{15}$ to the lowest terms, $\frac{1}{3}$.

Like Fractions Solved Examples

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Below are the examples based on like fractions:

Solved Examples

Question 1: Find the like fractions for the following fractions $\frac{5}{7}$ , $\frac{9}{6}$
Solution:
 
Given, Fractions $\frac{5}{7}$ , $\frac{9}{6}$

We need to find the like fractions:

To find the like fractions, first find least common denominator,

Multiples of 7 = 7, 14, 21, 28, 35, 42, 49, 56...............

Multiples of 6 = 6, 12, 18, 24, 30, 36, 42 , 48 .............

least common multiple of 6 , 7 = 42.

Multiply $\frac{5}{7}$ by 6 on both numerator and denominator,

$\frac{5}{7}$ = $\frac{5 * 6}{7 * 6}$

= $\frac{30}{42}$

Multiply `9/6` by 7 on both numerator and denominator,

$\frac{9}{6}$ = $\frac{9 * 7}{6 * 7}$

= $\frac{63}{42}$
 

Correct answer is Like fractions $\frac{30}{42}$, $\frac{63}{42}$
Question 2: Add the fractions by find like fractions $\frac{5}{4}$ + $\frac{11}{8}$
Solution:
 
Given, $\frac{5}{4}$ + $\frac{11}{8}$

Both fractions are unlike fractions,

So the given fraction we need to convert it into like fractions,

Let us find the least common denominator of the given fractions,

Multiple of 8 = 8 , 16 ,24 ,.....

Multiple of 4 = 4 ,8, 12 ,16 ,....

The least common multiple of 4 and 8 is 8.

Multiply $\frac{5}{4}$ by 2 on both numerator and denominator ,

$\frac{5*2}{4 * 2}$ = $\frac{10}{8}$

Now we can add the fractions,

$\frac{5}{4}$ + $\frac{11}{8}$ = $\frac{10}{8}$ + $\frac{11}{8}$

= $\frac{10+11}{8}$

= $\frac{21}{8}$
 

Correct answer is $\frac{5}{4}$ + $\frac{11}{8}$ = $\frac{21}{ 8}$
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