What are Like Fractions?
The fractions having same denominator are called like fractions.
We know that a fraction is made two parts, numerator and denominator.
The upper part of the fraction is called numerator.
The lower part of the fraction is called denominator.
Like Fractions are the fractions having the same lower part value ( i.e. denominator)
For Example;
In the above image you can see all the fractions have same denominator, hence they are like fractions.
Converting Fractions into Like Fractions
Is is possible to convert different fractions into Like fractions?
Yes, It is possible by following below steps;
(a) Take LCM of denominators.
(b) Convert the denominators of given fraction into LCM value by multiplication or division.
Example 01
Convert \mathtt{\frac{2}{3} \ \&\ \frac{3}{5}} into like fraction
Solution
Follow the below steps;
(a) Take LCM of the denominators
LCM ( 3, 5 ) = 15
(b) Multiply both fractions to make denominator 15.
Fraction 2/3
Multiply numerator and denominator by 5
\mathtt{\Longrightarrow \ \frac{2\times 5}{3\times 5}}\\\ \\ \mathtt{\Longrightarrow \ \frac{10}{15}}
Fraction 3/5
Multiply numerator and denominator by 3
\mathtt{\Longrightarrow \ \frac{3\times 3}{5\times 3}}\\\ \\ \mathtt{\Longrightarrow \ \frac{9}{15}}
Hence, we got the two fractions 10/15 and 9/15.
Both the fractions are like fraction.
Example 02
Convert \mathtt{\frac{1}{4} \ \&\ \frac{2}{7}} into like fraction
Solution
Follow the below steps;
(a) Find the LCM of denominators
LCM ( 4, 7 ) = 28
(b) Multiply the fractions to make denominator 28
Fraction 1/4
Multiply numerator and denominator by 7
\mathtt{\Longrightarrow \ \frac{1\times 7}{4\times 7}}\\\ \\ \mathtt{\Longrightarrow \ \frac{7}{28}}
Fraction 2/7
Multiply numerator and denominator by 4
\mathtt{\Longrightarrow \ \frac{2\times 4}{7\times 4}}\\\ \\ \mathtt{\Longrightarrow \ \frac{8}{28}}
Hence, we got the fractions 7/28 and 8/28.
Both the fractions are like fraction.
Addition of Like Fraction
Adding two or more like fraction is a straightforward process.
You simply have to add the given numerators and keep the denominator as it is.
Example 01
Add \mathtt{\frac{6}{7} \ \&\ \frac{4}{7}}
Solution
Since the given numbers are like fraction, you have to simply add the numerator.
Hence, 10/7 is the solution.
Example 02
Add the below fraction.
\mathtt{\frac{13}{6} \ \&\ \frac{9}{6}}
Solution
Both 13/6 and 9/6 are the like fraction as they have same denominator.
To add the fractions, simply add the numerator and retain the same denominator.
Hence, 22/6 is the solution of the addition.
Subtraction of Like Fraction
Similar to addition, the subtraction of like fraction is done by simply subtraction the numerator and retaining the same denominator.
Example 01
Subtract the below fractions.
\mathtt{\frac{8}{13} \ \&\ \frac{5}{13}}
Solution
Both the above fractions are like fractions since they have same denominator.
Simply subtract the numerator and keep the denominator as it is.
Hence, 3/13 is the solution.
Example 02
Subtract the following fractions.
\mathtt{\frac{14}{9} \ \&\ \frac{10}{9}}
Solution
Both the fractions have same denominator, hence are like fraction.
Subtract the numerator and retain the denominator.
Solved Problems – Like Fraction
(01) Check if the below fractions are like fractions or not.
\mathtt{( i) \ \frac{1}{2} \ \&\ \frac{3}{4}}\\\ \\ \mathtt{( ii) \ \frac{3}{7} \ \&\ \frac{5}{7}}\\\ \\ \mathtt{( iii) \ \frac{9}{6} \ \&\ \frac{2}{13}}\\\ \\ \mathtt{( iv) \ \frac{3}{5} \ \&\ \frac{9}{5}}\\\ \\ \mathtt{( v) \ \frac{6}{50} \ \&\ \frac{15}{55}}
Solution
\mathtt{( i) \ \frac{1}{2} \ \&\ \frac{3}{4}}
They are not Like Fractions as they have different denominator.
\mathtt{( ii) \ \frac{3}{7} \ \&\ \frac{5}{7}}
Fractions have same denominator, hence they are like fractions.
\mathtt{( iii) \ \frac{9}{6} \ \&\ \frac{2}{13}}
Fractions have different denominator, hence are unlike fraction.
\mathtt{( iv) \ \frac{3}{5} \ \&\ \frac{9}{5}}
Both fractions have same denominator, hence are like fraction.
\mathtt{( v) \ \frac{6}{50} \ \&\ \frac{15}{55}}
The fractions have different denominator, hence are unlike fractions.
(02) Convert the below fractions into like fraction.
\mathtt{( i) \ \frac{3}{2} \ \&\ \frac{4}{3}}\\\ \\ \mathtt{( ii) \ \frac{2}{5} \ \&\ \frac{7}{7}}\\\ \\ \mathtt{( iii) \ \frac{1}{5} \ \&\ \frac{4}{15}}\\\ \\ \mathtt{( iv) \ \frac{2}{9} \ \&\ \frac{10}{5}}
Solution
\mathtt{( i) \ \frac{3}{2} \ \&\ \frac{4}{3}}
Follow the below steps;
(i) Take LCM of denominator.
LCM (2, 3) = 6
(ii) Multiply the fractions to make denominator 6.
Fraction 3/2
Multiply numerator and denominator by 3
\mathtt{\Longrightarrow \ \frac{3\times 3}{2\times 3} \ =\ \frac{9}{6}}
Fraction 4/3
Multiply numerator and denominator by 2
\mathtt{\Longrightarrow \ \frac{4\times 2}{3\times 2} \ =\ \frac{8}{6}}
Hence, 8/6 and 9/6 are the like fractions.
\mathtt{( ii) \ \frac{2}{5} \ \&\ \frac{7}{7}}
(i) Find the LCM of denominators
LCM ( 5, 7 ) = 35
(ii) Multiply the fractions to make denominator 35
Fraction 2/5
multiply numerator and denominator by 7
\mathtt{\Longrightarrow \ \frac{2\times 7}{5\times 7} \ =\ \frac{14}{35}}
Fraction 7/7
Multiply numerator and denominator by 5
\mathtt{\Longrightarrow \ \frac{7\times 5}{7\times 5} \ =\ \frac{35}{35}}
Hence, 14/35 and 35/35 are the like fractions.
\mathtt{( iii) \ \frac{1}{5} \ \&\ \frac{4}{15}}
(i) Take LCM of denominators
LCM ( 5, 15 ) = 75
(ii) Multiply the fractions to make denominator 75.
Fraction 1/5
Multiply numerator and denominator by 15.
\mathtt{\Longrightarrow \ \frac{1\times 15}{5\times 15} \ =\ \frac{15}{75}}
Fraction 4/15
Multiply numerator and denominator by 5
\mathtt{\Longrightarrow \ \frac{4\times 5}{15\times 5} \ =\ \frac{20}{75}}
Hence, fraction 15/75 and 20/75 are like fractions.
\mathtt{( iv) \ \frac{2}{9} \ \&\ \frac{10}{5}}
(i) Find LCM of denominators
LCM ( 9, 5 ) = 45
(ii) Multiply fractions to make denominator 45
Fraction 2/9
Multiply numerator and denominator by 5
\mathtt{\Longrightarrow \ \frac{2\times 5}{9\times 5} \ =\ \frac{10}{45}}
Fraction 10/5
Multiply numerator and denominator by 9
\mathtt{\Longrightarrow \ \frac{10\times 9}{5\times 9} \ =\ \frac{90}{45}}
Hence 10/45 and 90/45 are the like fractions.