We already know that fraction is a part of the whole. Unlike fractions means all the denominators of the fractions are different. Comparing fractions is helpful to find which is the bigger one and which is the smaller one. Find the definition, different methods to compare unlike fractions in the below sections. You can also get solved questions on the comparing unlike fractions on this page.
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Comparing Fractions with Unlike Denominators
A fraction has two parts they are numerator and denominator. The numerator is the number that is above the division symbol and the denominator is the number below the division symbol. A fraction can be defined as part of a whole also called a ratio. Unlike fractions are the fractions which are having different denominators.
Comparison of unlike fractions is nothing but determining which fraction is greater and which fraction is lesser one out of the given fractions.
Comparing Unlike Fractions Methods | How to Compare Unlike Fractions?
The four different methods of comparing unlike fractions are listed here:
- L.C.M
- Decimal Method
- Cross Multiplication Method
- Visualization
Check out the detailed steps of each of the method in the below-provided sections.
Comparing Unlike Fractions Using LCM
- Take unlike fractions
- Find the LCM of denominators
- Make the unlike fractions as like fractions by multiplying the same number in the numerator, denominator.
- Compare the numerators and fractions
Decimal Method to Compare Unlike Fractions
- Write the given fractions in decimal form.
- Compare the decimal values.
- The fraction with a larger decimal value is the larger fraction.
Comparison of Unlike Fractions Using Cross Multiplication
- The numerator of the first fraction should be multiplied by the denominator of the other fraction.
- Compare the obtained values.
- The larger value means the larger fraction.
Comparing Fractions Using Visualization
- Express the fraction using a graph or model.
- The larger shaded area means a lesser fraction.
Examples on Comparison of Unlike Fractions
Example 1:
Compare the following fractions using the LCM method.
\(\frac { 1 }{ 2 } \), \(\frac { 5 }{ 3 } \), \(\frac { 2 }{ 7 } \), \(\frac { 6 }{ 4 } \)
Solution:
The given unlike fractions are \(\frac { 1 }{ 2 } \), \(\frac { 5 }{ 3 } \), \(\frac { 2 }{ 7 } \), \(\frac { 6 }{ 4 } \)
Find the L.C.M of denominators
LCM of 2, 3, 7, 4 = 84
So, make denominators of all fractions as
\(\frac { 1 }{ 2 } \) x \(\frac { 42 }{ 42 } \) = \(\frac { 42 }{ 84 } \)
\(\frac { 5 }{ 3 } \) x \(\frac { 28 }{ 28 } \) = \(\frac { 140 }{ 84 } \)
\(\frac { 2 }{ 7 } \) x \(\frac { 12 }{ 12 } \) = \(\frac { 24 }{ 84 } \)
\(\frac { 6 }{ 4 } \) x \(\frac { 21 }{ 21 } \) = \(\frac { 126 }{ 84 } \)
Now, all the fractions have the same denominator.
Compare numerators 24 < 42 < 126 < 140
The fractions comparison is \(\frac { 24 }{ 84 } \) < \(\frac { 42 }{ 84 } \) < \(\frac { 126 }{ 84 } \) < \(\frac { 140 }{ 84 } [/latex
The comparison of fractions is [latex]\frac { 2 }{ 7 } \) < \(\frac { 1 }{ 2 } \) < \(\frac { 6 }{ 4 } \) < \(\frac { 5 }{ 3 } \)
Example 2:
Which one is greater \(\frac { 5 }{ 3 } \) or \(\frac { 3 }{ 5 } \)?
Solution:
The given fractions are \(\frac { 5 }{ 3 } \), \(\frac { 3 }{ 5 } \)
Cross multiply the fractions
5 x 5 = 25
3 x 3 = 9
25 > 9
So, \(\frac { 5 }{ 3 } \) > \(\frac { 3 }{ 5 } \)
The greater fraction is \(\frac { 5 }{ 3 } \).
Example 3:
Which one is smaller \(\frac { 1 }{ 5 } \) or \(\frac { 6 }{ 7 } \)?
Solution:
Given fractions are \(\frac { 1 }{ 5 } \), \(\frac { 6 }{ 7 } \)
Find the decimal value of fractions.
\(\frac { 1 }{ 5 } \) = 0.2
\(\frac { 6 }{ 7 } \) = 0.85
0.85 > 0.2
So, \(\frac { 6 }{ 7 } \) > \(\frac { 1 }{ 5 } \)
Example 4:
Compare \(\frac { 2 }{ 3 } \), \(\frac { 7 }{ 9 } \) using visualisation.
Solution:
Given fractions are \(\frac { 2 }{ 3 } \), \(\frac { 7 }{ 9 } \)
The visual representation of \(\frac { 2 }{ 3 } \) is 
The visual representation of \(\frac { 7 }{ 9 } \) is
\(\frac { 2 }{ 3 } \) has lesser shaded region compared to \(\frac { 7 }{ 9 } \)
So, \(\frac { 2 }{ 3 } \) < \(\frac { 7 }{ 9 } \)