Are you feeling difficulty in comparing the fractions? If you want to know which fraction is greater or smaller then you should know the methods of how to compare the fractions. This web page gives you clear information on methods of how to compare two fractions. You can also check the solved examples on comparing fractions for a better understanding of the concept.
Also, refer:
- Identification of the Parts of a Fraction
- Fraction as a Part of Collection
- Converting Fractions to Decimals
Comparing Fractions | How to Know which Fraction is Greater or Smaller?
We need to compare fractions to find out which fraction is larger and which is smaller. We can compare fractions by using two methods. They are
1. By converting the fractions into decimals
2. Using the same denominator method.
Converting Fractions into Decimals
In this method, convert the fractions which you want to compare into decimals and then compare to find out the greatest fraction and the smallest fraction.
Example 1:
Compare the fractions \(\frac { 1 }{ 8 } \), \(\frac { 5 }{ 12 } \).
Solution:
Convert the fractions into decimals.
i.e. \(\frac { 1 }{ 8 } \) is 1÷8, \(\frac { 5 }{ 12 } \) is 5÷12.
\(\frac { 1 }{ 8 } \)=0.125
\(\frac { 5 }{ 12 } \)=0.4166
0.4166 is greater.
Therefore, \(\frac { 5 }{ 12 } \) is greater.
Example 2:
Compare the fractions \(\frac { 3 }{ 8 } \), \(\frac { 7 }{ 12 } \).
Solution:
Convert the fractions into decimals.
i.e. \(\frac { 3 }{ 8 } \) is 1÷8, \(\frac { 7 }{ 12 } \) is 5÷12.
\(\frac { 3 }{ 8 } \)=0.375
\(\frac { 7 }{ 12 } \)=0.583
0.583 is greater.
Therefore, \(\frac { 7 }{ 12 } \) is greater.
Using the Same Denominator Method
When two fractions have the same denominators, it is easy to compare the fractions. When the denominators are different we have to make them the same for easily comparing fractions (using equivalent fractions).
Example 1:
Compare the fractions \(\frac { 1 }{ 4 } \), \(\frac { 5 }{ 6 } \) .
Solution:
To get the same denominators multiply the denominator 4 with 3 and the denominator 6 with 2.
When you multiply the denominator you should also multiply the numerator.
\(\frac { 1 }{ 4 } \)=\(\frac { 3 }{ 12 } \)
\(\frac { 5 }{ 6 } \)=\(\frac { 10 }{ 12 } \)
\(\frac { 3 }{ 12 } \) is smaller (As 3<10)
\(\frac { 10 }{ 12 } \) is larger.
We can make denominators the same by using two methods namely 1. Common Denominator Method and 2. Least Common Denominator method.
Common Denominator Method:
In this method, we multiply each fraction by the denominator of the other.
Example:
Compare the fractions \(\frac { 2 }{ 9 } \), \(\frac { 7 }{ 3} \).
Solution:
We multiply each fraction by the denominator of the other.
\(\frac { 2 }{ 9 } \) × 3=\(\frac { 6 }{ 27 } \)
\(\frac { 7 }{ 3} \) × 9=\(\frac { 63 }{ 27} \)
\(\frac { 63 }{ 27} \) is larger.(since 63>6).
Least Common Denominator
We multiply the fraction by the smallest number of all the common multiples of denominators.
Example:
Compare the fractions \(\frac { 1 }{ 6 } \), \(\frac { 7 }{ 12 } \).
Solution:
multiples of 6 are 6, 12,18, 24,30 ,etc.
multiples of 12 are 12,24,36,48,60 ,etc.
The least multiple is 12.
we want both fractions to have 12.
So multiply first fraction with 2
The second fraction already has 12 on the denominator.
\(\frac { 1 }{ 6 } \)×2= \(\frac { 2 }{ 12 } \)
Compare \(\frac { 2 }{ 12 } \), \(\frac { 7 }{ 12 } \)
\(\frac { 7 }{ 12 } \) is greater.(As 7>2)
Examples On Greater or Smaller Fraction
Example 1:
Compare the fractions \(\frac { 1 }{ 5 } \), \(\frac { 7 }{ 3 } \) using same denominator method.
Solution:
Multiply \(\frac { 1 }{ 5 } \) with 3
=\(\frac { 3 }{ 15 } \)
Multiply \(\frac { 7 }{ 3 } \) with 5
=\(\frac { 35 }{ 15 } \)
=\(\frac { 35 }{ 15 } \) is greater.(since 35>3)
Hence, \(\frac { 7 }{ 3 } \) is greater.
Example 2:
Compare the two fractions \(\frac { 6 }{ 5 } \),\(\frac { 8 }{ 5 } \) and find out which is greater?
Solution:
In the given fractions both the denominators are the same so it is very easy to compare.
compare the numbers 6,8 in the numerator.
clearly 8 >6.
Hence, \(\frac { 8 }{ 5 } \) is greatest.
Example 3:
Compare the two fractions \(\frac { 4 }{ 15 } \),\(\frac { 3 }{ 5 } \) using decimal method.
Solution:
Convert the fractions into decimal numbers.
Calculate 4÷15, 3÷5
4÷15=0.266
3÷5=0.6
Hence, 3÷5 is greater.
Example 4:
Compare the two fractions \(\frac { 4 }{ 2 } \),\(\frac { 8 }{ 3 } \) using the same denominator method?
Solution:
Multiply the first fraction with 3
\(\frac { 4 }{ 2 } \) ×3=\(\frac { 12 }{ 6 } \)
Multiply the second fraction with 2.
\(\frac { 8 }{ 3 } \)×2=\(\frac { 16 }{ 6 } \)
\(\frac { 16 }{ 6 } \) is greatest.
Hence \(\frac { 8 }{ 3 } \) is greater than \(\frac { 4 }{ 2 } \).
Example 5:
Compare \(\frac { 8 }{ 3 } \) ,\(\frac { 7 }{ 3 } \)
Solution:
As both have the same denominators compare the numerators 8,7.
8 is greater than 7.
Hence,\(\frac { 8 }{ 3 } \) is greatst.