Comparing fractions


Before learning about comparing fractions, please read the primer on fractions.


When you compare fractions, it’s helpful to consider whether the fractions being compared have like (the same) numerators, like (the same) denominators or unlike (different) denominators.


How to compare fractions with like numerators

 

If two fractions have the same numerator, the fraction with the higher denominator will be of lesser value.

 

For example, 1/2 and 1/3 have the same numerator (1). But 1/3 has a higher denominator than 1/2 (3 compared to 2).


Therefore

1/3     <     1/2


- a third is less than a half.



Next compare 4/5 and 4/9


4/5 and 4/9 both have numerator 4. However, 4/9's denominator (9) is higher than 4/5's denominator (5).


So

4/9     <     4/5


- four ninths is less than four fifths.


Comparing fractions with like denominators


If two fractions have the same denominator, the fraction with the lower numerator will be of lesser value.


For instance, 4/5 and 2/5 have the same denominator (5), but as 2/5 has a lower numerator than 4/5 (2 compared to 4)


2/5     <     4/5


- two fifths is less than four fifths.



Consider 13/11 and 8/11


Notice both fractions have denominator 11. Because 8/11's numerator (8) is lower than 13/11's numerator (13)


8/11     <     13/11


- eight elevenths is less than thirteen elevenths.


How to compare fractions with unlike denominators


To compare fractions with unlike denominators, first express as fractions with like denominators by finding the least common denominator, then follow the rules for comparing fractions with like denominators.


Let's take a look at 3/14 and 2/7.


First work out the least common denominator - the lowest number into which the denominators of both fractions will divide exactly. 14 and 7 both divide into 14.


You can leave 3/14 alone as it already contains the denominator 14, but you'll need to express 2/7 as an equivalent fraction with denominator 14. To get from denominator 7 to denominator 14, times by 2 - also multiply the numerator 2 by the same factor



2/7 = 4/14.


You can now compare 3/14 and 4/14 - fractions with the same denominator (14). As 3/14's numerator (3) is lower than 4/14's numerator (4)


3/14     <     4/14


or since 2/7 = 14/4

3/14     <     2/7


- three fourteenths is less than two sevenths.


Another example


Take a look at how the answer to 'Compare 2/3 and 6/7' might be set out in an exam. Notice here how both fractions need to be converted to equivalent fractions.



Ready to move on?


Hopefully you now have a basic grasp of how to compare fractions. It's time to move onto ordering fractions!


For more on fractions click:

Math fractions

Equivalent fractions

Simplifying fractions

Adding fractions

How to subtract fractions

Multiplying fractions

How to divide fractions

Improper fractions

Mixed fractions (mixed numbers)

Ordering fractions

Fraction to decimal

Fraction to decimal chart

Decimal to fraction

Fraction to percent

Percent to fraction


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