How to subtract fractions


Before learning about how to subtract fractions, please read the primer on fractions.


You can approach subtracting fractions in a similar way to adding fractions i.e. the technique you use depends on whether you're dealing with fractions with like (the same) denominators or unlike (different) denominators.


Just remember you'll be taking away rather than adding!


Subtracting fractions with like denominators


Remember - do nothing to the denominators, subtract the numerators, simplify if you can


For starters consider

3/4  -  1/4


Leaving the denominators alone and subtracting the numerators, you can write

3/4  -  1/4  =  2/4


Now simplify to the equivalent fraction 1/2 by dividing numerator and denominator by 2



Altogether

3/4  -  1/4  =  2/4  =  1/2


Three quarters minus a quarter equals a half.


Another example


8/9  -  6/9


Don't do anything to the denominators. Take numerator 6 from 8

8/9  -  6/9  =  2/9


Eight ninths minus six ninths equals two ninths.


Something a little different


Let's think about

1/8  -  6/8


Leave the denominators alone, subtract the numerators

1/8  -  6/8  =  -5/8


One eighth minus six eighths equals negative five eighths.

 

Subtracting fractions with unlike denominators


Remember - express as fractions with like denominators by working out the least common denominator, then apply the rules for subtracting fractions with like denominators


Begin by looking at this example of how to subtract fractions with different denominators

1/5  -  1/10


What's the lowest number into which both 5 and 10 will divide? The answer's 10 - the least common denominator.


Don't change 1/10 - its denominator's already 10.


But you need to express 1/5 as a fraction with denominator 10. To get from denominator 5 to denominator 10, times by 2. Also multiply the numerator 1 by the same factor 2

 


So

1/5  -  1/10  =  2/10  -  1/10


Now you have fractions with like denominators. Leaving the denominators alone and subtracting the numerators

2/10  -  1/10  =  1/10


Therefore

1/5  -  1/10  =  2/10  -  1/10  =  1/10


One fifth minus one tenth is equal to one tenth.


One more - how to subtract fractions 1/16 and 1/8 from 2/16


2/16  -  1/16  -  1/8


First ask yourself what's the lowest number into which 16, 16 and 8 will divide? The answer is 16.


The fractions 2/16 and 1/16 can be left alone - they already contain the denominator 16.


How can you express 1/8 as a fraction containing the denominator 16? To get from denominator 8 to denominator 16, multiply by 2. Times the numerator by the same factor 2

 


You can then write

2/16  -  1/16  -  1/8  =  2/16  -  1/16  -  2/16


Notice how you're now dealing with fractions with like denominators - do nothing to the denominators, subtract the numerators

2/16  -  1/16  -  2/16  =  -1/16


So

2/16  -  1/16  -  1/8  =  2/16  -  1/16  -  2/16  =  -1/16


Two sixteenths minus one sixteenth minus one eighth equals negative one sixteenth.


Have a go yourself!


Remember the methods used for adding and subtracting fractions are similar.


Think about some different fractions and practice taking them away from each other. You can then face problems involving how to subtract fractions with confidence!


For more on fractions click:

Math fractions

Equivalent fractions

Simplifying fractions

Adding fractions

Multiplying fractions

How to divide fractions

Improper fractions

Mixed fractions (mixed numbers)

Comparing fractions

Ordering fractions

Fraction to decimal

Fraction to decimal chart

Decimal to fraction

Fraction to percent

Percent to fraction


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