Subtracting Proper Fractions

1. The video below explains how to subtract proper fractions.

A proper fraction is a fraction in which the numerator is smaller than the denominator.

2. Monica had   
1
4
of a pie and Sarah had   
3
4
of the pie.
How much more of the pie had Sarah than Monica?

Sarah  =>  
3
4

Monica  =>  
1
4

Sarah  −  Monica  =>  
3
4
 − 
1
4

square metre or square meter
   
3
4
 − 
1
4

3 - 1
4

2
4

2 / 2
4 / 2
(simplify)
1
2

Sarah had
1
2
a pie more than Monica.

3. Elly gives   
1
2
of a pizza to Charlie and   
1
3
of the pizza to Derek.
How much more of the pizza does Elly give to Charlie than Derek?

Charlie  =>  
1
2

Derek  =>  
1
3

Charlie  −  Derek  =>  
1
2
 − 
1
3


square metre or square meter
Both Charlie and Derek had 1 slice each but Charlie's slice was bigger than Derek's slice because Charlie's pizza was cut into 2 while Derek's pizza was cut into 3.

To compare the two slices, first cut both pizzas into equal number of slices.
   
1
2
 − 
1
3

1 x 3
2 x 3
 − 
1 x 2
3 x 2

3
6
 − 
2
6
  (changed the denominator to 6)
1
6


Elly gives
1
6
of a pizza more to Charlie than to Derek.
Since the two fractions,
1
2
and
1
3
are unlike fractions (as the denominators are different), we must first change them to like fractions before we can subtract them (that is, find a common denominator).