Sum of  
-2/5
and
5/3
in Simplest Form

Given:  
-2/5
+
5/3

Since the denominators are not common (not the same), we need to find the Least Common Denominator (LCD), which is equivalent to the Least Common Multiple of 3 and 5:
LCD = LCM(3, 5) = 15
Express the given fractions as equivalent fractions with respect to the LCD (15):
-2/5
=
-6/15
  and  
5/3
=
25/15
As a result,  
-2/5
+
5/3
=
-6/15
+
25/15

Since the equivalent fractions have common denominators, we can add the numerators:
-6/15
+
25/15
=
-6 + 25/15
=
19/15
19/15
is in Simplest Form since the Greatest Common Factor of 15 and 19 equals 1, GCF(15, 19) = 1
Therefore, the Sum of  
-2/5
and
5/3
is equal to
19/15
in Simplest Form:  
-2/5
+
5/3
=
19/15

Notes:
  • 19/15
    is an improper fraction, and as a mixed number,  
    19/15
    = 1
    4/15
  •  
    -2/5
    +
    5/3
    =
    5/3
    2/5

The solution above and other related solutions were provided by the Sum of Fractions Application.