Sum of  
-3/10
and
11/6
in Simplest Form

Given:  
-3/10
+
11/6

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 6 and 10:
LCD = LCM(6, 10) = 30
Express the given fractions as equivalent fractions with respect to the LCD (30):
-3/10
=
-9/30
  and  
11/6
=
55/30
As a result,  
-3/10
+
11/6
=
-9/30
+
55/30

Since the equivalent fractions have common denominators, we can add the numerators:
-9/30
+
55/30
=
-9 + 55/30
=
46/30
However,  
46/30
  is NOT in Simplest Form since the Greatest Common Factor of 30 and 46 does not equal 1, GCF(30, 46) ≠ 1
Upon inspection, the GCF(30, 46) = 2
In Simplest Form,  
46/30
=
46 ÷ 2/30 ÷ 2
=
23/15
 (1 is the only factor common to 23 and 15)
Therefore, the Sum of  
-3/10
and
11/6
is equal to
23/15
in Simplest Form:  
-3/10
+
11/6
=
23/15

Notes:
  • 23/15
    is an improper fraction, and as a mixed number,  
    23/15
    = 1
    8/15
  •  
    -3/10
    +
    11/6
    =
    11/6
    −
    3/10

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

Find the Sum of Fractions in Simplest Form

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