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Adding and Subtracting Fractions with Negatives
Once you've learned how to add and subtract positive fractions , you can extend the method to include negative fractions.
Note that:
−23 is the same as
−
2
3
is the same as
−2 3 and 2−3
−
2
3
and
2
−
3
−2−3 simplifies to 23
−
2
−
3
simplifies to
2
3
When you are adding or subtracting a negative fraction, you usually want to consider the numerator as negative. The method is just the same, except now you may need to add negative or positive numerators.
Example 1:
Find the sum.
95+(−43)
9
5
+
(
−
4
3
)
The LCM of 5
5
and 3
3
is 15
15
.
To add the fractions with unlike denominators, rename the fractions with a common denominator.
95=9 × 35 × 3=2715−43=−4 × 53 × 5=−2015
9
5
=
9
×
3
5
×
3
=
27
15
−
4
3
=−
4
×
5
3
×
5
=−
20
15
So,
95+(−43)=2715+(−2015)
9
5
+
(
−
4
3
)
=
27
15
+
(
−
20
15
)
Since the denominators are the same, add the numerators.
=27+(−20)15=715 =
27
+
(
−
20
)
15
=
7
15
Example 2:
Find the difference.
−710−215
−
7
10
−
2
15
The LCM of 10
10
and 15
15
is 30
30
.
To subtract the fractions with unlike denominators, rename the fractions with a common denominator.
−710=−710×33=−2130215=215×22=430 −
7
10
=−
7
10
×
3
3
=−
21
30
2
15
=
2
15
×
2
2
=
4
30
So,
−710−215=−2130−430
−
7
10
−
2
15
=
−
21
30
−
4
30
Since the denominators are the same, subtract the numerators.
−2130−430=−21−430
−
21
30
−
4
30
=
−
21
−
4
30
Simplify. We get:
−2530 or −56