Question

How do u add and subtract positive and negative fractions?

Answer 1

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
−
25
30
or
−
5
6

Answer 2

So basically, if you know how to add and subtract with negative numbers, it applies the same rules in negative fractions.

Integers:

$4 - (-5) = 4 + 5 = 9$

Fractions:

$\frac{1}{4} - (- \frac{1}{5} ) = \frac{1}{4} + \frac{1}{5} = \frac{5}{20} +\frac{4}{20} = \frac{9}{20}$