Adding and Subtracting Fractions Calculator

Add & Subtract Fractions
I want fractions
= ?
Answer:
= -
3
10

Solution Work:

Simplifying the use and arrangement of
negative numbers and rewriting our equation

=
1
5
1
16
+
-1
16
3
8
Changing operations to eliminate
negative numerators

=
1
5
1
16
1
16
3
8
With unlike denominators find the
Least Common Denominator (LCD)

LCD = 80

Multiplying numerators and denominators
to get the LCD in all fractions
=
1 × 16
5 × 16
1 × 5
16 × 5
1 × 5
16 × 5
3 × 10
8 × 10
Then rewriting the equation
with the equivalent fractions
=
16
80
5
80
5
80
30
80
With like denominators we can
operate on just the numerators

=
16 5 5 30
80
=
-24
80
Simplifying our Answer
= -
3
10

How to Add Fractions

Adding Fractions with like Denominators

When we have the same denominator in our fractions we need only add the numerators then put the result over the common denominator.  If necessary we can then simplify it to lowest terms or a mixed number.

Adding Fractions with unlike Denominators

When we have unlike denominators, our first step is to find equivalent fractions such that all of the denominators are the same.  We find the Least Common Denominator (LCD) then rewrite all fractions in our equation to equivalent fractions using the LCD as the denominator.  Now that all denominators are alike, we solve the equation of fractions with like denominators.

How to Add and Subtract Fractions

When the Denominators are the Same

When we have like (the same) denominators in our fractions we need only add or subtract the numerators as indicated and then put the result over the common denominator.  If necessary we can then simplify it to lowest terms or a mixed number.

When the Denominators are Different

When we have unlike (different) denominators, our first step is to find equivalent fractions such that all of the denominators are the same.  We find the Least Common Denominator (LCD) then rewrite all fractions in our equation to equivalent fractions using the LCD as the denominator.  Now that all denominators are alike, we add or subtract the fractions in the equation exactly the same way as we did for like denominators. The final result can be simplified to lowest terms or written as a mixed number.

Working With Negative Fractions

When an equation calls for adding a negative fraction, we can rewrite the equation as subtracting a positive fraction. Likewise, if the equation calls for subtracting a negative fraction, this is the same as adding a positive fraction and can be rewritten this way. The calculator will rewrite negative fractions automatically.

Simplifying Operations on Negative Numbers
Original
  Operation Operand Sign
Adding a Positive Number + +
Adding a Negative Number + -
Subtracting a Positive Number +
Subtracting a Negative Number -
Changes to
Operation Operand Sign  
+ + Adding a Positive Number
+ Subtracting a Positive Number
+ Subtracting a Positive Number
+ + Adding a Positive Number

 

For these and some more basic methods of working with fractions see also Help With Fractions.

 

Cite this content, page or calculator as:

Furey, Edward "Adding Fractions Calculator" From http://www.CalculatorSoup.com - Online Calculator Resource.