Adding or Subtracting 2 Fractions Calculator for Like or Unlike Denominators

This calculator will add one fraction to another, or subtract one fraction from another -- regardless of whether or not the two fractions have the same or different denominators -- and give the result in simplest form.

Plus, unlike other online fraction calculators, this calculator will show its work and give a detailed step-by-step explanation as to how it arrived at the answer.

Also, be sure to check out my other online math calculators for help with fractions:

Add or Subtract 2 Fractions Calculator

Add or subtract 2 fractions with like or unlike denominators.

Special Instructions

Selected Data Record:

A Data Record is a set of calculator entries that are stored in your web browser's Local Storage. If a Data Record is currently selected in the "Data" tab, this line will list the name you gave to that data record. If no data record is selected, or you have no entries stored for this calculator, the line will display "None".

DataData recordData recordSelected data record: None
Augend/Minuend

Augend/Minuend:

Enter the numerator and denominator for the Augend (addition) or Minuend (subtraction) for the first fraction in the equation. If you would like the fraction to be a whole number, simply enter the desired whole number in the numerator field and enter a 1 in the denominator field (4/1 = 4).

Numerator:Numerator:Numerator:Numerator:
 # Fraction #1 numerator
Denominator:Denominator:Denominator:Denominator:
 # Fraction #1 denominator

Enter the numerator and denominator for the Addend (addition) or Subtrahend (subtraction) for the second fraction in the equation. If you would like the fraction to be a whole number, simply enter the desired whole number in the numerator field and enter a 1 in the denominator field (4/1 = 4).

Numerator:Numerator:Numerator:Numerator:
 # Fraction #2 numerator
Denominator:Denominator:Denominator:Denominator:
 # Fraction #2 denominator

Result:

This is the result of the addition or subtraction of the two fractions. After calculating the addition or subtraction, the calculator will show its work and give a detailed explanation of each step it took to arrive at this answer.

If you would like to save the current entries to the secure online database, tap or click on the Data tab, select "New Data Record", give the data record a name, then tap or click the Save button. To save changes to previously saved entries, simply tap the Save button. Please select and "Clear" any data records you no longer need.

Learn

How to add and subtract fractions.

The answer to that question depends on whether you are adding fractions with like denominators or adding fractions with unlike denominators.

Adding fractions with like denominators is easy. All you do is add the numerators together and keep the denominator the same, like this:

 Adding with Like Denominators 1 + 2 = 3 5 5 5

Adding fractions with unlike denominators requires a little more work (unless you use the calculator on this page), because in order to add the fractions you must first turn their unlike denominators into like denominators. You do that by finding the lowest common multiple (LCM) of the denominators.

To illustrate how you use LCM to turn unlike denominators into like denominators, let's suppose you want to add the fraction 1/3 to the fraction 2/5.

The first step is to find the lowest number that both 3 and 5 will divide into evenly (the LCM). According to my calculations, the LCM of the two denominators (3 & 5) is 15.

Once we have found the LCM for the two denominators, the next step is to multiply the top and bottom of each fraction by the number of times each fraction's denominator goes into the LCM.

Since 3 goes into 15 a total of 5 times, you would multiply the top and bottom of 1/3 by 5, which results in 5/15.

Next, since 5 goes into 15 a total of 3 times, you would multiply the top and bottom of 2/5 by 3, which results in 6/15.

Finally, since both denominators are now the same, you simply add the numerators (5 + 6) while keeping the denominator (15) the same -- giving you a result of 11/15. Here is how our example of adding fractions with unlike denominators might appear on paper:

 Adding with Unlike Denominators 1x 5 + 2x 3 = 5 + 6 = 11 3x 5 5x 3 15 15 15

What About the Steps to Subtract Fractions?

The steps to subtract fractions are the same as the steps to add fractions.

If you are subtracting fractions with like denominators, you simply subtract the second numerator from the first numerator and keep the denominator the same.

 Subtracting with Like Denominators 2 - 1 = 1 5 5 5

If you are subtracting fractions with unlike denominators, you go through the same process as when adding fractions with unlike denominators.

 Subtracting with Unlike Denominators 2x 5 - 1x 3 = 10 - 3 = 7 3x 5 5x 3 15 15 15

So for like denominators you simply add or subtract the numerators, and for unlike denominators you multiply the top and bottom by the least common multiple of each denominator, and then add or subtract the numerators.

Move the slider to left and right to adjust the calculator width. Note that the Help and Tools panel will be hidden when the calculator is too wide to fit both on the screen. Moving the slider to the left will bring the instructions and tools panel back into view.

Also note that some calculators will reformat to accommodate the screen size as you make the calculator wider or narrower. If the calculator is narrow, columns of entry rows will be converted to a vertical entry form, whereas a wider calculator will display columns of entry rows, and the entry fields will be smaller in size ... since they will not need to be "thumb friendly".

Select Show or Hide to show or hide the popup keypad icons located next to numeric entry fields. These are generally only needed for mobile devices that don't have decimal points in their numeric keypads. So if you are on a desktop, you may find the calculator to be more user-friendly and less cluttered without them.

Stick/Unstick Tools:

Select Stick or Unstick to stick or unstick the help and tools panel. Selecting "Stick" will keep the panel in view while scrolling the calculator vertically. If you find that annoying, select "Unstick" to keep the panel in a stationary position.

If the tools panel becomes "Unstuck" on its own, try clicking "Unstick" and then "Stick" to re-stick the panel.