Add or Subtract Three Fractions or Mixed Numbers Having Like or Unlike Denominators

Add or Subtract 3 Fractions Calculator Sign

This calculator will perform any combination of addition and subtraction on three fractions -- regardless if the three 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:

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Add or Subtract 3 Fractions Calculator

Add or subtract 3 fractions with like or unlike denominators.

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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
Fraction #1

Fraction #1:

Enter the numerator and denominator for the first fraction in the equation. If you would like the fraction to be 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:
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Denominator:Denominator:Denominator:Denominator:
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Fraction #2

Fraction #2:

Enter the numerator and denominator for the second fraction in the equation. If you would like the fraction to be 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:
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Denominator:Denominator:Denominator:Denominator:
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Fraction #3

Fraction #3:

Enter the numerator and denominator for the third fraction in the equation. If you would like the fraction to be 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:
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Denominator:Denominator:Denominator:Denominator:
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Result:Result:Result:Result of addition or subtraction:

Result:

This is the result of performing the selected operations on the three 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.

All Step Explanations

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.

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Help and Tools

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How to add and subtract 3 fractions.

How Do You Add 3 Fractions?

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

Adding 3 Fractions with Like Denominators

Adding 3 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+3+5=9 
10101010

Adding 3 Fractions with Unlike Denominators

Adding 3 fractions with unlike denominators requires a little more work (unless you use the calculator on this page), because in order to add the 3 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 fractions 1/2, 2/3, and 3/4.

The first step is to find the lowest number that 2, 3, and 4 will each divide into evenly (the LCM). According to my calculations, the LCM of the three denominators is 12.

Once we have found the LCM for the three 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. Remember, as long as you multiply the top and bottom of a fraction by the same number, the fraction's decimal value does not change, as in 1/2 = 2/4 = 4/8 and so on -- because all of the latter divide out to 0.5.

Since 2 goes into 12 a total of 6 times, you would multiply the top and bottom of 1/2 by 6, which results in 6/12.

Next, since 3 goes into 12 a total of 4 times, you would multiply the top and bottom of 2/3 by 4, which results in 8/12.

Then, since 4 goes into 12 a total of 3 times, you would multiply the top and bottom of 3/4 by 3, which results in 9/12.

Finally, since all three denominators are now the same, you simply add the numerators (6 + 8 + 9) while keeping the denominator (12) the same -- giving you a result of 23/12. But since 23/12 is an improper fraction, you would convert it to the mixed number 1 and 11/12.

Here is how our example of adding 3 fractions with unlike denominators might appear on paper:

Adding 3 Fractions with Unlike Denominators

=1x 6+2x 4+3x 3
2x 63x 44x 3

=6+8+9=23
12121212

=23
12

=111
12

The steps to subtract 3 fractions with like or different denominators are the same as the steps to add fractions; you just subtract the numerators while keeping the denominators the same.

Happy adding and subtracting!

Adjust Calculator Width:

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".

Show/Hide Popup Keypads:

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.