Subtracting Fractions Calculator

Omni's subtracting fractions calculator is the tool you need whenever you stumble upon some fractions (whatever their form) that require subtracting. No matter if it's a math assignment or some real-life everyday problems, our tool solves it all immediately and displays a step-by-step solution to the problem, in case you need to know all the calculations it performed along the way.

Never again will you struggle while subtracting fractions with unlike denominators. We'll also explain how to subtract mixed fractions, a.k.a fractions with whole numbers. Let's go!

Subtracting fractions works very similar to adding fractions (if you're not yet familiar with it, we highly recommend you visit our adding fractions calculator). In fact, to subtract a fraction, you simply need to add the negative version of that fraction. This recipe is very simple, very true, and very... impractical. So, let's discuss how fraction subtraction works in practice with the help of an example.

Let's compute ⁶/₈ − ¹/₄.

• Simplify the fractions. While ¹/₄ is already in its simplest form, we can transform ⁶/₈ to ³/₄. To get this result, we divided both the numerator (6) and the denominator (8) by 2, which is their greatest common divisor: GCD(6, 8) = 2. See the greatest common divisor calculator for more details.

• We have ³/₄ − ¹/₄. Do you see what happened? Now both fractions have the same denominator!

• The result will be a fraction with the same denominator (that is, 4) as well.

• The numerator of the result is the difference of the numerators: 3 − 1 = 2.

• So the long-awaited result of our fraction subtraction is ³/₄ − ¹/₄ = ²/₄.

• We're almost done! Almost, because it is always nice to give your result in its simplest form: ²/₄ = ¹/₂.

You may feel this example was so easy because the simplification of ⁶/₈ gave us a fraction with the same denominator as the other fraction. What if this weren't the case? Let's discuss subtracting fractions with unlike denominators!

To subtract fractions with unlike denominators, use the trick called common denominators.

1. Simplify each fraction: divide the numerator and denominator by their greatest common factor.

2. Find the least common denominator by determining the least common multiple (LCM) of the two denominators. This is the denominator of the result.

3. Expand each fraction: multiply its numerator and denominator to get the LCM as the new denominator.

4. The numerator of the result is the difference between the new numerators.

If you have not yet heard about LCMs and common denominators, you may benefit from visiting the least common multiple calculator and the least common denominator calculator.

Let's look at an example to see this procedure in action.

Example

We'll calculate ²/₄ − ¹/₃.

1. We simplify ²/₄ to ¹/₂.

2. We calculate LCM(2,3) = 6. So the denominator of the result will be equal to 6.

3. We expand the two fractions to get 6 as their new denominators:

   • First one is ¹/₂ = ³/₆.

   • And then ¹/₃ = ²/₆.

4. We compute the difference of the new numerators: 3 − 2 = 1. So the numerator of our result is 1. The result in all of its glory is ¹/₆. It cannot be simplified any further, so we're done.

We hope that you will never again have to wonder how to subtract fractions with different denominators!

But what if there is no denominator? 😱 Let's discuss how to perform subtractions between fractions and whole numbers!

To subtract a fraction from a whole number:

1. The fraction's denominator is the common denominator in our subtraction.

2. Write the whole number as a fraction: it has the same denominator as our fraction, and its numerator is the original whole number times our fraction's numerator.

3. Subtract the numerators of our two fractions.

4. The result is a fraction with the numerator from Step 3 and the denominator from Step 1.

Not hard, right? But... what if I have to do it the other way round, you wonder? In other words, the question now is:

How do I subtract a whole number from a fraction?

Use the properties of subtraction!

Recall the formula: x − y = − (y − x).

In our context: ^a / _b - k = − (k − ^a / _b).

This formula says that if you need to subtract the whole number k from the fraction ^a / _b, you might as well subtract ^a / _b from k by following the procedure we described above and then just flip the sign (i.e., go from plus to minus or from minus to plus, depending on what you initially got).

Okay, we're almost done. The last question that may haunt you is how do I subtract fractions with whole numbers?. That is, how does the subtraction of mixed fractions work? Ready?

To subtract mixed fractions:

1. Convert the mixed fractions to improper fractions. To do so, take the mixed fraction w ⁿ/_d and rewrite it as ^(w×d)+n/_d.

2. Find the LCM of the two denominators.

3. Expand each of the two fractions to get the number from Step 2 as its denominator.

4. Subtract the new numerators. This is the numerator of the result.

5. The denominator of the result is the number from Step 2.

6. Simplify the result if necessary.

Omni's subtracting fractions calculator is really straightforward to use! Just input the numbers you need to subtract and enjoy the result appearing immediately.

• Note that you can choose between simple fraction form and mixed fraction form. As you can see, with our subtracting fractions calculator nearby, the question how to subtract mixed fractions gets the answer: just pick the mixed numbers in the menu 🙃

• Tip: To enter a whole number, choose the mixed fraction form mode and leave the numerator and denominator empty.

• As simple as our subtracting fractions calculator is, it is also very powerful. It produces a step-by-step solution to your subtraction problem — it can display all the calculations along with explanations so that you not only know the correct result but also understand how to get it.

The answer is ¹/₈, that is, one eighth. To arrive at this result, it suffices to note that ³/₄ expands to ⁶/₈, which has the same denominator as ⁷/₈. Now it remains to perform the fraction subtraction ⁷/₈ − ⁶/₈ = ¹/₈. Equivalently, we can write down the answer as the decimal 0.125.

The answer is ⁵/₁₂, which we read as five twelfths. To get this answer, we need to first find the common denominator of our two fractions. It is given by the least common multiple of their denominators: LCM(4,3) = 12

Then our subtraction problem reads:

³/₄ − ¹/₃
= ⁹/₁₂ − ⁴/₁₂
= ⁵/₁₂

A decimal approximation of this result is 0.42.