How to Subtract Fractions

By: Jesslyn Shields & Austin Henderson  | 
Learning how to subtract fractions is easier than math students might expect it to be. outline2design

Anyone can learn how to subtract fractions. It's about as simple as multiplying fractions, but the process of subtraction is different depending on whether the two fractions' denominators, or bottom numbers, are the same.


Subtracting Fractions With the Same Denominator

When subtracting numbers with a like denominator (meaning the same number is on the bottom of both fractions) the calculation is easy. You just subtract the numerators, or top numbers, from each other and keep the two denominators the same. Here's an example:

3/4 – 1/4 = 2/4

When the numerator and denominator share a common factor, simplify the fraction by finding the common factor and divide both by it. In the case of 2/4, the common factor is 2, and the simplified version of 2/4 is 1/2.


Note that 2/4 and 1/2 represent exactly the same quantity.


Subtracting Fractions With Unlike Denominators

Step 1: Find the Least Common Denominator

When subtracting fractions with different denominators, the first task is to find a common denominator. Look at the two unlike denominators and find a number that is a multiple of both, meaning it's a number that can divide by each of the denominators evenly.

Suppose we're subtracting fraction B (2/5) from fraction A (3/4):


3/4 – 2/5 = ?

The denominator of fraction A is 4 and that of fraction B is 5, and we know the lowest common multiple of 4 and 5 is 20. It's OK in the process of subtraction to use another common multiple such as 40, but it's customary to use the least common denominator (LCD), which is the smallest number that works for both denominators.

Note: You'll sometimes encounter a mixed number (also called a mixed fraction), which is the combination of a whole number and a proper fraction. When subtracting mixed fractions, such as 2 1/2 – 1 3/4, you'll need to convert the values into improper fractions before finding the least common denominator. In this example, 2 1/2 would become 5/2, and 1 3/4 would become 7/4.

Step 2: Convert Both Fractions

In an arithmetic expression, you can multiply any fraction by 1; that's always legal.

So, for each fraction, you want to find out what you could multiply the denominator by in order to get the least common denominator when subtracting fractions. This figure will always have the same denominator as the other fraction.

Since fraction A has 4 as the denominator, you'd have to multiply by 5 — but you can't just multiply the denominator by 5. Instead you multiply the entire fraction by 5/5, which is equal to 1, and therefore fair game. You'd multiply fraction B by 4/4.

Here is what it looks like to convert the two unlike fractions to ones with common denominators:

3/4 – 2/5 = [(5/5) x (3/4)] – [(4/4) x (2/5)]
[(5/5) x (3/4)] – [(4/4) x (2/5)] = 15/20 – 8/20

Step 3: Subtract the Two Numerators

Now you're ready to subtract the numerators.

15/20 – 8/20 = 7/20

No simplification is necessary in this problem because there's no common factor of 7 and 20.


Common Mistakes to Avoid When Subtracting Fractions

Subtracting fractions can be straightforward, but even small slip-ups can lead to incorrect answers. Here are some common errors to watch out for.

Overlooking the Common Denominator

One of the most frequent mistakes is subtracting fractions with unlike denominators without first finding the LCD. Always remember, fractions must share a common denominator to be subtracted. For instance, 2/3 − 4/5​ requires an LCD of 15.


Confusing Numerators with Denominators

After aligning denominators, keep track of which numbers are the numerators (top) and which are the denominators (bottom). Mixing these up can lead to incorrect subtraction and an erroneous result.

Improper Handling of Mixed Numbers

Subtracting mixed numbers without first converting them to improper fractions is a recipe for error. For example, 2 1/2 − 1 3/4 should be converted to 5/2 − 7/4, with an LCD found thereafter.

Simplifying Fractions Prematurely

Avoid the temptation to simplify any fractions before you've performed the subtraction. Simplify only the final answer to ensure you haven't missed any common factors.

This article was updated in conjunction with AI technology, then fact-checked and edited by a HowStuffWorks editor.


Frequently Answered Questions

Can you subtract two fractions?
Yes. To subtract two fractions, find a common denominator between the two fractions and subtract the numerators.
Can I subtract fractions with different denominators directly?
No, you cannot subtract fractions with different denominators directly. First, you need to find the least common multiple (LCM) of the denominators to make them the same. This common denominator allows you to subtract the numerators properly.
How do I subtract mixed numbers?
To subtract mixed numbers, you first convert them into improper fractions. This involves multiplying the whole number by the denominator and adding the numerator to the result. Once both mixed numbers are converted, proceed with the subtraction as you would with regular fractions.
Is there a quick way to subtract fractions with the same denominator?
When subtracting fractions with the same denominator, you simply subtract the numerators and keep the denominator unchanged. Then, simplify the resulting fraction if possible.
What should I do if I get an improper fraction as a result?
If your subtraction results in an improper fraction (where the numerator is larger than the denominator), you may convert it into a mixed number for a clearer representation or simply it as an improper fraction.
How do I simplify a fraction after subtracting?
To simplify a fraction, find the greatest common divisor (GCD) of both the numerator and the denominator and divide both by this number. If there is no GCD other than 1, the fraction is already in its simplest form.