How Do You Subtract Fractions with the Same Denominator?
To subtract fractions that share the same denominator, subtract the second numerator from the first and write the difference over the common denominator. The denominator never changes — only the numerators are subtracted. Simplify the resulting fraction to lowest terms by dividing by the greatest common factor.
When two fractions already share the same denominator, subtraction is straightforward. The denominator stays exactly the same — you never subtract the denominators.
Check the Denominators
Confirm both fractions have the same bottom number. If they do, you can subtract immediately.
Subtract the Numerators
Subtract the second numerator from the first. Write this difference over the shared denominator.
Simplify If Possible
Reduce the result to its lowest terms by dividing the numerator and denominator by their greatest common factor (GCF).
Visual Example: 5/8 − 3/8
⚠ Common Mistake
Never subtract the denominators. The denominator tells you the size of each piece — it doesn't change when you subtract. Only the numerators (the count of pieces) change.
How Do You Subtract Fractions with Different Denominators?
To subtract fractions with different denominators, find the least common denominator (LCD), convert each fraction to an equivalent fraction with the LCD, subtract the numerators, keep the LCD as the denominator, and simplify the result. You cannot subtract fractions directly when the denominators differ because the pieces represent different sizes.
You first need to find a common denominator — ideally the least common denominator (LCD) — so both fractions describe equal-sized pieces.
Find the Least Common Denominator (LCD)
The LCD is the smallest number that both denominators divide into evenly. For example, the LCD of 4 and 6 is 12. You can use our LCD Calculator if you need help.
Create Equivalent Fractions
Multiply the numerator and denominator of each fraction by whatever factor makes the denominator equal to the LCD. This changes the form but not the value.
Subtract the Numerators
Now that both fractions share the same denominator, subtract the second numerator from the first. Keep the denominator unchanged.
Simplify the Result
Divide the numerator and denominator by their greatest common factor to reduce the fraction to lowest terms.
Visual Example: 3/4 − 1/6
💡 Quick Shortcut: The Cross-Multiply Method
For any two fractions a/b − c/d, you can use the formula: (a×d − c×b) / (b×d). This always gives a correct common denominator, though the result may need simplifying. For 3/4 − 1/6: (3×6 − 1×4) / (4×6) = (18−4) / 24 = 14/24 = 7/12. ✓
How Do You Subtract Mixed Numbers with Borrowing?
To subtract mixed numbers, subtract the whole numbers and fractions separately. If the fraction being subtracted is larger, borrow 1 from the whole number and convert it to a fraction with the same denominator. Add the borrowed fraction to the existing fraction part, then subtract normally. This process is called borrowing or regrouping.
A mixed number combines a whole number with a fraction, like 3 1/4. Subtracting mixed numbers follows the same principles, but you may encounter a situation where the fraction being subtracted is larger than the fraction you're subtracting from. When that happens, you need to borrow — just like borrowing in whole-number subtraction.
When Borrowing Isn't Needed
If the first fraction part is larger than or equal to the second, simply subtract the whole numbers separately and the fractions separately. For example, 5 3/4 − 2 1/4 = 3 2/4 = 3 1/2.
When Borrowing Is Needed
Consider 4 1/6 − 1 5/6. Here, 1/6 is smaller than 5/6, so you cannot subtract the fraction parts directly. You must borrow 1 from the whole number and convert it into sixths.
Check if Borrowing Is Needed
Compare the fraction parts. If the first fraction is smaller than the second, you need to borrow.
Borrow 1 from the Whole Number
Take 1 away from the whole number and convert it to a fraction with the same denominator. So 1 = 6/6 when the denominator is 6.
Add the Borrowed Fraction
Add the borrowed fraction to the existing fraction part. So 4 1/6 becomes 3 + 1/6 + 6/6 = 3 7/6.
Subtract Normally
Now subtract both the whole numbers and the fractions: 3 7/6 − 1 5/6 = 2 2/6 = 2 1/3.
💡 Alternative Method: Convert to Improper Fractions
If borrowing feels confusing, convert both mixed numbers to improper fractions first. For the example above: 4 1/6 = 25/6 and 1 5/6 = 11/6. Then 25/6 − 11/6 = 14/6 = 7/3 = 2 1/3. Same answer, no borrowing needed.
What If Mixed Numbers Have Different Denominators?
When the fraction parts also have different denominators, handle that first. Find the LCD, convert both fractions to equivalent fractions with the LCD, then check whether borrowing is necessary. For example, to solve 5 1/4 − 2 2/3, first convert to twelfths: 5 3/12 − 2 8/12. Since 3/12 is less than 8/12, borrow 1 from the 5 to get 4 15/12 − 2 8/12 = 2 7/12.
Fraction Subtraction Examples with Solutions
Let's walk through several complete examples covering the different scenarios you'll encounter when subtracting fractions.
The denominators are both 10 — they match, so no conversion is needed.
Subtract the numerators: 7 − 3 = 4. The denominator stays 10.
Simplify: The GCF of 4 and 10 is 2. Divide both by 2.
Multiples of 6: 6, 12, 18 … Multiples of 4: 4, 8, 12 … The LCD is 12.
5/6 × 2/2 = 10/12 and 1/4 × 3/3 = 3/12.
10/12 − 3/12 = 7/12.
7 and 12 share no common factor other than 1, so the answer is already in lowest terms.
Same denominator (5) ✓, but 1/5 < 4/5 — borrowing is needed.
Take 1 from the 6: 6 1/5 becomes 5 + 1/5 + 5/5 = 5 6/5.
Whole numbers: 5 − 3 = 2. Fractions: 6/5 − 4/5 = 2/5.
LCD of 3 and 4 is 12.
1/3 × 4/4 = 4/12 and 3/4 × 3/3 = 9/12. So: 7 4/12 − 4 9/12.
4/12 < 9/12, so borrow 1 from 7: 7 4/12 → 6 16/12.
Whole: 6 − 4 = 2. Fractions: 16/12 − 9/12 = 7/12.
Practice: Subtract These Fractions
Try solving these on your own first, then tap "Show Answer" to check your work. If you get stuck, use our Subtract Fractions Calculator for step-by-step help.
Key Rules for Subtracting Fractions
The three fundamental rules for subtracting fractions are: (1) same denominators — subtract the numerators and keep the denominator, (2) different denominators — find the LCD, convert, then subtract, and (3) mixed numbers — borrow from the whole number when the fraction part is too small. Always simplify the result to lowest terms.
Quick-Reference Rules
Same denominator: Subtract the numerators directly. The denominator stays the same. Example: 7/9 − 2/9 = 5/9.
Different denominators: Find the least common denominator (LCD), convert both fractions to equivalent fractions with the LCD, then subtract the numerators. Example: 3/4 − 1/6 → LCD = 12 → 9/12 − 2/12 = 7/12.
Mixed numbers (borrowing): If the fraction being subtracted is larger, borrow 1 from the whole number and convert it to a fraction with the same denominator. Then subtract whole numbers and fractions separately. Example: 4 1/6 − 1 5/6 → borrow → 3 7/6 − 1 5/6 = 2 1/3.
Always simplify: After subtracting, divide the numerator and denominator by their greatest common factor (GCF) to reduce to lowest terms.
Frequently Asked Questions
Find the least common denominator (LCD) of the two fractions. Convert both fractions to equivalent fractions with that LCD by multiplying each numerator and denominator by the appropriate factor. Then subtract the numerators, keep the LCD as the denominator, and simplify the result if possible.
Borrowing (or regrouping) happens when the fraction you're subtracting is larger than the fraction you're subtracting from. You take 1 from the whole number and convert it into a fraction with the same denominator. For instance, if you need to subtract from fifths, you borrow 1 and write it as 5/5, adding it to the existing fraction part.
Yes. When you subtract a larger fraction from a smaller one, the result is a negative fraction. For example, 1/4 − 3/4 = −2/4, which simplifies to −1/2. Negative fractions follow the same arithmetic rules as positive fractions.
Yes. Just like with addition, fractions must share a common denominator before you can subtract them. The denominator represents the size of each piece, and you can only compare or combine pieces of the same size. If the denominators already match, you can subtract immediately.
The fastest method is to multiply the two denominators together — this always produces a valid common denominator, though not necessarily the smallest one. For the least common denominator (LCD), find the least common multiple of both denominators by listing multiples or using prime factorization. Our LCD Calculator can find it for you instantly.
The process is nearly identical. Both operations require a common denominator. The only difference is the operation on the numerators: you subtract instead of add. If you've mastered adding fractions, you already know most of what you need for subtraction.
The rule for subtracting fractions is: if the denominators are the same, subtract the numerators and keep the denominator. If the denominators are different, first find the least common denominator, convert both fractions to equivalent fractions with that denominator, then subtract the numerators. Always simplify the result to lowest terms.
Step 1: Check if the denominators are the same. Step 2: If not, find the least common denominator (LCD). Step 3: Convert both fractions so they share the LCD. Step 4: Subtract the second numerator from the first. Step 5: Keep the common denominator unchanged. Step 6: Simplify the result if possible.
Yes. To subtract a fraction from a whole number, rewrite the whole number as a fraction with a denominator of 1. For example, 3 − 1/4 becomes 3/1 − 1/4. Find a common denominator (4), convert to 12/4 − 1/4, and subtract to get 11/4, which equals 2 3/4.
Fractions need a common denominator because the denominator defines the size of each piece. You can only subtract pieces of the same size. Subtracting 1/3 from 1/2 directly would be like subtracting apples from oranges — the units don't match. A common denominator converts both fractions into equal-sized pieces so the subtraction is valid.