Fraction Calculator

📚 Full Explanation

Fraction Calculator (Add, Subtract, Multiply, Divide + Simplify)

Fractions show parts of a whole. They’re everywhere: recipes (¾ cup), construction (5⅛ inches), school math, discounts, probability, and even finance (fractional shares). But doing fraction math by hand can get messy—especially when denominators don’t match or you need to simplify the final answer. This Fraction Calculator helps you do the four core operations—add, subtract, multiply, divide— and instantly returns the result as a simplified fraction, plus optional mixed number and decimal forms.

What you can do here

Add: 1/4 + 2/3
Subtract: 7/8 − 1/6
Multiply: 3/5 × 10/9
Divide: 5/12 ÷ 7/8
Simplify: reduce results using GCF (greatest common factor)
Convert: show decimal and mixed number (when possible)
Steps: display a clear “how we got it” explanation you can screenshot

Fraction Basics (Quick Refresher)

A fraction has a numerator (top) and a denominator (bottom):

Numerator = how many parts you have
Denominator = how many equal parts make the whole

Example: 3/8 means you have 3 parts out of 8 equal parts in the whole.

Proper vs improper vs mixed numbers

Proper fraction: numerator < denominator (e.g., 5/7)
Improper fraction: numerator ≥ denominator (e.g., 9/4)
Mixed number: whole + fraction (e.g., 2 1/4)

How Fraction Addition Works

To add fractions, you need a common denominator (the same bottom number). If the denominators already match, you simply add the numerators:

a/b + c/b = (a + c)/b

If denominators are different, convert both fractions to an equivalent form with a shared denominator. A safe (not always smallest) approach is using the product of denominators:

a/b + c/d = (a·d + c·b)/(b·d)

Example: 1/4 + 2/3

Common denominator via product: 4×3 = 12
Convert: 1/4 = 3/12, 2/3 = 8/12
Add: 3/12 + 8/12 = 11/12

Then simplify if needed (11/12 is already simplified).

How Fraction Subtraction Works

Subtraction is identical to addition, but you subtract numerators after matching denominators:

a/b − c/d = (a·d − c·b)/(b·d)

Example: 7/8 − 1/6

Common denominator: 8×6 = 48
Convert: 7/8 = 42/48, 1/6 = 8/48
Subtract: 42/48 − 8/48 = 34/48
Simplify: 34/48 = 17/24

How Fraction Multiplication Works

Multiplying fractions is the easiest: multiply numerators together and denominators together.

(a/b) × (c/d) = (a·c)/(b·d)

You can often simplify before multiplying by canceling common factors (called cross-canceling), which keeps numbers smaller.

Example: 3/5 × 10/9

Cross-cancel: 10 with 5 → 10/5 = 2, so 10 becomes 2 and 5 becomes 1
Cross-cancel: 3 with 9 → 3/9 = 1/3, so 3 becomes 1 and 9 becomes 3
Now multiply: (1×2)/(1×3) = 2/3

How Fraction Division Works

To divide by a fraction, multiply by its reciprocal (flip it):

(a/b) ÷ (c/d) = (a/b) × (d/c) = (a·d)/(b·c)

Example: 5/12 ÷ 7/8

Flip the second fraction: 7/8 → 8/7
Multiply: 5/12 × 8/7 = (5×8)/(12×7) = 40/84
Simplify: 40/84 = 10/21

Simplifying Fractions (Reducing)

A fraction is simplified when the numerator and denominator share no common factor greater than 1. To reduce a fraction, divide the numerator and denominator by their GCF (greatest common factor).

Example: simplify 34/48

GCF(34, 48) = 2
34 ÷ 2 = 17, 48 ÷ 2 = 24
Result: 17/24

Converting Results: Mixed Number + Decimal

If the numerator is larger than the denominator, your result is an improper fraction. You can convert it to a mixed number:

Whole part = integer division of numerator ÷ denominator
Remainder becomes the new numerator over the same denominator

Example: 17/6

17 ÷ 6 = 2 remainder 5
Mixed number = 2 5/6

For a decimal: compute numerator ÷ denominator. Some fractions terminate (like 1/4 = 0.25), others repeat (like 1/3 = 0.333…).

How This Calculator Works (Under the Hood)

This calculator follows standard fraction rules with a few “quality of life” steps:

Parsing: It reads each input as numerator/denominator, and rejects invalid formats.
Normalization: If you enter a negative denominator, it moves the negative sign to the numerator.
Operation: It applies the correct formula depending on add/subtract/multiply/divide.
Reduction: It computes the GCF using the Euclidean algorithm, then reduces the fraction.
Conversion: It displays mixed number (when improper) and a rounded decimal for convenience.

Everything runs locally in your browser—fast, private, and easy to share via screenshot.

Worked Examples (Copy/Paste Friendly)

These examples match the exact logic used by the calculator. Try them to confirm your answers:

2/9 + 5/6 = (2×6 + 5×9)/(9×6) = (12 + 45)/54 = 57/54 = 19/18 = 1 1/18
3/10 − 7/20 = (3×20 − 7×10)/(10×20) = (60 − 70)/200 = −10/200 = −1/20
4/15 × 9/8 → cross-cancel 4 with 8 → 1/2, cancel 9 with 15 → 3/5 → (1×3)/(2×5) = 3/10
5/16 ÷ 3/8 = 5/16 × 8/3 → cancel 8 with 16 → 1/2 → 5/(2×3) = 5/6

Common Mistakes (And How to Avoid Them)

Adding denominators: 1/4 + 1/4 = 2/4 (not 2/8). Denominator stays the same when equal.
Forgetting the reciprocal: Division requires flipping the second fraction.
Not simplifying: 6/12 should be reduced to 1/2 for clean answers.
Sign confusion: A negative can live in the numerator: −1/4, or out front: −(1/4).

FAQs

Is this fraction calculator accurate for negative fractions?
Yes. Enter negative numerators like −3/8. If you enter a negative denominator, the calculator normalizes it so the negative sign sits in the numerator.
What if my denominator is 0?
A denominator of 0 is undefined in math. The calculator will show an error and ask you to fix the input.
Does this calculator always use the least common denominator (LCD)?
Internally it uses a safe common-denominator approach and then simplifies. The final simplified result matches what you’d get using LCD.
Why does my decimal repeat?
Some fractions don’t terminate in base-10 (like 1/3). The calculator shows a rounded decimal so it’s still useful for everyday calculations.
Can I use this for recipes and measurements?
Absolutely—add ingredient amounts, scale portions, and switch to decimals when a recipe wants numbers like 0.75.
How do I share my result?
After calculating, use the copy/share buttons to copy a clean text version. It’s perfect for texting, emailing, or adding to homework notes.

Pro Tips for Virality (Make People Share)

Screenshot-friendly: the result box includes steps—great for tutoring, homework checks, and class group chats.
Challenge a friend: “Solve 7/8 − 1/6 without a calculator” → then verify here.
Recipe scaling: show a “double the recipe” before/after using fractions.
Quick conversions: use the decimal view for shopping, carpentry, and spreadsheets.

Enter two fractions