Fraction Calculator
Add, subtract, multiply, and divide fractions, mixed numbers, whole numbers, and decimals. This calculator also helps you simplify fractions, find LCD / LCM, compare fractions, and convert values into decimals or percentages with step-by-step work.
Background
Fractions show parts of a whole, but they also appear in algebra, ratios, recipes, probability, and measurement. Students often need more than just one answer — they need the simplified fraction, mixed-number form, decimal form, the visual size of the fraction, and the steps that explain how the result was found.
How to use this calculator
- Choose a mode: operations, simplify / convert, compare, fraction to decimal / percent, or LCD / LCM helper.
- Type values directly as fractions, mixed numbers, whole numbers, or decimals.
- Examples: 3/4, 1 3/4, -1 3/4, 7, or 0.125.
- A negative mixed number such as -1 3/4 means the whole value is negative, not just the fraction part.
- Turn on Show unsimplified intermediate form first if you want to see results like 10/8 before 5/4.
How this calculator works
- Whole numbers and decimals are converted into fraction form automatically.
- Mixed numbers are converted into improper fractions.
- Fractions are simplified by dividing numerator and denominator by their greatest common divisor (GCD).
- Addition and subtraction use a least common denominator (LCD).
- Multiplication multiplies numerators together and denominators together.
- Division multiplies by the reciprocal of the second fraction.
Formula & Equations Used
Mixed to improper: a b/c = (ac + b) / c
Add: a/b + c/d = (ad + bc) / bd
Subtract: a/b − c/d = (ad − bc) / bd
Multiply: a/b × c/d = ac / bd
Divide: a/b ÷ c/d = a/b × d/c
LCD / LCM: LCM(a,b) = |ab| / GCD(a,b)
Decimal: decimal = numerator / denominator
Percent: percent = decimal × 100
Example Problem & Step-by-Step Solution
Example 1 — Add 1/2 and 3/4
- Find a common denominator: LCD(2,4)=4 or use eighths if teaching equivalent fractions more explicitly.
- Rewrite the fractions so they refer to equal-sized parts.
- Add numerators and keep the denominator.
- Simplify the result.
Example 2 — Convert 0.125 to a fraction
- Read 0.125 as 125/1000.
- Find the GCD of 125 and 1000.
- Simplify to 1/8.
Example 3 — Compare 2/3 and 3/5
- Cross multiply: 2 × 5 = 10 and 3 × 3 = 9.
- Since 10 > 9, 2/3 > 3/5.
Frequently Asked Questions
Q: Can I type decimals into this fraction calculator?
Yes. You can enter decimals like 0.125, and the calculator will convert them into fraction form automatically.
Q: Can I enter negative mixed numbers?
Yes. A value like -1 3/4 is treated as a negative mixed number, meaning the whole quantity is negative.
Q: What does the recognition badge mean?
It shows how the calculator interpreted your input, such as fraction, mixed number, whole number, or decimal.
Q: Why show an unsimplified intermediate result?
Many students and teachers want to see the raw result first, such as 10/8, before seeing the simplified result 5/4.
Q: Does the visual bar show a different value on each side?
No. It shows the same value in two forms: fraction on the left and decimal on the right.
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