Fraction Calculator
Add, subtract, multiply, or divide fractions with step-by-step working.
First fraction
Second fraction
Try an example
Simplified result
1/2 + 1/3 = 5/6
Lowest terms result.
Mixed number
5/6
Useful for improper fractions.
Decimal
0.8333333333
Numerator divided by denominator.
Before simplification
5/6
Raw operation result.
Operation
+
Addition
Step-by-step explanation
- 1.Find a common denominator: 2 × 3 = 6
- 2.Convert fractions: 1/2 = 3/6, 1/3 = 2/6
- 3.Add numerators: 3 + 2 = 5
- 4.Result before simplification: 5/6
- 5.Already in simplest form: 5/6
Fraction Formulas
Addition
a/b + c/d = (ad + bc) / bd
Subtraction
a/b − c/d = (ad − bc) / bd
Multiplication
a/b × c/d = ac / bd
Division
a/b ÷ c/d = a/b × d/c
Simplifying
Divide numerator and denominator by the GCD
Decimal form
Decimal = numerator ÷ denominator
Variable Explanations
Numerator
The top number in a fraction.
Denominator
The bottom number that shows the number of equal parts.
GCD
Greatest common divisor used to simplify fractions.
Reciprocal
A flipped fraction, used when dividing fractions.
Improper fraction
A fraction where the numerator is greater than or equal to the denominator.
Mixed number
A whole number plus a fraction.
How Fraction Operations Work
Add
Use a common denominator, then add numerators.
Subtract
Use a common denominator, then subtract numerators.
Multiply
Multiply numerators and denominators across.
Divide
Flip the second fraction, then multiply.
Worked Examples
Add 1/3 + 1/4
Rule: Use a common denominator
Step: 4/12 + 3/12
Answer: 7/12
The common denominator is 12.
Subtract 3/4 − 1/3
Rule: Use a common denominator
Step: 9/12 − 4/12
Answer: 5/12
Subtract only the converted numerators.
Multiply 2/3 × 3/4
Rule: Multiply across
Step: 6/12
Answer: 1/2
Simplify 6/12 by dividing by 6.
Divide 2/3 ÷ 4/5
Rule: Multiply by the reciprocal
Step: 2/3 × 5/4 = 10/12
Answer: 5/6
Flip the second fraction before multiplying.
Convert 7/4 to a mixed number
Rule: Divide numerator by denominator
Step: 7 ÷ 4 = 1 remainder 3
Answer: 1 3/4
The remainder becomes the new numerator.
Convert 3/8 to a decimal
Rule: Divide numerator by denominator
Step: 3 ÷ 8
Answer: 0.375
Decimals are useful for comparisons.
Common Fraction Mistakes
Understanding Your Result
Simplified fraction
The answer in lowest terms.
Mixed number
A readable form for improper fractions.
Decimal
The numerator divided by the denominator.
Raw result
The fraction before simplification.
Step-by-step work
Shows how the answer was calculated.
Frequently Asked Questions
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