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Fraction Calculator – Add, Subtract, Multiply & Divide Fractions

Easily add, subtract, multiply, and divide fractions with our free online fraction calculator. Get instant simplified results and step-by-step solutions for all fraction operations.

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Examples:

Understanding Fraction Operations

Fractions represent parts of a whole. When you work with fractions, you're dealing with numbers that have a numerator (top number) showing how many parts you have, and a denominator (bottom number) showing how many parts make up the whole.

Each operation with fractions follows its own logic. Addition and subtraction need common denominators because you can only combine parts of the same size. Multiplication is straightforward – multiply across. Division flips the second fraction and multiplies. Mixed numbers combine whole numbers with fractions, requiring conversion to improper fractions for calculations.

How to Work with Fractions

Adding & Subtracting Fractions

  1. Find a common denominator (LCM of both denominators)
  2. Convert each fraction to equivalent form with common denominator
  3. Add or subtract the numerators, keep the denominator
  4. Simplify the result if possible
1/4 + 1/6 = 3/12 + 2/12 = 5/12

Multiplying Fractions

  1. Multiply the numerators together
  2. Multiply the denominators together
  3. Simplify the resulting fraction
2/3 × 3/4 = 6/12 = 1/2

Dividing Fractions

  1. Keep the first fraction as is
  2. Flip the second fraction (find reciprocal)
  3. Multiply the first by the reciprocal of the second
  4. Simplify the result
3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 3/2 = 1½

Mixed Numbers to Improper

  1. Multiply the whole number by the denominator
  2. Add the numerator to that product
  3. Keep the same denominator
2⅓ = (2×3 + 1)/3 = 7/3

Worked Examples

Example 1: Add 1/3 + 1/4

LCM(3, 4) = 12
1/3 = 4/12
1/4 = 3/12
4/12 + 3/12 = 7/12
Answer: 7/12 (already simplified)

Example 2: Subtract 5/6 - 1/3

LCM(6, 3) = 6
5/6 stays as 5/6
1/3 = 2/6
5/6 - 2/6 = 3/6
Simplify: 3/6 = 1/2
Answer: 1/2

Example 3: Multiply 3/5 × 10/9

Multiply across: (3 × 10) / (5 × 9) = 30/45
Find GCD(30, 45) = 15
30 ÷ 15 = 2
45 ÷ 15 = 3
Answer: 2/3

Example 4: Divide 2½ ÷ 1¼

Convert to improper: 2½ = 5/2, 1¼ = 5/4
5/2 ÷ 5/4 = 5/2 × 4/5
= 20/10 = 2
Answer: 2

Example 5: Add 1⅔ + 2¾

Convert: 1⅔ = 5/3, 2¾ = 11/4
LCM(3, 4) = 12
5/3 = 20/12
11/4 = 33/12
20/12 + 33/12 = 53/12
Convert to mixed: 53/12 = 4⅚
Answer: 4⅚

Quick Fact

The fraction bar (vinculum) we use today was introduced by Arab mathematicians around the 12th century. Before that, fractions were written with the numerator above the denominator but without a line between them. The horizontal fraction bar made mathematical expressions much clearer.

Frequently Asked Questions

How do I enter mixed numbers?

Use the whole number box alongside the fraction boxes. For 2½, enter 2 in the whole box, 1 in the numerator, and 2 in the denominator.

Why do I need a common denominator for addition?

Fractions represent parts of a whole. You can only add parts when they're the same size. 1/2 and 1/3 are different-sized pieces – converting to 3/6 and 2/6 makes them comparable.

What if my denominator is zero?

Division by zero is undefined in mathematics. The calculator won't let you compute with zero denominators.

How do I simplify a fraction?

Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by it. For 12/18, GCD is 6, so 12÷6 = 2 and 18÷6 = 3, giving 2/3.

Can I work with negative fractions?

Yes. Enter a negative whole number or numerator. The calculator handles negative values correctly for all operations.

When should I use improper fractions vs mixed numbers?

Improper fractions are easier for calculations. Mixed numbers are clearer for understanding quantities. Most math classes prefer mixed numbers for final answers, but improper fractions for intermediate steps.

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