Fraction Calculator

✓ Free online calculator · No signup · Instant results

Add, subtract, multiply, and divide fractions with step-by-step results. Work with percentages using our Percentage Calculator, or calculate time fractions with the Time Calculator.

Enter two fractions and choose an operation to add, subtract, multiply, or divide them—result shown as a simplified fraction and decimal.

Simplify a Fraction

Convert Decimal to Fraction

Step-by-Step Examples

Addition: 1/2 + 1/3

  1. Step 1 — Find LCD: LCD(2, 3) = 6
  2. Step 2 — Convert: 1/2 = 3/6  |  1/3 = 2/6
  3. Step 3 — Add numerators: 3/6 + 2/6 = 5/6 ≈ 0.833

Subtraction: 3/4 − 1/6

  1. Step 1 — Find LCD: LCD(4, 6) = 12
  2. Step 2 — Convert: 3/4 = 9/12  |  1/6 = 2/12
  3. Step 3 — Subtract: 9/12 − 2/12 = 7/12 ≈ 0.583

Multiplication: 2/3 × 3/4

  1. Step 1 — Multiply numerators: 2 × 3 = 6
  2. Step 2 — Multiply denominators: 3 × 4 = 12
  3. Step 3 — Simplify: 6/12 = 1/2

Division: 2/3 ÷ 1/2

  1. Step 1 — Flip second fraction: 1/2 → 2/1
  2. Step 2 — Multiply: 2/3 × 2/1 = 4/3
  3. Step 3 — Mixed number: 4/3 = 1 and 1/3

Formulas & Calculations

  • Addition/Subtraction: Find common denominator, then add/subtract numerators
  • Multiplication: Multiply numerators, multiply denominators
  • Division: Multiply by the reciprocal of the second fraction
  • Simplification: Divide both parts by their greatest common divisor (GCD)

Real-World Uses of Fractions

Area Example
Cooking & Recipes½ cup flour, ¾ teaspoon salt, ⅓ tablespoon oil
Construction3/8 inch pipe, ¼ inch plywood, 5/16 inch drill bit
Finance1/3 of budget for rent, 2/5 of portfolio in shares
Time¾ hour = 45 min, ½ hour = 30 min, ⅓ hour = 20 min
Sports2/3 of the race completed, 3/4 of the season remaining

FAQ

How do I add fractions with different denominators?
Find the least common denominator (LCD), convert each fraction to have that denominator, then add the numerators. Example: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
How do I subtract fractions step by step?
Find the LCD, convert both fractions to that denominator, then subtract the numerators. Keep the denominator the same. Example: 3/4 − 1/6 → LCD = 12 → 9/12 − 2/12 = 7/12.
How do I multiply two fractions?
Multiply the numerators together and the denominators together, then simplify. Example: 2/3 × 3/4 = 6/12 = 1/2.
How do I divide fractions (flip and multiply)?
Flip the second fraction to get its reciprocal, then multiply. Example: 2/3 ÷ 1/2 = 2/3 × 2/1 = 4/3.
What is the least common denominator (LCD)?
The LCD is the smallest number that is a multiple of both denominators. For 1/4 and 1/6, the LCD is 12, because 12 is the smallest number divisible by both 4 and 6.
How do I simplify a fraction to its lowest terms?
Divide both the numerator and denominator by their greatest common divisor (GCD). Example: 6/8 → GCD(6,8) = 2 → 6/2 = 3, 8/2 = 4 → 3/4.
What is a mixed number and how do I convert to an improper fraction?
A mixed number has a whole part and a fraction, e.g. 1 and 1/2. To convert: multiply the whole number by the denominator, add the numerator. 1½ = (1×2 + 1)/2 = 3/2.
How do I convert a decimal to a fraction?
Write the decimal as a fraction with a power of 10 in the denominator, then simplify. Example: 0.75 = 75/100 = 3/4. Use the Decimal to Fraction calculator above for instant results.
How do I convert a fraction to a percentage?
Divide the numerator by the denominator, then multiply by 100. Example: 3/4 = 0.75 × 100 = 75%. Or use our Percentage Calculator for more options.
What is the difference between a proper and improper fraction?
A proper fraction has a numerator smaller than the denominator (e.g. 3/4). An improper fraction has a numerator equal to or greater than the denominator (e.g. 5/3), which equals a mixed number (1 and 2/3).
How do I add a whole number and a fraction?
Convert the whole number to a fraction with the same denominator, then add. Example: 2 + 3/4 = 8/4 + 3/4 = 11/4 = 2¾.
How do I compare two fractions (which is bigger)?
Convert both fractions to the same denominator, then compare numerators. Example: 2/3 vs 3/5 → 10/15 vs 9/15 → 2/3 is larger.
Why do I need to find a common denominator to add fractions?
Fractions can only be added when they represent equal-sized parts. Finding a common denominator ensures both fractions are divided into the same number of parts before adding.
How do fractions apply to cooking and recipe scaling?
Recipes often use fractions: ½ cup, ¾ teaspoon, ⅓ tablespoon. To double or halve a recipe, multiply or divide all fractions accordingly. Example: ¾ cup × 2 = 3/2 cup = 1½ cups.
How do I calculate 3/4 of a number?
Multiply the number by 3, then divide by 4. Example: 3/4 of 200 = (200 × 3) / 4 = 600 / 4 = 150. Or use the fraction calculator: enter 3/4 × 200/1.

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