Fraction Calculator

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Use our free fraction calculator to add, subtract, multiply, divide, and simplify fractions instantly. Whether you’re a student working on homework or need quick fraction math for everyday tasks, this tool handles all operations with step-by-step clarity.

What is a Fraction?

A fraction represents a part of a whole. It consists of a numerator (the top number) and a denominator (the bottom number), written as numerator/denominator. For example, 1/2 means one part out of two equal parts, and 3/4 means three parts out of four.

Fractions appear everywhere in real life — splitting a pizza into slices, measuring ingredients in a recipe, calculating discounts on a price, or reading measurements on a ruler.

Types of Fractions

  • Proper fractions — the numerator is smaller than the denominator (e.g., 3/4, 1/2). The value is always less than 1.
  • Improper fractions — the numerator is greater than or equal to the denominator (e.g., 7/4, 5/5). The value is 1 or more.
  • Mixed numbers — a whole number combined with a proper fraction (e.g., 1¾, 2½). These can be converted to improper fractions and back.

Fraction Formulas & Rules

Adding Fractions

To add fractions with the same denominator, add the numerators and keep the denominator: a/b + c/b = (a+c)/b. To add fractions with different denominators, find the least common multiple (LCM) of the denominators, convert each fraction, then add.

Subtracting Fractions

Subtracting fractions follows the same rules as addition. For the same denominator: a/b − c/b = (a−c)/b. For different denominators, find the LCM and convert before subtracting.

Multiplying Fractions

To multiply fractions, multiply the numerators together and the denominators together: (a/b) × (c/d) = (a×c) / (b×d). Always simplify the result if possible.

Dividing Fractions

To divide fractions, flip the second fraction (find its reciprocal) and then multiply: (a/b) ÷ (c/d) = (a/b) × (d/c) = (a×d) / (b×c). This is known as the “keep, change, flip” rule.

How to Calculate Fractions (Step-by-Step)

1. Adding Fractions: 1/2 + 1/4

  1. Find the LCM of 2 and 4, which is 4.
  2. Convert 1/2 to an equivalent fraction: 1/2 = 2/4.
  3. Add: 2/4 + 1/4 = 3/4.
  4. Result: 3/4

2. Subtracting Fractions: 3/4 − 1/2

  1. Find the LCM of 4 and 2, which is 4.
  2. Convert 1/2 = 2/4.
  3. Subtract: 3/4 − 2/4 = 1/4.
  4. Result: 1/4

3. Multiplying Fractions: 3/5 × 2/3

  1. Multiply numerators: 3 × 2 = 6.
  2. Multiply denominators: 5 × 3 = 15.
  3. Simplify by GCF (3): 6/15 = 2/5.

4. Dividing Fractions: 4/7 ÷ 2/3

  1. Flip the second fraction: 2/3 becomes 3/2.
  2. Multiply: (4/7) × (3/2) = 12/14.
  3. Simplify: GCF is 2, so 12/14 = 6/7.

Simplifying Fractions

To simplify (reduce) a fraction to its lowest terms, find the Greatest Common Factor (GCF) of the numerator and denominator, then divide both by it.

Example — Simplify 8/12: GCF of 8 and 12 is 4. Divide: 8÷4 = 2, 12÷4 = 3. Result: 2/3.

More simplification examples: 6/9 = 2/3 | 10/15 = 2/3 | 4/8 = 1/2 | 15/25 = 3/5

Fraction to Decimal Conversion

To convert a fraction to a decimal, simply divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75.

  • 1/2 = 1 ÷ 2 = 0.5
  • 3/4 = 3 ÷ 4 = 0.75
  • 1/3 = 1 ÷ 3 = 0.333… (repeating)
  • 2/5 = 2 ÷ 5 = 0.4
  • 7/8 = 7 ÷ 8 = 0.875

Decimal to Fraction Conversion

To convert a decimal to a fraction: write the decimal over 1, multiply by 10 for each decimal place, then simplify. For example, 0.75 → 75/100 → 3/4.

  • 0.5 = 1/2
  • 0.25 = 1/4
  • 0.1 = 1/10
  • 0.6 = 3/5
  • 0.125 = 1/8

Examples

ProblemAnswer
1/2 + 1/43/4
3/4 − 1/21/4
2/3 × 3/52/5
4/7 ÷ 2/36/7
1/3 + 1/61/2
5/8 − 1/43/8
3/4 × 8/92/3
5/6 ÷ 5/122
Simplify 8/122/3
Simplify 15/203/4
Simplify 6/181/3
Convert 0.25 to fraction1/4
Convert 0.75 to fraction3/4
Convert 1/4 to decimal0.25
Convert 3/8 to decimal0.375

FAQs

How do you add fractions with different denominators?

Find the least common denominator (LCD) of the two fractions. Convert each fraction to an equivalent fraction using the LCD, then add the numerators. For example, 1/3 + 1/4: LCD is 12, so 4/12 + 3/12 = 7/12.

How do you simplify fractions?

Find the Greatest Common Factor (GCF) of the numerator and denominator, then divide both by the GCF. For example, 8/12 has a GCF of 4, so 8/12 simplified is 2/3.

What is 1/2 + 1/4?

1/2 + 1/4 = 3/4. Convert 1/2 to 2/4, then add: 2/4 + 1/4 = 3/4.

How do you convert a fraction to a decimal?

Divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75. You can do this on a calculator or by long division.

What is an improper fraction?

An improper fraction has a numerator greater than or equal to its denominator — for example, 7/4 or 9/3. Improper fractions can be converted to mixed numbers (e.g., 7/4 = 1¾).

How do you multiply fractions?

Multiply the numerators together and the denominators together: (a/b) × (c/d) = (a×c)/(b×d). Then simplify. For example, 2/3 × 3/4 = 6/12 = 1/2.

How do you divide fractions?

Keep the first fraction, change ÷ to ×, then flip the second fraction. For example, 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.

What is a mixed number?

A mixed number combines a whole number and a proper fraction, such as 2½ or 1¾. To convert an improper fraction to a mixed number, divide the numerator by the denominator and write the remainder as a fraction.

Why Use This Fraction Calculator?

  • Instant results — get answers to fraction problems in seconds.
  • Step-by-step solutions — learn and verify your work.
  • All operations covered — add, subtract, multiply, divide, and simplify fractions.
  • Perfect for homework — ideal for students from elementary through college math.
  • Real-life ready — useful for cooking, construction, and financial calculations.
  • Mobile-friendly — works seamlessly on phones, tablets, and desktops.

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