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Fraction Calculator

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A fraction represents a part of a whole. The top number (numerator) counts how many parts you have. The bottom number (denominator) tells how many equal parts the whole is divided into.

This free fraction calculator handles addition, subtraction, multiplication, and division of fractions. It works with proper fractions, improper fractions, mixed numbers, and negative fractions. Every result includes step-by-step work so you can follow the math or check homework.

Enter your fractions, pick an operation, and the calculator simplifies the answer automatically.

How to Use the Fraction Calculator

  1. Enter the numerator and denominator of your first fraction.
  2. Choose an operation: add, subtract, multiply, or divide.
  3. Enter the second fraction.
  4. Click Calculate.

The calculator shows your result in simplified form. It also displays each step so you can see how it found the answer.

What if I have a mixed number? Enter the whole number in the separate whole-number field. The calculator converts it to an improper fraction before solving.

Can I type decimals into this fraction calculator? Not directly. Convert the decimal to fraction form first. For example, 0.75 becomes 3/4.

Adding Fractions

Adding fractions is straightforward when they share a common denominator. Just add the numerators and keep the denominator the same.

Example: 2/7 + 3/7 = 5/7.

When fractions have different denominators, you need a common denominator first. Find the least common multiple (LCM) of the two denominators, rewrite each fraction as an equivalent fraction with that denominator, then add the numerators.

Why do fractions need a common denominator for addition? You can only combine parts that are the same size. A common denominator makes sure both fractions describe equal-sized pieces.

Subtracting Fractions

Subtracting fractions follows the same logic as addition. With a common denominator, subtract the numerators and keep the denominator.

For fractions with different denominators:

  1. Find the least common denominator (LCD).
  2. Convert each fraction to an equivalent fraction with the LCD.
  3. Subtract the numerators.
  4. Simplify if needed.

Example: 5/6 − 1/4. The LCD of 6 and 4 is 12. Rewrite: 10/12 − 3/12 = 7/12.

Multiply Fractions

Fraction multiplication is the simplest operation. Multiply the numerators together, then multiply the denominators together.

Example: 2/3 × 4/5 = 8/15.

No common denominator is required. After multiplying, simplify the result by dividing the numerator and denominator by their greatest common factor (GCF).

Tip: You can cross-cancel before multiplying. If a numerator and the other denominator share a common factor, divide both by that factor first. This keeps the numbers smaller and often gives you a reduced fraction right away.

What does "of" mean in fraction problems? The word "of" usually means multiply. "1/2 of 3/4" means 1/2 × 3/4 = 3/8.

Divide Fractions

Dividing fractions is similar to multiplying, with one extra step. Flip the second fraction (find its reciprocal), then multiply.

What is a reciprocal? The reciprocal of a fraction swaps the numerator and denominator. The reciprocal of 3/5 is 5/3.

Example: 2/3 ÷ 4/7 = 2/3 × 7/4 = 14/12 = 7/6.

If the result is an improper fraction, the calculator converts it to a mixed number for you.

Simplify Fractions

A fraction is fully simplified (in lowest terms) when the numerator and denominator share no common factor other than 1.

What is the fastest way to simplify a fraction?

  1. Find the greatest common divisor (GCD) of the numerator and denominator.
  2. Divide both by the GCD.

Example: 18/24. The GCD of 18 and 24 is 6. Divide both: 18 ÷ 6 = 3, 24 ÷ 6 = 4. The reduced fraction is 3/4.

If you cannot spot the GCD quickly, try dividing by small primes (2, 3, 5, 7) until no common factor remains.

Simplify Fractions Calculator

Enter any fraction and the simplify fractions calculator divides the numerator and denominator by their greatest common factor. It returns the reduced fraction instantly and shows the GCF it used.

This is helpful when you have already done the arithmetic by hand and just want to confirm the simplest form.

Improper Fraction and Mixed Number

What is the difference between a proper fraction and an improper fraction? A proper fraction has a numerator smaller than its denominator (like 3/8). An improper fraction has a numerator equal to or larger than its denominator (like 9/4).

What is a mixed number? A mixed number combines a whole number with a proper fraction, such as 2 1/4. It is just another way to write an improper fraction.

Mixed Numbers Calculator

The mixed numbers calculator lets you add, subtract, multiply, or divide mixed numbers directly. Enter the whole number part and the fractional part separately.

Behind the scenes, the calculator converts each mixed number to an improper fraction, performs the operation, simplifies, and converts back to a mixed number when appropriate.

Can this fraction calculator online handle mixed numbers? Yes. Use the whole-number field for the integer part. The calculator handles the conversion automatically.

Can I enter negative mixed numbers? Yes. Place the negative sign on the whole number. The calculator treats the entire mixed number as negative.

Convert Fractions: Improper to Mixed Number

To convert an improper fraction to a mixed number:

  1. Divide the numerator by the denominator.
  2. The quotient is the whole number.
  3. The remainder becomes the new numerator over the original denominator.

Example: 17/5. 17 ÷ 5 = 3 remainder 2. So 17/5 = 3 2/5.

To go the other direction, multiply the whole number by the denominator, add the numerator, and place that result over the denominator. 3 2/5 = (3 × 5 + 2)/5 = 17/5.

Fraction to Decimal

To convert a fraction to a decimal, divide the numerator by the denominator. You can use long division or let the calculator do it.

Example: 7/8 = 0.875.

Some fractions produce repeating decimals. 1/3 = 0.333… The calculator shows the decimal equivalent alongside the fraction result.

How do fractions relate to percentages and decimals? A fraction, a decimal, and a percentage are three ways to express the same value. To go from fraction to percentage, convert to a decimal first, then multiply by 100. 3/4 = 0.75 = 75%.

Negative Fraction Operations

Negative fractions follow the same rules as positive fractions. The sign simply carries through the arithmetic.

Key points:

  • A negative sign can sit in front of the fraction, on the numerator, or on the denominator. All three mean the same thing: −3/5 = (−3)/5 = 3/(−5).
  • Multiplying or dividing two negative fractions gives a positive result.
  • Adding a negative fraction is the same as subtracting the positive version.

Can I use this calculator for negative fractions? Yes. Enter a minus sign with the numerator or in the whole-number field for mixed numbers. The calculator applies standard sign rules in every step.

Visual Fraction

Visual fraction models show fractions as shaded portions of a shape, usually a circle or a bar. They help you compare two fractions at a glance and confirm whether your arithmetic makes sense.

When fractions share a denominator, the shaded areas are easy to compare because the pieces are the same size. When denominators differ, the visual makes it clear why you need a common denominator before adding or subtracting.

Visuals are especially useful for checking whether an answer is reasonable. If your result is 11/12, the shape should be nearly full.

Fraction Problems with Algebra

Fractions appear often in algebra. The same operations apply, but variables sit in the numerator, denominator, or both.

Common tasks:

  • Solving equations with fractions. Multiply every term by the LCD to clear the denominators.
  • Adding algebraic fractions. Find a common denominator for the variable expressions, combine, then simplify.
  • Simplifying complex fractions. Treat the main fraction bar as division and flip the denominator fraction.

The order of operations still applies. Handle parentheses and exponents first, then multiplication and division, then addition and subtraction.

Fraction Calculator Step-by-Step Examples

Adding Fractions with a Common Denominator

Problem: 3/8 + 2/8

  1. The denominators are the same (8).
  2. Add the numerators: 3 + 2 = 5.
  3. Keep the denominator: 5/8.
  4. 5 and 8 share no common factor, so 5/8 is already simplified.

Answer: 5/8

Subtracting Fractions with Unlike Denominators

Problem: 5/6 − 1/4

  1. Find the LCD of 6 and 4. The least common multiple is 12.
  2. Convert: 5/6 = 10/12, 1/4 = 3/12.
  3. Subtract the numerators: 10 − 3 = 7.
  4. Keep the denominator: 7/12.
  5. 7 and 12 share no common factor. The fraction is simplified.

Answer: 7/12

Multiply Fractions and Simplify

Problem: 4/9 × 3/8

  1. Multiply the numerators: 4 × 3 = 12.
  2. Multiply the denominators: 9 × 8 = 72.
  3. Result: 12/72.
  4. Find the GCF of 12 and 72. It is 12.
  5. Divide both: 12 ÷ 12 = 1, 72 ÷ 12 = 6.

Answer: 1/6

Cross-cancel shortcut: Before multiplying, notice 4 and 8 share factor 4, and 3 and 9 share factor 3. Cancel first: (1/3) × (1/2) = 1/6. Same answer, smaller numbers.

Divide Fractions Using the Reciprocal

Problem: 5/6 ÷ 2/3

  1. Find the reciprocal of the second fraction: 2/3 becomes 3/2.
  2. Multiply: 5/6 × 3/2.
  3. Numerators: 5 × 3 = 15.
  4. Denominators: 6 × 2 = 12.
  5. Result: 15/12.
  6. GCF of 15 and 12 is 3. Simplify: 5/4.
  7. Convert to a mixed number: 1 1/4.

Answer: 1 1/4

Frequently Asked Questions

What is a fraction calculator? A fraction calculator is an online tool that performs arithmetic on fractions. Enter two fractions (or mixed numbers), choose an operation, and get a simplified result with step-by-step work.

How do I find the least common denominator (LCD)? List the multiples of each denominator until you find the smallest number they share. For 4 and 6, the multiples of 4 are 4, 8, 12… and the multiples of 6 are 6, 12… The LCD is 12. You can also calculate the least common multiple using the formula: LCM(a, b) = (a × b) / GCD(a, b).

How do I reduce a fraction to lowest terms? Divide both the numerator and the denominator by their greatest common factor. Repeat until no common factor remains. The calculator simplifies automatically after every operation.

How can I compare two fractions? Convert both fractions to equivalent fractions with a common denominator. Then compare the numerators. The fraction with the larger numerator is the larger fraction. You can also convert both to decimals.

How do you add or subtract fractions with different denominators? Find the LCD, rewrite each fraction with that denominator, then add or subtract the numerators. Keep the LCD as the denominator and simplify the result.

Need a calculator for fractional inches or tape measure readings? This fraction calculator works with any fractions, including those used in measurements. Enter the fractional inch values and calculate. For specialized construction or woodworking conversions, a dedicated measurement calculator may be more convenient.