Fraction Calculator

To add or subtract fractions:

• find the Least Common Denominator (LCD)
• convert fractions to equivalent fractions with the LCD
• then add or subtract numerators

Our calculator handles this automatically and shows each step.

Multiply fractions by multiplying numerators together and denominators together.

Divide by flipping the second fraction and multiplying. Remember: Keep, Change, Flip for division.

Simplify fractions by finding the Greatest Common Divisor (GCD) of numerator and denominator, then dividing both by it.

A fraction is fully simplified when GCD equals 1.

Our converter handles all these transformations:

• Convert fractions to decimals by dividing.
• Convert decimals to fractions by placing over powers of 10.
• Learn how to calculate percentages by multiplying a fraction by 100.

Mixed numbers combine whole numbers with fractions (2 1/2).

Improper fractions have numerators larger than denominators (5/2).

Convert between them easily with our calculator.

Every calculation shows detailed steps so you can learn the process.

Perfect for students learning fraction arithmetic or anyone who wants to understand the math behind the answer.

A fraction represents a part of a whole, written as two numbers separated by a bar: the numerator on top and the denominator on the bottom. The denominator tells you how many equal parts the whole is divided into, while the numerator tells you how many of those parts you are counting.

For example, in 3/4 the whole is split into 4 equal parts and you are taking 3 of them.

According to Encyclopaedia Britannica, fractions extend the natural numbers so that quantities between whole numbers can be expressed exactly. Any fraction with a denominator that is not zero represents a rational number, and equal fractions like 2/4 and 1/2 name the same value.

The Greatest Common Divisor (GCD) is the largest number that divides two integers evenly, and the Least Common Denominator (LCD) is the smallest number that both denominators divide into.

To simplify 12/18, find GCD(12, 18) = 6, then divide to get 2/3.

To add 1/4 + 1/6, find the LCD, which equals the least common multiple of 4 and 6: since LCM(4, 6) = 4 × 6 / GCD(4, 6) = 24 / 2 = 12, the LCD is 12.

As Wolfram MathWorld explains, the GCD and LCM are linked by the identity a × b = GCD(a, b) × LCM(a, b), which our calculator uses to keep denominators as small as possible.

To compare two fractions quickly, cross-multiply — the same step you use to solve a proportion: multiply the numerator of each fraction by the denominator of the other, then compare the products.

For 2/3 versus 3/4, multiply 2 × 4 = 8 and 3 × 3 = 9; because 8 is less than 9, 2/3 is smaller than 3/4. This works because both products share the same effective denominator, a technique Khan Academy teaches for ordering fractions.

You can also convert each fraction to a decimal and compare: 2/3 ≈ 0.667 and 3/4 = 0.75, confirming 3/4 is larger.

Our comparison mode shows the cross-multiplication and the decimal check side by side.

Fractions appear constantly in daily life, which makes fast, accurate fraction math genuinely useful.

• Cooking recipes call for 3/4 cup of flour or half of a 2/3-cup measure, so scaling a recipe up or down requires multiplying fractions.
• Woodworking and construction rely on inch fractions like 5/8 and 7/16, where adding board thicknesses means finding a common denominator.
• Finance uses fractions and their decimal equivalents for interest rates and stock quotes, and probability expresses chances as fractions such as 1/6 for rolling a specific number on a die.

Encyclopaedia Britannica notes that fractional notation predates decimals by millennia, and it still gives exact answers where rounding a decimal would introduce error.

• The most frequent fraction error is adding numerators and denominators directly, such as writing 1/2 + 1/3 = 2/5, which is wrong; you must first find the LCD, giving 3/6 + 2/6 = 5/6.
• Another common slip is forgetting to flip only the second fraction when dividing, since a ÷ b uses the reciprocal of b, not of a.
• Students also skip simplifying the final answer, leaving 6/12 instead of 1/2, or misconvert mixed numbers by adding instead of using (whole × denominator + numerator).

Khan Academy stresses checking that a final fraction is fully reduced, meaning the GCD of numerator and denominator equals 1.

Our step-by-step output flags each of these stages so mistakes are easy to catch.