Fraction Calculator

About the Fraction Calculator

What is a Fraction Calculator?

A fraction represents a part of a whole: the numerator (top number) counts how many parts you have, and the denominator (bottom number) shows how many equal parts the whole is divided into. A fraction calculator performs the four basic arithmetic operations — addition, subtraction, multiplication, and division — on any two fractions, then automatically reduces the answer to its lowest terms and shows the decimal equivalent. Instead of hunting for common denominators and simplifying by hand, you get the finished result plus the step-by-step work behind it in a single click, which makes it useful for checking homework, scaling recipes, or working with measurements.

How to Use

Enter the numerator and denominator of the first fraction, choose an operation (+, −, ×, ÷), enter the second fraction, and click Calculate. The tool displays the simplified fraction, its decimal value rounded to six places, and a step-by-step breakdown of the calculation. Negative numerators and denominators are supported. Two inputs are not allowed: a denominator of zero, and dividing by a fraction whose numerator is zero, because both make the result undefined. All calculations run locally in your browser — nothing you type is sent anywhere.

How to Add, Subtract, Multiply, and Divide Fractions

Each operation follows a simple formula. Throughout this section the first fraction is a/b and the second is c/d, where:

• a — numerator of the first fraction
• b — denominator of the first fraction (never zero)
• c — numerator of the second fraction
• d — denominator of the second fraction (never zero)

Adding Fractions

a/b + c/d = (a·d + b·c)/(b·d)

Addition requires a common denominator. Rewrite each fraction over the product b·d, then add the numerators and simplify.

Example: 3/4 + 2/3

1. Common denominator: 4 × 3 = 12
2. Convert: 3/4 = 9/12 and 2/3 = 8/12
3. Add the numerators: 9 + 8 = 17, giving 17/12
4. 17 and 12 share no common factor, so the result is already in lowest terms: 17/12 = 1 5/12 ≈ 1.416667

Subtracting Fractions

a/b − c/d = (a·d − b·c)/(b·d)

Subtraction works exactly like addition: build a common denominator, then subtract the second numerator from the first.

Example: 3/4 − 2/3 becomes 9/12 − 8/12 = 1/12. Since 1 and 12 have no shared factors, the answer is already simplified: 1/12 ≈ 0.083333.

Multiplying Fractions

a/b × c/d = (a·c)/(b·d)

Multiplication is the simplest operation — no common denominator is needed. Multiply straight across: numerators together, denominators together, then simplify.

Example: 5/6 × 2/3 = (5 × 2)/(6 × 3) = 10/18. Dividing top and bottom by their greatest common divisor, 2, gives 5/9 ≈ 0.555556.

Dividing Fractions

a/b ÷ c/d = (a·d)/(b·c)

To divide, multiply the first fraction by the reciprocal of the second — flip the second fraction upside down, then multiply as usual. Dividing by a fraction equal to zero is undefined, which is why the calculator rejects a second numerator of 0.

Example: 5/6 ÷ 2/3 = 5/6 × 3/2 = 15/12. Simplifying by the greatest common divisor, 3, gives 5/4 = 1 1/4 = 1.250000.

Simplifying Fractions with the Greatest Common Divisor

A fraction is in lowest terms when its numerator and denominator share no factor larger than 1. To reduce any fraction, divide both numbers by their greatest common divisor (GCD) — the largest whole number that divides both evenly:

• 10/18 → GCD(10, 18) = 2 → (10÷2)/(18÷2) = 5/9
• 84/96 → GCD(84, 96) = 12 → (84÷12)/(96÷12) = 7/8

This calculator applies GCD reduction automatically to every result. To find the GCD of larger numbers by hand, use the Euclidean algorithm — repeatedly replace the larger number with the remainder of dividing the two until the remainder is zero — or let our GCF Calculator do it for you.

Finding the Least Common Denominator

The least common denominator (LCD) of two fractions is the least common multiple (LCM) of their denominators — the smallest number both denominators divide into evenly. For 3/4 and 2/3, LCM(4, 3) = 12, so 12 is the LCD. Using the LCD instead of the raw product keeps the numbers small and often means less simplification afterward: for denominators 4 and 6, the LCD is 12 rather than 24.

This calculator uses the product of the denominators (b·d) as the common denominator, which always works even when it is larger than the LCD, and then reduces the answer with the GCD — so the final simplified result is identical either way. To find LCMs of larger numbers, try our LCM Calculator.

Mixed Numbers and Improper Fractions

An improper fraction has a numerator at least as large as its denominator, like 17/12. A mixed number expresses the same value as a whole part plus a proper fraction: 1 5/12. Converting between the two forms is straightforward.

Improper Fraction to Mixed Number

Divide the numerator by the denominator. The quotient becomes the whole number, and the remainder becomes the new numerator over the original denominator. Example: 17 ÷ 12 = 1 with remainder 5, so 17/12 = 1 5/12.

Mixed Number to Improper Fraction

Multiply the whole number by the denominator, add the numerator, and place the total over the original denominator. Example: 2 3/5 = (2 × 5 + 3)/5 = 13/5. This calculator accepts improper-fraction inputs, so convert mixed numbers before entering them — enter 1 1/2 as 3/2.

Fraction to Decimal Conversion Table

These common equivalents come up constantly in cooking, carpentry, and schoolwork. Decimals are shown to six places, matching this calculator's output.

To turn any decimal into a percentage, multiply by 100 — or use the Percentage Calculator.