Fraction Calculator

Fractions, explained step by step

A fraction describes how many equal parts of a whole you have. The number on top is the numerator and the number below the line is the denominator: 34 means three of four equal parts. When the numerator is smaller than the denominator it is a proper fraction; otherwise it is an improper fraction. An improper fraction such as 74 can also be written as a mixed number, 1 34.

Adding and subtracting fractions

If the denominators match, add or subtract the numerators and keep the denominator. If they differ, first find a common denominator. The smallest one is the least common denominator (LCD), the least common multiple of the denominators. Scale each fraction up to it, then combine the numerators. For 12 + 23 the LCD is 6: 36 + 46 = 76 = 1 16. Try it in the calculator.

Multiplying and dividing fractions

Multiplication needs no common denominator: multiply the numerators together and the denominators together. 23 × 34 = 612 = 12. To divide, keep the first fraction, flip the second one (its reciprocal) and multiply: 34 ÷ 12 = 34 × 21 = 32. With mixed numbers, convert to improper fractions first; 1 12 × 2 13 is not the whole parts times each other plus the fractions times each other. Solve this example.

Simplifying fractions with the GCD

Dividing the numerator and denominator by the same number does not change a fraction’s value. To reach the simplest form, divide both by their greatest common divisor (GCD). The quickest way to find it is Euclid’s algorithm: divide the larger number by the smaller one, then divide the divisor by the remainder, and repeat until the remainder is 0. The last divisor is the GCD. For 8460: 84 = 1 × 60 + 24, 60 = 2 × 24 + 12, 24 = 2 × 12 + 0, so the GCD is 12 and 8460 = 75. See the steps.

Converting between decimals and fractions

To turn a fraction into a decimal, divide the numerator by the denominator. If the simplified denominator has no prime factors other than 2 and 5, the decimal ends: 38 = 0.375. Otherwise it repeats forever: 512 = 0.416. Going the other way, write a terminating decimal over a power of ten and simplify: 0.375 = 3751000 = 38. For a repeating decimal, multiply by powers of ten and subtract so the repeating part cancels, which gives 0.3 = 13 and 0.16 = 16. Convert 0.1666….

This calculator works with exact whole numbers and never rounds along the way, so answers are exact for numbers up to 15 digits per box. The step-by-step solution under each answer is written for checking homework and reviewing the method. Everything runs in your browser and nothing you type is sent anywhere.