What is 1/2 ÷ 1/4?

1/2 ÷ 1/4 = 2. Dividing by a fraction means multiplying by its reciprocal: 1/2 × 4/1 = 4/2 = 2, so 1/4 fits into 1/2 exactly twice. Add, subtract, multiply, or divide any two fractions in the calculator below.

Math

Fraction Calculator

Add, subtract, multiply or divide two fractions and see the full working — the common denominator, the un-reduced result and its lowest terms — as a fraction, mixed number and decimal.

Decimal: 0.833333
Mixed: 5/6

Result

5/6

1/2 + 1/3

Mixed number

5/6

Decimal

0.833333

Common denominator

Working

Common denominator (LCM): 6

Combine: 5/6 → simplify to 5/6

How fraction arithmetic works

To add or subtract fractions they must share a denominator. The calculator uses the least common multiple of the two denominators, rewrites each fraction over it, then adds or subtracts the numerators. Multiplication multiplies numerators and denominators straight across; division multiplies the first fraction by the reciprocal of the second.

Every result is reduced to lowest terms by dividing the numerator and denominator by their greatest common divisor, and the sign is kept on the numerator. If the result is top-heavy it is also shown as a mixed number and as a decimal.

How do I enter a mixed number?

Convert it to an improper fraction first: a whole number w with fraction n/d becomes (w·d + n)/d. For example 2 1/3 is 7/3. The result is shown back to you as a mixed number when it is top-heavy.

Why use the least common multiple?

Any common denominator works, but the least common multiple keeps the numbers as small as possible, which makes the arithmetic and the final reduction easier.

Does it simplify the answer automatically?

Yes. The result is always reduced to lowest terms using the greatest common divisor, so 6/12 is reported as 1/2.

How it's calculated

For addition and subtraction the calculator finds the LCM of the two denominators, rewrites each fraction over that common denominator, and combines the numerators. For multiplication it multiplies numerator by numerator and denominator by denominator. For division it multiplies the first fraction by the reciprocal of the second. In every case the result is then reduced by dividing numerator and denominator by their GCD (computed via the Euclidean algorithm), and a mixed-number form is derived when the absolute numerator exceeds the denominator.

Sources

Reviewed by the YouCalc Team · Last reviewedMay 24, 2026

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