WiseCalcs

Fraction calculator

Enter two fractions and pick an operation. The calculator combines them, reduces the result to its simplest form, and shows the decimal and mixed-number equivalents.

Written by Kenneth Schrøder, Founder of WiseCalcs

Updated ·Sources verified

Use it to add, subtract, multiply, or divide two fractions and compare the exact simplified answer with its decimal and mixed-number forms.

Result

5/6

Decimal
0.8333
Mixed number
5/6

The result updates as you type. The simplified fraction is exact within the accepted input range, the decimal shows up to four places and is rounded when needed, and the mixed number makes an improper fraction easier to read.

How does it work?

Add and subtract over a common denominator; multiply across; divide by flipping the second fraction. The result is reduced with the greatest common divisor.

Fraction operations

ab±cd=ad±cbbd,ab×cd=acbd\frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm cb}{bd},\quad \frac{a}{b}\times\frac{c}{d}=\frac{ac}{bd}
a, c
The numerators of the two fractions.
b, d
The denominators of the two fractions.

1/2 + 1/3 = (1×3 + 1×2) / (2×3) = 5/6 ≈ 0.833. To divide, multiply by the reciprocal of the second fraction.

Method & sources

Numerators are integers; denominators are positive integers. Add and subtract use a common denominator; multiply and divide go across. The result is reduced with the greatest common divisor.

Sources

Where this method comes from — use these references to understand the formula, assumptions, and limits.

How we calculate

  • Numerators are integers; denominators are positive integers.
  • Add and subtract use a common denominator; multiply and divide go across.
  • The result is reduced with the greatest common divisor.
  • Dividing by a zero fraction is undefined.

Rounding

Within the accepted input range, the fraction result is exact. The decimal shows up to four places and is rounded when needed.

What this calculator does

Fraction arithmetic has different rules for each operation. This calculator handles them all: a common denominator for adding and subtracting, multiplying across for products, and flipping the second fraction for division — then it reduces the answer.

How to use it

  1. Enter the first numerator and denominator.
  2. Pick an operation: add, subtract, multiply, or divide.
  3. Enter the second numerator and denominator.
  4. Read the simplified fraction, decimal, and mixed number.

A worked example

1/2 + 1/3 uses a common denominator of 6: 3/6 + 2/6 = 5/6, which is about 0.833 and stays as 5/6 since it's already in lowest terms.

Reducing and mixed numbers

The result is always reduced using the greatest common divisor, so 4/8 becomes 1/2. If the fraction is top-heavy, the mixed-number form shows it as a whole number plus a fraction, like 7/3 = 2 1/3.

Exact fraction or decimal?

The simplified fraction keeps the exact value, while the decimal shows up to four places and is rounded when necessary. For example, 1/2 appears as 0.5, while 1/3 appears as 0.3333. Use the fraction when you will continue calculating or need an exact ratio; use the decimal when you need an approximate measurement or an easy size comparison.

A practical recipe-scaling example

If a recipe needs 3/4 cup and you make 2/3 of the recipe, multiply 3/4 by 2/3. The raw product is 6/12, which reduces to 1/2 cup. Keeping the answer as a fraction is more useful here than converting it to 0.5 and then trying to translate the decimal back into a measuring cup.

Subtraction, division, and zero

  • For 1/4 − 3/4, the common denominator is already 4, so the result is −2/4 = −1/2.
  • For 2/3 ÷ 4/5, multiply by the reciprocal: 2/3 × 5/4 = 10/12 = 5/6.
  • A zero numerator is valid and represents 0, but a denominator of 0 has no value. Dividing by a zero fraction such as 0/5 is also undefined.

Compare the result as a percentage in the percentage calculator, round a decimal approximation with the rounding calculator, or use the basic calculator when the problem no longer needs exact fraction arithmetic.

Common mistakes

  • Adding numerators and denominators directly without a common denominator.
  • Entering a denominator of zero, which has no value.
  • Forgetting that dividing flips the second fraction.

When it's useful

For homework, cooking and recipe scaling, measurements, or any time you need an exact fraction rather than a rounded decimal.

FAQ

How do you add two fractions?
Put them over a common denominator, add the numerators, then reduce. 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
How do you divide fractions?
Multiply the first fraction by the reciprocal (flip) of the second. Dividing by 2/3 is the same as multiplying by 3/2.
What does 'simplified' mean?
The fraction is divided by the greatest common divisor of its numerator and denominator, so 6/8 becomes 3/4.
What is a mixed number?
A whole number plus a proper fraction. An improper fraction like 7/3 becomes the mixed number 2 1/3.
Can the result be negative?
Yes. Enter a negative numerator, or subtract a larger fraction, and the result carries the sign.
Can I share a calculation?
Yes. Use Share to copy a link that reopens the calculator with the same fractions and operation.

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