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
Calculator
Working
Common denominator (LCM): 6
Combine: 5/6 → simplify to 5/6
About this calculator
This calculator adds, subtracts, multiplies or divides two fractions and shows every step along the way. Use it to double-check homework, understand how a common denominator is found, or convert a fraction to its decimal equivalent in one click.
How to read your results
The main result card shows the simplified fraction — for example 17/12 — along with the equivalent mixed number (1 5/12) and the decimal value. Below the result, the step-by-step breakdown explains the common denominator used for addition or subtraction, or how the numerators and denominators were multiplied together for multiplication or division. Three pie charts visualise each fraction and the result.
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.
Worked example
Add 2/3 and 3/4.
The LCM of 3 and 4 is 12, so 2/3 becomes 8/12 and 3/4 becomes 9/12. Adding gives 17/12, which simplifies to the mixed number 1 5/12 and the decimal 1.417.
Frequently asked questions
Why do you need a common denominator for addition and subtraction?
Fractions can only be added or subtracted when they refer to equal-sized parts. Finding the lowest common multiple (LCM) of the two denominators gives the smallest denominator that both fractions can be rewritten with, so the numerators become directly comparable.
Why does multiplication not need a common denominator?
When multiplying, you combine two fractions into a new fraction by multiplying numerator by numerator and denominator by denominator. No alignment of parts is required — the operation works directly on the two fractions as given.
What does it mean to simplify a fraction?
A fraction is in its simplest (or lowest) terms when its numerator and denominator share no common factor other than 1. The calculator divides both by their greatest common divisor (GCD) automatically, so the result is always fully reduced.
How do you add or subtract fractions with different denominators?
Rewrite both fractions over their lowest common denominator, then add or subtract the numerators. For 2/3 + 3/4 the common denominator is 12, so 2/3 becomes 8/12 and 3/4 becomes 9/12, giving 17/12 (1 5/12). Subtraction works the same way: 3/4 − 1/2 = 3/4 − 2/4 = 1/4.
How do you multiply fractions?
Multiply the numerators together and the denominators together, then simplify — no common denominator is needed. For example, 2/3 × 3/4 = (2 × 3) / (3 × 4) = 6/12, which reduces to 1/2.
How do you divide fractions?
Keep the first fraction, flip the second, and multiply (keep–change–flip). For example, 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2. Dividing by a fraction is the same as multiplying by its reciprocal.
How do I convert an improper fraction to a mixed number?
Divide the numerator by the denominator: the whole-number quotient is the integer part, and the remainder over the denominator is the fractional part. For example, 17/12 = 1 remainder 5 = 1 5/12.
Popular scenarios
Sources
Reviewed by the YouCalc Team · Last reviewed
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