Fraction Calculator

Simple fraction: A fraction with just a numerator and denominator, like 3/4.

Mixed number: A whole number plus a fraction, like 2 1/3.

Numerator: The top number in a fraction.

Denominator: The bottom number in a fraction. It cannot be 0.

Simplified fraction: A fraction reduced to lowest terms so the top and bottom share no greater common factor.

Improper fraction: A fraction whose numerator is at least as large as its denominator, like 7/3.

Common denominator: The same bottom number used to rewrite fractions before adding, subtracting, or some comparisons.

Decimal places: How many digits are shown to the right of the decimal point in Result as decimal.

Mistake: Entering 0 in First denominator or Second denominator .
Fix: Use any nonzero denominator. A fraction cannot have a bottom number of 0.

Mistake: Leaving First numerator , First denominator , Second numerator , or Second denominator blank and expecting the calculator to treat it as 0.
Fix: Fill every visible numerator and denominator box with a real number before you calculate.

Mistake: Typing a mixed number like 2 1/3 as First numerator = 21 and First denominator = 3.
Fix: Change First value format to Mixed number, then enter First whole number = 2, First numerator = 1, and First denominator = 3.

Mistake: Using Operation = Divide when the second value equals 0.
Fix: In Divide mode, make sure the second fraction is not zero overall, such as 0/5.

Mistake: Thinking Result as decimal is exact when it ends or repeats strangely.
Fix: Treat Result as simplified fraction as the exact answer and use Decimal places only to control display rounding.

Mistake: Ignoring Common denominator used when adding, subtracting, or comparing unlike fractions.
Fix: Check that line to see how the calculator matched denominators before combining or comparing the values.

• The calculator only works with the shown tasks: arithmetic, comparison, and one-fraction conversion or simplification.
• Any entered denominator must be nonzero, or the calculation is invalid.
• In Divide mode, the second fraction must not equal zero overall because division by zero is undefined.
• Result as decimal may be rounded, especially for repeating decimals, so the exact answer is the fraction output.
• When a value format is Simple fraction, any hidden whole-number field is ignored and does not affect the result.
• Outputs are normalized so the displayed denominator stays positive; the sign is carried by the whole value or numerator instead.
• Very large numerators or denominators can be harder to read and may be less practical for school-style checking by hand.

How the calculator works

The tool first reads each visible fraction entry. If a value is entered as a mixed number, it converts that value to an improper fraction before doing any math. After the operation, it simplifies the final fraction and then shows the same answer in fraction, mixed-number, and decimal forms.

Core formulas

mixed to improper = sign * (abs(whole) * denominator + numerator) / denominator

add or subtract: a/b +/- c/d = (a*d +/- c*b) / (b*d)

multiply: a/b * c/d = (a*c) / (b*d)

divide: a/b / c/d = (a*d) / (b*c)

simplify by gcd: n/d -> (n/g) / (d/g), where g = gcd(|n|,|d|)

lcd = lcm(b,d) = |b*d| / gcd(b,d)

compare by cross-products: compare a*d and c*b

mixed number output: whole = floor(|n|/d), remainder = |n| mod d

When the common denominator is used

For addition, subtraction, and comparison displays, the calculator can show a least common denominator so unlike fractions line up cleanly [1][2]. For multiplication and division, a common denominator is not needed.

Worked mini-example

Example: add 1/2 and 1/3.

lcd = lcm(2,3) = 6

1/2 = 3/6 and 1/3 = 2/6

3/6 + 2/6 = 5/6

decimal = 5 / 6 = 0.833333...

So the outputs are 5/6 as the simplified fraction, 5/6 as the mixed number, and a rounded decimal based on the selected decimal places.

Compare example

To compare 2/3 and 4/6, the calculator checks cross-products.

2*6 = 12

4*3 = 12

Since the products match, the fractions are equal.

Assumptions used

The calculator assumes numerators, denominators, and whole-number parts are entered as valid numbers. It blocks denominator 0, blocks division by a zero-valued second fraction, ignores hidden mixed-number whole fields, keeps negative results when they are mathematically correct, and rounds only the decimal display, not the exact fraction answer.