Fraction Calculator

Basic Fraction Concepts

A fraction represents a part of a whole. It appears as two numbers separated by a line. The number above the line is the numerator, and the number below the line is the denominator. The numerator shows how many equal parts are taken. The denominator shows how many equal parts form the whole.

A simple example uses the fraction 3 over 8. The value 3 stands in the numerator position and shows three parts. The value 8 stands in the denominator position and shows that the whole contains eight parts. A person with a pie cut into eight slices and three slices removed sees the remaining part as 5 over 8.

The denominator cannot equal zero. A value of zero in the denominator makes the fraction undefined, since no whole can contain zero parts.

Fraction Operations Explained

A fraction contains two values. The numerator stands above the line, and the denominator stands below it. Each operation in the online fraction calculator follows established math rules that apply to two fractions, mixed fractions, or a proper fraction.

Addition

Addition requires equal denominators. If the values show different denominators, the calculator forms a common denominator by scaling both values. After that step, the user may add the numerators, and the denominator remains the same. The result may return as a reduced fraction when the values allow it.

Example:

\( 34 + 16\frac{3}{4} + \frac{1}{6} \cdot 43 + 61 \)

The denominators differ, so the system forms a common base of 12:

\( 3 \times 34 \times 3 + 1 \times 26 \times 2\frac{3 \times 3}{4 \times 3} + \frac{1 \times 2}{6 \times 2} \times 4 \times 33 \times 3 + 6 \times 21 \times 2 \)

\( \frac{9}{12} + \frac{2}{12} = \frac{11}{12} \)

Subtraction

The method for subtraction mirrors the structure of addition. The denominators match first. Once aligned, the system may subtract the numerators. A case with one negative sign follows the same rule without altering the final position of each value.

Example:

\( 58−14\frac{5}{8} – \frac{1}{4}85​−41​ \)

The common denominator is 8:

\( 58−28=38\frac{5}{8} – \frac{2}{8} = \frac{3}{8}85​−82​=83​ \)

A case with one negative sign follows the same steps.

Multiplication

Multiplying fractions does not require equal denominators.

The operation forms one new numerator from the product of the two numerators.

The denominator forms in the same way.

If the numbers share a factor, the output may show a reduced value.

Example:

\( 25×34\frac{2}{5} \times \frac{3}{4}52​×43​ \)

\( 2×35×4=620=310\frac{2 \times 3}{5 \times 4} = \frac{6}{20} = \frac{3}{10}5×42×3​=206​=103​ \)

Division

Division uses the reciprocal of the second value. The denominator and numerator of the second fraction trade positions, and the operation proceeds as multiplication. This rule also applies inside the mixed numbers calculator.

Example:

\( 37÷12\frac{3}{7} \div \frac{1}{2}73​÷21​ \)

The second value flips:

\( 37×21=67\frac{3}{7} \times \frac{2}{1} = \frac{6}{7}73​×12​=76​ \)

Simplification

A fraction reaches a reduced form when both values share a factor. The system identifies the factor and divides both values. The same rule may apply when a user enters input fractions with large numbers.

Example:

\( 1824\frac{18}{24}2418​ \)

A factor of 6 appears in both values:

\( 18÷624÷6=34\frac{18 \div 6}{24 \div 6} = \frac{3}{4}24÷618÷6​=43​ \)

Conversion to Decimal

The calculator divides the numerator by the denominator and returns a decimal value.

Example:

\( 78=0.875\frac{7}{8} = 0.87587​=0.875 \)

Conversion From Decimal

Decimal places determine the denominator. Digits to the right of the decimal point form the numerator. The system applies the same reduction step used in fraction simplification.

Example:
0.125 uses three decimal places:

\( 1251000=18\frac{125}{1000} = \frac{1}{8}1000125​=81​ \)