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Mathematics & calculation

Fraction Calculator with Steps

Calculate with fractions, mixed numbers and decimals: simplified result, mixed number, exact decimal form and step-by-step explanations.

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First fraction
Second fraction
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Enter the numerator above the bar and the denominator below it. The optional box on the left is for mixed numbers (2 and 1/3); the numerator and denominator also accept decimals (0.75).

Mixed number
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Decimal form
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Percentage
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Calculation steps

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    How does this tool work?

    This fraction calculator performs the four operations (addition, subtraction, multiplication, division) and simplification with exact arithmetic: no rounding ever occurs, even with very large numbers. The result is given as a fraction in simplest form, as a mixed number, as a decimal (with its repeating block when it repeats) and as a percentage, and every step is explained the way you would write it in a notebook.

    A fraction a/b represents the quotient of a divided by b: a is the numerator and b the denominator, which can never be zero. Two fractions are equal when you go from one to the other by multiplying or dividing the numerator and the denominator by the same non-zero number: 3/4 = 6/8 = 75/100.

    To add or subtract, the fractions must first share the same denominator. The tool uses the least common denominator, that is the LCM (least common multiple) of the denominators, which keeps the numbers small. The numerators are then added or subtracted while the denominator stays the same.

    To multiply, multiply the numerators together and the denominators together. To divide, multiply by the reciprocal of the second fraction, obtained by swapping its numerator and denominator; dividing by a zero fraction is impossible.

    The result is finally simplified: the numerator and the denominator are divided by their greatest common divisor (GCD, also called GCF or HCF). The resulting fraction is in simplest form, meaning it cannot be reduced any further. Decimal numbers you enter (0.75) are converted exactly into fractions (3/4) before the calculation.

    The decimal form of a fraction in simplest form is finite when its denominator has no prime factor other than 2 and 5 (3/8 = 0.375). Otherwise it is an infinite repeating decimal: 1/6 = 0.1(6) means 0.16666…, with the digit 6 repeating forever.

    How to use this tool

    1. Enter the first fraction

      Type the numerator above the bar and the denominator below it; for a mixed number such as 1 and 1/2, also fill in the whole number. Decimals are accepted.

    2. Choose the operation

      Addition, subtraction, multiplication, division, or simply simplify a fraction.

    3. Enter the second fraction

      The result updates as you type; this field is hidden in simplify mode.

    4. Read the result and the steps

      Simplest form, mixed number, exact decimal, percentage and a step-by-step explanation.

    Formulas for fraction operations

    For fractions a/b and c/d, with b and d non-zero:

    Addition

    a/b + c/d = (a × d + c × b) / (b × d)

    In practice, the LCM of b and d is used as the common denominator.

    Subtraction

    a/b − c/d = (a × d − c × b) / (b × d)

    Multiplication

    a/b × c/d = (a × c) / (b × d)

    Division

    a/b ÷ c/d = (a × d) / (b × c), with c ≠ 0

    Simplification

    a/b = (a ÷ GCD(a, b)) / (b ÷ GCD(a, b))

    Mixed number

    a/b = q + r/b, where a = q × b + r and 0 ≤ r < b

    a, c
    numerators
    b, d
    denominators, always different from 0
    GCD
    greatest common divisor (also called GCF or HCF)
    q, r
    quotient and remainder of the division of a by b

    Use cases

    Homework and revision

    Check a middle school or high school fractions exercise by comparing your own steps with the tool’s.

    Cooking and recipes

    Scale quantities written as fractions (3/4 cup, 1/3 liter) or add up portions.

    DIY and measurements in inches

    Add or subtract lengths such as 5 3/8 and 2 11/16 inches without rounding errors.

    Fraction ↔ decimal conversion

    Get the exact decimal form of a fraction, or find the fraction that matches a decimal.

    Examples

    Add two fractions

    The LCM of 6 and 4 is 12: 1/6 = 2/12 and 1/4 = 3/12, so 2/12 + 3/12 = 5/12, already in simplest form.

    Input

    1/6 + 1/4

    Result

    5/12

    Subtract with a mixed number

    2 1/3 = 7/3. Over the denominator 12: 28/12 − 9/12 = 19/12, which is 1 and 7/12.

    Input

    2 1/3 − 3/4

    Result

    19/12 = 1 7/12

    Multiply, then simplify

    (2 × 9) / (3 × 10) = 18/30, then divide by the GCD 6: 3/5 = 0.6.

    Input

    2/3 × 9/10

    Result

    3/5

    Divide by a fraction

    3/4 × 8/9 = 24/36, which simplifies by 12 to 2/3 = 0.(6).

    Input

    3/4 ÷ 9/8

    Result

    2/3

    Simplify a fraction

    The GCD of 84 and 126 is 42: 84 ÷ 42 = 2 and 126 ÷ 42 = 3.

    Input

    84/126

    Result

    2/3

    Tips and best practices

    • When adding, look for the least common denominator rather than the product of the denominators: the numbers stay smaller and the final simplification is easier.
    • Simplify before multiplying when possible: in 4/9 × 3/8, you can cancel 4 with 8 and 3 with 9 before calculating.
    • A minus sign is best written in front of the fraction or on the numerator: −3/4 = (−3)/4 = 3/(−4).
    • The mixed number 2 1/3 means 2 + 1/3, which is 7/3: multiply the whole part by the denominator and add the numerator.
    • To compare two fractions, put them over the same denominator or compare their decimal forms.

    Sources and references

    Frequently asked questions

    How do you add fractions with different denominators?

    Rewrite them over a common denominator, ideally the LCM of the two denominators, by multiplying the numerator and denominator of each fraction by the same number. Then add the numerators, keep the common denominator, and simplify. Example: 1/6 + 1/4 = 2/12 + 3/12 = 5/12.

    How do you simplify a fraction?

    Divide the numerator and the denominator by their greatest common divisor (GCD, also called GCF). If the GCD is 1, the fraction is already in simplest form. Example: the GCD of 18 and 24 is 6, so 18/24 = 3/4.

    What is a fraction in simplest form?

    It is a fraction whose numerator and denominator have no common divisor other than 1. Every fraction has exactly one simplest form with a positive denominator, which makes it easy to compare results.

    How do you divide one fraction by another?

    Dividing by a fraction is the same as multiplying by its reciprocal: a/b ÷ c/d = a/b × d/c = (a × d)/(b × c). Division is impossible if the second fraction is zero.

    How do you turn an improper fraction into a mixed number?

    Divide the numerator by the denominator: the quotient is the whole part and the remainder becomes the new numerator. Example: 19/12 → 19 = 1 × 12 + 7, so 19/12 = 1 7/12.

    How do you convert a decimal to a fraction?

    Write the decimal over a power of 10, then simplify: 0.75 = 75/100 = 3/4. The tool does this conversion automatically when you enter a decimal such as 0.75 or 2.5.

    Why do some fractions give a decimal that never ends?

    A fraction in simplest form has a finite decimal only if its denominator contains no prime factors other than 2 and 5. Otherwise the division never comes out even and the digits repeat periodically: 1/3 = 0.333…, written 0.(3) by the tool.

    Is the calculation exact?

    Yes. Fractions are computed with arbitrary-precision integers, never with floating-point numbers. Only the displayed percentage is rounded, to four decimal places.

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