Skip to calculator
Mixed Number Calculator

A finer way to compute

Mixed Number Calculator

Add, subtract, multiply and divide mixed numbers with jeweler-grade precision. Type a value and watch the result, the working, and the diagram update instantly — no button required.

See it Visualized How it Works
Live — updates as you type

Type the whole number, numerator, and denominator into their own fields. For a negative value such as −2 3/4, use the sign toggle or type −2 in the whole-number field.

Result

View step-by-step working

    Visual Studio

    Watch the Fractions Move

    A live, interactive diagram redraws itself with every value you enter — gold wedges fill in, bars stretch and points glide as your fraction grows.

    First value

    Second value

    Result

    Each filled dot is one complete unit and the partly filled dot is the fraction left over. The ring sweep shows how far past the last whole unit the value sits, so 5 3/4 draws five dots and a three-quarter sweep.

    Definition

    What Is a Mixed Number?

    A mixed number is a whole number joined with a proper fraction, such as 2 3/4 or 1 1/2. The whole number counts complete units. The fraction counts a part left over, and its numerator is smaller than its denominator.

    An improper fraction differs from a mixed number in one way: its numerator is equal to or larger than its denominator, such as 11/4. A whole number differs too — it has no fraction part at all, such as 5.

    Four examples of mixed numbers:

    • 1 1/2 — one whole unit and one half
    • 2 3/4 — two whole units and three quarters
    • 25 3/32 — twenty-five whole units and three thirty-seconds
    • −2 3/8 — negative two whole units and three eighths
    The anatomy of the mixed number 2 3/4 The whole number 2 sits in its own block beside a fraction block holding the numerator 3 above the denominator 4. A plus sign between the blocks shows that the two parts are added together. 2 WHOLE NUMBER + 3 4 FRACTION numerator denominator
    A mixed number is written as two parts side by side, with no symbol between them. The blocks above show why: 2 3/4 means 2 plus 3/4, joined without a plus sign.

    Conversion

    Convert a Mixed Number to an Improper Fraction

    The formula multiplies the whole number by the denominator, adds the numerator, and places the result over the same denominator.

    Formula

    (whole × denominator + numerator) / denominator

    Example — 1 3/4 to an improper fraction

    1 3/4 = (1×4 + 3) / 4 = 7/4

    Example — 2 3/8 to an improper fraction

    2 3/8 = (2×8 + 3) / 8 = (16 + 3) / 8 = 19/8

    Negative example — −2 3/8 to an improper fraction

    The negative sign carries through the whole conversion: −2 3/8 = −((2×8 + 3) / 8) = −19/8

    Conversion

    Convert an Improper Fraction to a Mixed Number

    Divide the numerator by the denominator. The quotient becomes the whole number, and the remainder becomes the new numerator over the same denominator.

    Formula

    numerator ÷ denominator = whole number, remainder → new numerator

    Example — 7/4 to a mixed number

    7 ÷ 4 = 1 remainder 3, so 7/4 = 1 3/4

    Example — 43/12 to a mixed number

    43 ÷ 12 = 3 remainder 7, so 43/12 = 3 7/12

    Operation

    Adding Mixed Numbers

    Add mixed numbers by adding the whole numbers and the fractions separately, then simplifying the result.

    Adding fractions formula

    a/b + c/d = (ad + bc) / bd

    Adding Mixed Numbers with the Same Denominator

    Add mixed numbers with the same denominator by adding the whole numbers, adding the numerators, and keeping the denominator unchanged.

    1. Add the whole numbers

      2 + 3 = 5

    2. Add the numerators

      1/8 + 5/8 = 6/8 — the denominator stays at 8

    3. Simplify the fraction

      6/8 → 3/4

    4. Combine

      5 + 3/4 = 5 3/4

    2 1/8 + 3 5/8 = 5 3/4

    Adding Mixed Numbers with Different Denominators

    Add mixed numbers with different denominators by converting both fractions to a shared least common denominator (LCD) first.

    1. Find the LCD

      of 3 and 2: multiples of 3 are 3, 6, 9; multiples of 2 are 2, 4, 6; the LCD is 6

    2. Rewrite each fraction over 6

      2/3 → 4/6, and 1/2 → 3/6

    3. Add the fractions

      4/6 + 3/6 = 7/6 = 1 1/6

    4. Add the whole numbers

      4 + 1 = 5, plus the extra whole unit from 7/6, giving 6 1/6

    4 2/3 + 1 1/2 = 6 1/6

    Adding Mixed Numbers Using the Improper Fraction Method

    The improper fraction method converts both mixed numbers first, then applies the adding fractions formula directly.

    1. Convert to improper fractions

      1 2/6 → 8/6, and 2 1/4 → 9/4

    2. Apply the formula

      8/6 + 9/4 = (8×4 + 9×6) / (6×4) = (32 + 54) / 24 = 86/24

    3. Simplify

      86/24 → GCF 2 → 43/12

    4. Convert back to a mixed number

      43/12 = 3 7/12

    1 2/6 + 2 1/4 = 3 7/12

    Operation

    Subtracting Mixed Numbers

    Subtract mixed numbers by subtracting the whole numbers and the fractions separately, borrowing from the whole number when the first fraction is smaller than the second.

    Subtracting fractions formula

    a/b − c/d = (ad − bc) / bd

    Subtracting Mixed Numbers with the Same Denominator

    Subtract mixed numbers with the same denominator by subtracting the whole numbers and the numerators separately, then keeping the denominator unchanged.

    1. Subtract the whole numbers

      5 − 2 = 3

    2. Subtract the numerators

      3/4 − 1/4 = 2/4 — the denominator stays at 4

    3. Simplify the fraction

      2/4 → 1/2

    4. Combine

      3 + 1/2 = 3 1/2

    5 3/4 − 2 1/4 = 3 1/2

    Subtracting Mixed Numbers with Borrowing

    Borrowing is required when the first fraction is smaller than the second. Borrow 1 from the whole number and add a full denominator's worth to the fraction before subtracting.

    1. Compare the fractions

      1/4 is smaller than 3/4, so borrowing is needed

    2. Borrow 1 from the 6

      making it 5, and add 4/4 to 1/4, giving 5/4

    3. Rewrite the problem

      as 5 5/4 − 2 3/4

    4. Subtract the whole numbers

      5 − 2 = 3

    5. Subtract the fractions

      5/4 − 3/4 = 2/4 → 1/2

    6. Combine

      3 + 1/2 = 3 1/2

    6 1/4 − 2 3/4 = 3 1/2

    Borrowing 1 from the whole number of 6 1/4 Before borrowing the value is 6 and 1 quarter. After borrowing the whole number drops from 6 to 5 and the fraction gains four quarters, so 1 quarter becomes 5 quarters. The value stays the same. BEFORE 6 1 4 1/4 is too small to subtract 3/4 BORROW 1 1 = 4/4 AFTER 5 5 4 5/4 is large enough to subtract 3/4 6 × 4 + 1 = 25 quarters · 5 × 4 + 5 = 25 quarters · same value, easier to subtract
    The whole number drops by 1 while the fraction gains a full denominator's worth of parts. Both cards hold 25 quarters, so the value never changes — only its shape does.

    Subtracting Mixed Numbers Using the Improper Fraction Method

    The improper fraction method converts both mixed numbers first, applies the subtracting fractions formula, then simplifies.

    1. Convert to improper fractions

      1 2/6 → 8/6, and 2 1/4 → 9/4

    2. Apply the formula

      8/6 − 9/4 = (8×4 − 9×6) / (6×4) = (32 − 54) / 24 = −22/24

    3. Simplify

      −22/24 → GCF 2 → −11/12

    1 2/6 − 2 1/4 = −11/12 — negative, because the second value is larger than the first

    Operation

    Multiplying Mixed Numbers

    Multiply mixed numbers by converting both to improper fractions, then multiplying straight across. No common denominator is needed.

    Multiplying fractions formula

    a/b × c/d = ac / bd

    Multiplying Mixed Numbers — Basic Method

    Convert, multiply the numerators, multiply the denominators, then reduce.

    1. Convert to improper fractions

      1 1/2 → 3/2, and 2 1/3 → 7/3

    2. Multiply straight across

      3/2 × 7/3 = 21/6

    3. Simplify

      21/6 → 7/2

    4. Convert back

      7/2 = 3 1/2

    1 1/2 × 2 1/3 = 3 1/2

    Multiplying Mixed Numbers with Cross-Simplification

    Cross-simplification cancels common factors between a numerator and the opposite denominator before multiplying, so the numbers stay small.

    Cross-simplifying 18/5 times 25/6 before multiplying A dashed diagonal connects the numerator 18 to the opposite denominator 6, and both divide by their greatest common factor 6 to give 3 and 1. A second dashed diagonal connects the denominator 5 to the opposite numerator 25, and both divide by 5 to give 1 and 5. The reduced product is 3 times 5, which equals 15. CANCEL DIAGONALLY, THEN MULTIPLY 18 5 25 6 ÷ GCF 6 ÷ GCF 5 × 3 1 × 5 1 = 15 PRODUCT

    1. Convert to improper fractions

      3 3/5 → 18/5, and 4 1/6 → 25/6

    2. Cross-cancel

      18 and 6 share a GCF of 6, reducing to 3 and 1; 25 and 5 share a GCF of 5, reducing to 5 and 1

    3. Multiply the reduced numbers

      3 × 5 = 15

    3 3/5 × 4 1/6 = 15

    Multiplying Mixed Numbers Using the Improper Fraction Method

    The same two-step conversion works whatever the denominators are.

    1. Convert to improper fractions

      1 2/6 → 8/6, and 2 1/4 → 9/4

    2. Multiply straight across

      8/6 × 9/4 = 72/24

    3. Simplify

      72/24 → GCF 24 → 3

    1 2/6 × 2 1/4 = 3 — a whole number, since the fraction part reduced away completely

    Operation

    Dividing Mixed Numbers

    Divide mixed numbers by converting both to improper fractions, then multiplying the first by the reciprocal of the second.

    Dividing fractions formula

    a/b ÷ c/d = ad / bc

    Dividing Mixed Numbers — Basic Method

    Flip the second fraction and the division turns into a multiplication you already know how to do.

    1. Convert to improper fractions

      3 1/2 → 7/2, and 1 1/4 → 5/4

    2. Flip the second fraction

      5/4 becomes its reciprocal, 4/5

    3. Multiply

      7/2 × 4/5 = 28/10

    4. Simplify

      28/10 → 14/5

    5. Convert back

      14/5 = 2 4/5

    3 1/2 ÷ 1 1/4 = 2 4/5

    Flipping 5/4 to its reciprocal 4/5 Two crossing arrows swap the parts of the fraction: the numerator 5 moves down to become the denominator, and the denominator 4 moves up to become the numerator, turning 5 over 4 into 4 over 5. Dividing by a fraction becomes multiplying by this flipped fraction. RECIPROCAL 5 4 4 5 Dividing by 5/4 is the same as multiplying by 4/5
    The reciprocal swaps the numerator and denominator. Multiplying by 4/5 asks the same question as dividing by 5/4: how many of those parts fit inside the first value.

    Dividing Mixed Numbers with Cross-Simplification

    Cancel diagonally after the flip and the multiplication becomes trivial.

    1. Convert to improper fractions

      5 1/3 → 16/3, and 2 2/3 → 8/3

    2. Flip and cross-cancel

      16/3 × 3/8 — the two 3s cancel, and 16 and 8 share a GCF of 8, reducing to 2 and 1

    3. Multiply the reduced numbers

      2 × 1 = 2

    5 1/3 ÷ 2 2/3 = 2

    Dividing Mixed Numbers Using the Improper Fraction Method

    One formula covers every division: multiply the outer terms over the inner terms.

    1. Convert to improper fractions

      1 2/6 → 8/6, and 2 1/4 → 9/4

    2. Flip and multiply

      8/6 × 4/9 = 32/54

    3. Simplify

      32/54 → GCF 2 → 16/27

    1 2/6 ÷ 2 1/4 = 16/27

    Common Mixed Number Division Examples

    Ten frequently searched division problems, solved.

    ProblemResult
    2 1/2 ÷ 5 1/2
    9 ÷ 1/5 45
    25 3/4 ÷ 2 12 7/8
    15 3/8 ÷ 2 7 11/16
    9 1/4 ÷ 2 4 5/8
    3 5/8 ÷ 2 1 13/16
    1 1/2 ÷ 1/2 3
    1 2/3 ÷ 1/6 10
    3 1/3 ÷ 5 2/3
    half of 15 3/4 7 7/8

    Reduce

    Simplifying Mixed Numbers

    Simplify a mixed number by dividing its numerator and denominator by their greatest common factor (GCF) until no common factor remains.

    Simplifying 86/24 to 43/12 by dividing by the GCF 86 over 24 becomes 43 over 12 when both the numerator and the denominator are divided by their greatest common factor of 2. 86 24 ÷ 2 43 12

    86/24 → GCF 2 → 43/12 = 3 7/12

    Conversion

    Converting Between Mixed Numbers and Decimals

    Mixed numbers and decimals represent the same values in two different formats. Converting between them runs in both directions.

    Mixed Number to Decimal

    Convert a mixed number to a decimal by dividing the numerator by the denominator, then adding the result to the whole number.

    Mixed numberDecimal
    1 1/2 1.5
    2 3/4 2.75
    3 7/12 3.583

    Decimal to Mixed Number

    Convert a decimal to a mixed number by writing the digits after the decimal point over the matching power of 10, then simplifying.

    DecimalFraction
    1.375 1 3/8
    0.8 4/5 (no whole number part)

    Special cases

    Special Cases

    Two situations that still follow the same four formulas: negative values, and a whole number paired with a plain fraction.

    Negative Mixed Numbers

    A negative mixed number carries its sign across the whole value, not just the whole-number part.

    1. Convert to an improper fraction

      −2 3/4 = −11/4, since the sign applies to the full amount (2×4 + 3 = 11)

    2. Operate as usual

      (−11×2 + 3×4) / (4×2) = −10/8 = −5/4 = −1 1/4

    −2 3/4 + 1 1/2 = −1 1/4

    Whole Numbers and Fractions Together

    A whole number is a mixed number with 0/1 as its fraction part, so it follows the same four formulas when paired with a fraction.

    5 + 3/4 = 5 3/4

    5 − 3/4 = 4 1/4

    3 × 2/4 = 1 1/2

    6 ÷ 1/3 = 18

    Lookup

    Improper Fraction to Mixed Number — Reference Table

    44 improper fractions with denominators from 2 to 16, already converted and simplified. Filter by typing any part of a fraction.

    Improper fractions converted to mixed numbers, with denominators from 2 to 16
    Improper fractionMixed number
    7/4 1 3/4
    3/2 1 1/2
    5/4 1 1/4
    5/3 1 2/3
    7/3 2 1/3
    4/3 1 1/3
    7/2 3 1/2
    8/3 2 2/3
    11/6 1 5/6
    20/3 6 2/3
    5/2 2 1/2
    7/5 1 2/5
    11/5 2 1/5
    11/3 3 2/3
    12/5 2 2/5
    13/8 1 5/8
    11/2 5 1/2
    11/4 2 3/4
    9/2 4 1/2
    8/5 1 3/5
    16/3 5 1/3
    13/12 1 1/12
    16/5 3 1/5
    9/8 1 1/8
    10/3 3 1/3
    16/12 1 1/3
    22/4 5 1/2
    22/6 3 2/3
    22/9 2 4/9
    12/9 1 1/3
    16/6 2 2/3
    10/6 1 2/3
    10/9 1 1/9
    9/7 1 2/7
    9/6 1 1/2
    20/8 2 1/2
    12/6 2
    24/4 6
    24/3 8
    12/10 1 1/5
    20/12 1 2/3
    23/16 1 7/16
    25/16 1 9/16
    27/16 1 11/16

    Applications

    Real-World Uses of Mixed Numbers

    Mixed numbers show up anywhere a measurement runs past a whole unit.

    Recipe Scaling

    A recipe calls for 2 1/4 cups of flour and serves 4 people. Doubling it for 8 people needs 2 1/4 × 2 = 4 1/2 cups.

    Carpentry Measurement

    A shelf board measures 32 5/8 inches (82.9 cm). Cutting two equal shelves from it means dividing by 2: 32 5/8 ÷ 2 = 16 5/16 inches (41.4 cm) each.

    Concrete Mixing Ratio

    A concrete mix ratio calls for 1 3/4 parts cement to 3 1/2 parts sand. Tripling the batch needs 1 3/4 × 3 = 5 1/4 parts cement.

    Medication Dosing

    A liquid medication dose is 1 1/2 teaspoons (7.5 mL) every 8 hours. Three doses in a day total 1 1/2 × 3 = 4 1/2 teaspoons (22.5 mL).

    Fabric and Sewing Measurement

    A skirt pattern needs 1 5/8 yards (1.49 m) of fabric per panel. Four panels need 1 5/8 × 4 = 6 1/2 yards (5.94 m).

    Fuel Blending

    A small engine fuel mix uses 2 1/2 gallons (9.46 L) of gasoline per 1/2 pint (0.24 L) of oil. Doubling the ratio gives 5 gallons (18.93 L) of gasoline and 1 pint (0.47 L) of oil.

    Questions

    Frequently Asked Questions

    12 questions not already answered in full above, grouped by topic.

    What is the difference between a mixed number and an improper fraction?

    A mixed number pairs a whole number with a proper fraction, while an improper fraction is a single fraction whose numerator is at least as large as its denominator. Both name the same quantity in two formats — 2 3/4 and 11/4 are equal. Mixed numbers read faster on a tape measure or in a recipe; improper fractions calculate faster, which is why every operation on this page converts to improper form before it does any arithmetic.

    What is a mixed numeral?

    A mixed numeral is another name for a mixed number: a whole number written beside a proper fraction, such as 2 3/4. Textbooks also call it a mixed fraction. All three terms mean exactly the same thing, and all three convert to an improper fraction the same way — multiply the whole number by the denominator, add the numerator, keep the denominator.

    Are mixed numbers integers?

    No. Integers are the whole numbers and their negatives (… −2, −1, 0, 1, 2 …) with no fractional part. A mixed number always carries a nonzero proper fraction, so 2 3/4 sits between 2 and 3 and never lands on an integer. Mixed numbers are rational numbers: every one of them can be written as a ratio of two integers, such as 11/4.

    Is a mixed number a type of fraction?

    Yes — a mixed number is a fraction written in compact form. The space between the parts of 2 3/4 stands for addition, so 2 3/4 means 2 + 3/4, which equals the single fraction 11/4. Because every mixed number rewrites as one numerator over one denominator, mixed numbers sit inside the rational numbers alongside proper and improper fractions.

    More tools

    Related Tools

    Improper Fraction Converter

    Turn any mixed number into an improper fraction instantly.

    Decimal Converter

    Switch between mixed numbers and decimals in both directions.

    Simplify Fractions Calculator

    Reduce any fraction to its lowest terms using the GCF.

    Mixed Number Addition

    Add two mixed numbers with full step-by-step working.

    Mixed Number Subtraction

    Subtract mixed numbers, including borrowing cases.

    Mixed Number Multiplication

    Multiply mixed numbers with cross-simplification shown.

    Mixed Number Division

    Divide mixed numbers using the reciprocal method.

    Equivalent Fractions Finder

    Find equal fractions at any denominator.

    Least Common Denominator Calculator

    Find the LCD for two or more fractions.

    Worked Examples Library

    Browse solved mixed number problems by type.

    Fraction Converter

    Convert between fractions, mixed numbers, and percents.