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Mixed Number Calculator

Operation

Adding Mixed Numbers

Add two mixed numbers or plain fractions and watch the result, and the full working, update as you type. This calculator handles matching denominators, finding the LCD when they differ, carrying a whole unit when the fractions add past one, and simplifying the final answer — all in real time, no button required.

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

    Formula

    The Adding Fractions Formula

    Adding fractions formula

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

    This single formula always works, whatever the denominators are, because multiplying each fraction by the other's denominator (top and bottom) rewrites both over the same shared denominator, bd, before adding. It's the same result you'd get from finding the LCD by hand — the formula just automates that step.

    Method

    Adding Fractions with the Same Denominator

    Worked Example — 2 1/8 + 3 5/8

    When the denominators already match, add the whole numbers and the numerators separately.

    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

    Method

    Adding Fractions with Different Denominators

    Worked Example — 4 2/3 + 1 1/2

    Different denominators need a shared denominator first — the least common multiple of the two.

    1. Find the LCD

      of 3 and 2: 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

    MULTIPLES OF 3 3 6 9 12 MULTIPLES OF 2 2 4 6 8
    Multiples of 3 and 2, with the first shared value circled — that's the LCD.

    Method

    Adding Mixed Numbers Using the Improper Fraction Method

    Worked Example — 1 2/6 + 2 1/4

    Converting both values to improper fractions first lets one formula handle the whole problem in a single pass.

    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) = 86/24

    3. Simplify with the GCF

      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

    Special Case

    Adding Negative Mixed Numbers

    A negative mixed number carries its sign across the whole value. Convert to an improper fraction first and the sign travels through the formula untouched.

    1. Convert to an improper fraction

      −2 3/4 = −11/4, since the sign applies to the full amount

    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

    Choosing a Method

    Same-Denominator Method vs. Improper Fraction Method

    Both methods on this page always agree — they're the same arithmetic organised two different ways. Adding the whole numbers and fractions separately tends to be faster by hand for small numbers, because the whole-number addition is trivial and only the fraction part needs real attention. It's also the method most people are taught first, so it tends to feel more intuitive.

    The improper fraction method trades that intuition for consistency: converting first means there's exactly one formula to apply, with no separate carrying step and no risk of forgetting to add the whole numbers. It scales better to larger, messier numbers and to problems mixed in with multiplication or division, where everything needs to be in improper form anyway.

    A practical rule of thumb: use the same-denominator method when the whole numbers are small and the denominators are simple, like 2 1/8 + 3 5/8. Switch to the improper fraction method once a problem involves negative values, since converting first lets the sign travel through the formula automatically instead of requiring a separate borrowing step.

    Either way, the calculator above always shows both the direct result and the full working, so you can check your own by-hand method against it regardless of which approach you used.

    More Examples

    A Few More Worked Additions

    Same denominator

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

    7/5 is improper, so it carries into one whole unit plus 2/5.

    Different denominators

    1/2 + 1/3 = 5/6

    LCD of 2 and 3 is 6: 3/6 + 2/6 = 5/6.

    Three whole numbers involved

    3 3/4 + 2 1/4 = 6

    3/4 + 1/4 = 1 whole exactly, so the result is a clean whole number.

    Whole number plus a fraction

    5 + 3/4 = 5 3/4

    A whole number is a mixed number with 0/1 as its fraction part.

    Large denominators

    7/12 + 5/8 = 1 5/24

    LCD of 12 and 8 is 24: 14/24 + 15/24 = 29/24 = 1 5/24.

    Recipe scaling

    2 1/4 + 2 1/4 = 4 1/2

    Doubling 2 1/4 cups of flour for a bigger batch.

    Questions

    Frequently Asked Questions

    Questions specific to adding fractions, not already covered elsewhere on the site.

    Why can't I just add numerators and denominators straight across?

    Because a denominator names the SIZE of each part, not a quantity to combine. Adding 1/2 + 1/3 straight across as 2/5 would claim that a half plus a third equals two fifths, which is false — 1/2 alone is already larger than 2/5. The parts have to be the same size (the same denominator) before the numerators can be added meaningfully.

    Do I need to convert to improper fractions to add mixed numbers?

    Not always. Adding the whole numbers and the fractions separately works fine and is usually faster by hand. Converting to improper fractions first is a single-formula alternative that some people find easier to keep track of — both methods always agree.

    What happens if the fraction parts add up to more than one whole?

    The fraction part carries into the whole-number part, the same way carrying works in ordinary addition. 4 2/3 + 1 1/2 adds the fractions to 7/6, which is more than one whole — so one whole unit carries over, leaving 4 + 1 + 1 = 6 and a leftover fraction of 1/6, for a final answer of 6 1/6.