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Mixed Number Calculator

Operation

Multiplying Mixed Numbers

Multiply two mixed numbers or plain fractions and watch the result, and the full working, update as you type. This calculator converts both values to improper fractions, multiplies the numerators and denominators, and simplifies the product — 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 Multiplying Fractions Formula

    Multiplying fractions formula

    a/b × c/d = (a×c) / (b×d)

    Notice what's missing: no shared denominator, no rewriting either fraction first. Addition and subtraction need matching piece sizes because they combine numerators directly, but multiplication combines the numerators together and the denominators together as two independent products. b and d can be any two numbers at all — the formula never cares whether they match.

    Method

    Multiplying Mixed Numbers Step by Step

    Worked Example — 2 1/2 × 1 1/3

    Convert both mixed numbers to improper fractions first, then multiply straight across.

    1. Convert to improper fractions

      2 1/2 → 5/2, and 1 1/3 → 4/3

    2. Multiply the numerators

      5 × 4 = 20

    3. Multiply the denominators

      2 × 3 = 6

    4. Simplify the product

      20/6 → GCF 2 → 10/3

    5. Convert back to a mixed number

      10/3 = 3 1/3

    2 1/2 × 1 1/3 = 3 1/3

    Shortcut

    Cross-Simplifying Before You Multiply

    Worked Example — 18/5 × 25/6

    Before multiplying straight across, check whether a numerator shares a common factor with the opposite denominator — dividing both down first keeps the numbers small.

    1. Compare each numerator with the opposite denominator

      18 and 6 share a GCF of 6  ·  5 and 25 share a GCF of 5

    2. Divide diagonally by each GCF

      18÷6 = 3, and 6÷6 = 1  ·  25÷5 = 5, and 5÷5 = 1

    3. Multiply the reduced fraction straight across

      3/1 × 5/1 = 15/1

    4. Read off the product

      15

    18/5 × 25/6 = 15

    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
    Each numerator cancels diagonally against the opposite denominator before the straight-across multiplication ever happens.

    Common Confusion

    Why Multiplying Two Fractions Can Give a Smaller Answer

    Everyday experience with whole numbers trains most people to expect multiplication to make things bigger — 3 × 4 is bigger than either 3 or 4. That expectation quietly breaks the moment both factors are proper fractions, and it's one of the most common sources of doubt when a calculator result looks "too small" to be right.

    Multiplying by a fraction less than one means taking a fractional part of a fractional part — asking for half of two-thirds, rather than adding a whole half onto a whole two-thirds. A part of a part is always smaller than the piece it was taken from, so the product ends up smaller than both of the original values, not larger.

    1. Set up the multiplication

      1/2 × 2/3

    2. Read it as "a part of a part"

      half of two-thirds

    3. Multiply straight across

      (1×2)/(2×3) = 2/6

    4. Simplify

      2/6 → 1/3

    1/2 × 2/3 = 1/3, smaller than both 1/2 and 2/3

    Common Mistakes

    Where Multiplication Calculations Go Wrong

    More Examples

    A Few More Worked Multiplications

    Two proper fractions

    3/4 × 2/3 = 1/2

    The 3 in the first numerator cancels the 3 in the second denominator before multiplying.

    Mixed number times a whole number

    2 1/3 × 4 = 9 1/3

    4 is treated as 4/1, so 7/3 × 4/1 = 28/3 = 9 1/3.

    Two mixed numbers

    1 1/2 × 2 1/4 = 3 3/8

    3/2 × 9/4 = 27/8, which converts to 3 3/8.

    Squaring a fraction

    3/4 × 3/4 = 9/16

    Multiplying a proper fraction by itself always shrinks it further.

    Large denominators, cross-simplified

    8/9 × 3/4 = 2/3

    8 and 4 share a GCF of 4, and 9 and 3 share a GCF of 3, before multiplying.

    Recipe scaling

    1 1/2 × 3 = 4 1/2

    Tripling a recipe that calls for 1 1/2 cups of an ingredient.

    Questions

    Frequently Asked Questions

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

    Why don't I need a common denominator to multiply fractions?

    A common denominator only matters when numerators are being added or subtracted, because the denominator names the size of each piece and pieces of different sizes can't be combined directly. Multiplication never combines numerators that way — it multiplies the numerators together and the denominators together as two separate products, so mismatched piece sizes are never an issue. 1/2 × 1/3 = 1/6 works with no rewriting at all, regardless of how different 2 and 3 are.

    How do I multiply a mixed number by a plain whole number?

    Treat the whole number as a fraction with a denominator of 1, then multiply as usual. For 3 × 2 1/4, convert 2 1/4 to the improper fraction 9/4, write 3 as 3/1, and multiply straight across: (3×9)/(1×4) = 27/4, which simplifies to 6 3/4. The whole number never needs its own separate step.

    Why does multiplying two proper fractions give an answer smaller than either one?

    Multiplying by a fraction less than 1 means taking a fractional part of a fractional part, and a part of a part is always smaller than the piece you started with. 1/2 × 2/3 asks for half of two-thirds, and half of anything less than a whole is smaller than that thing — the result, 1/3, is smaller than both 1/2 and 2/3. This only feels surprising because addition and everyday counting train us to expect operations to make numbers grow.