Fraction Calculator: Solve Fractions Step by Step

Add, subtract, multiply or divide fractions and mixed numbers. You get the simplified answer, the decimal value and every step of the working. Free, with no signup.

Fraction 1
Fraction 2
Whole = the big number in front (e.g. 2 in 2 1/3) Numerator = top number Denominator = bottom number

Answer

Step-by-step solution

    Tip: leave the Whole box empty for a simple fraction like 3/4. To enter only a whole number, fill in just the Whole box. Press Enter to calculate.

    How to Use the Fraction Calculator

    This fraction calculator handles four operations: addition, subtraction, multiplication and division. It accepts proper fractions, improper fractions, mixed numbers and whole numbers.

    01 Enter the first fraction

    Type the numerator in the upper box and the denominator in the lower box. For a mixed number like 2 1⁄2, put the 2 in the whole-number box.

    02 Pick the operation

    Choose +, −, × or ÷.

    03 Enter the second fraction

    Enter the second fraction the same way.

    04 Press Calculate

    You get a step-by-step solution and get the final answer in simplified fraction, mixed number, decimal, or percent.

    Negative fractions: type the minus sign in front of the numerator or the whole number. A negative fraction carries one sign, written in front (−3/4).

    A denominator of 0 is not allowed, because no fraction can split a whole into zero parts.

    For homework, solve the problem on paper first and use the online fraction calculator to check it. If your answer differs, compare your working line by line with the steps.

    What Is a Fraction?

    A fraction is a number that names equal parts of a whole. It is written as a/b. The numerator and denominator tell that in how many equal parts a whole number is divided. The fraction tells you how many of those parts you have. In 3/8, the whole has 8 equal parts and you have 3.

    A fraction is one way of writing a rational number. The value 1.5 can be written as the fraction 3/2. The denominator can never be 0.

    Type

    Rule

    Example

    Proper fraction

    Numerator smaller than denominator

    3/4

    Improper fraction

    Numerator equal to or larger than denominator

    7/3

    Mixed number

    Whole number plus a proper fraction

    2 1⁄3

    Unit fraction

    Numerator is 1

    1/5

    Mixed Numbers Fraction Calculator

    A mixed number combines a whole number and a proper fraction, such as 4 2⁄3. Use the fraction calculator mixed number input when your problem includes values like these.

    Mixed to improper:

    (whole × denominator + numerator) / denominator

    Example: 2 3⁄4 → (2 × 4 + 3)/4 = 11/4

    Improper to mixed: divide the numerator by the denominator. The quotient is the whole number and the remainder becomes the new numerator. Example: 17/5 → 17 ÷ 5 = 3 remainder 2 → 3 2⁄5

    Two notation traps catch a lot of students:

    • 2 1⁄2 means 2 + 1/2, not 2 × 1/2. The space between the parts stands for addition.
    • A minus sign applies to the whole mixed number. −2 3⁄4 means −(2 + 3/4) = −11/4.

    Simplify Fractions Calculator

    A fraction is in simplest form, also called lowest terms, when its numerator and denominator have no common factor other than 1. Each fraction has exactly one simplest form, so 12/16, 9/12 and 6/8 all reduce to 3/4.

    To simplify a single fraction with this tool, open the Simplify Fractions tab and enter your fraction only.

    Improper fractions simplify too: 22/8 = 11/4, which is 2 3⁄4 as a mixed number. For a negative fraction, simplify the numbers and keep one minus sign in front: −18/24 = −3/4.

    Steps to Simplify a Fraction

    1. Find the GCF (greatest common factor) of the numerator and denominator. This is the largest number that divides both evenly.
    2. Divide both numbers by the GCF.
    3. Check: if the new numerator and denominator share no factor other than 1, the fraction is in simplest form.

    (a ÷ GCF) / (b ÷ GCF)

    Example: 18/24. Factors of 18 are 1, 2, 3, 6, 9, 18. Factors of 24 include 1, 2, 3, 4, 6, 8, 12, 24. The GCF is 6, so 18 ÷ 6 = 3 and 24 ÷ 6 = 4. Answer: 3/4.

    Reducing Equivalent Fractions with the Fraction Calculator

    Equivalent fractions have the same value but different numbers, like 1/2, 2/4 and 4/8. You make one by multiplying or dividing the numerator and denominator by the same non-zero number:

    a/b = (n × a)/(n × b)

    Reducing moves toward smaller numbers (12/16 → 3/4). Raising to higher terms goes the other way, and you’ll need it to build common denominators: 3/4 → 24/32 by multiplying both parts by 8 (32 ÷ 4 = 8).

    How Do I Reduce a Fraction to Lowest Terms?

    Divide the numerator and denominator by their greatest common factor. When the two numbers share no factor except 1, the fraction is in lowest terms. For 36/48, the GCF is 12, so 36 ÷ 12 = 3 and 48 ÷ 12 = 4, giving 3/4.

    If finding the GCF feels hard, use prime factorization. Write both numbers as products of primes and cancel the pairs they share:

    6/18 = (2 × 3)/(2 × 3 × 3) = 1/3

    Cancel only factors that are multiplied, never terms that are added.

    What Is the Fastest Way to Simplify a Fraction?

    For small numbers, find a common factor. For most fractions, divide once by the greatest common factor. For large numbers, find the GCF, which needs very few steps. The fastest method is our fraction calculator, which does that work for you.

    The best method depends on the size of the numbers:

    Numbers

    Fastest method

    Example

    Small

    Spot a shared factor

    4/8 → 1/2

    Medium

    Divide by the GCF once

    36/48 → 3/4

    Large

    Euclidean algorithm

    1071/462 → 51/22

    Decimal to Fraction Calculator

    Enter a decimal and the fraction calculator returns it as a fraction in simplest form.

    Terminating decimals (they stop): write the digits over the matching power of 10, then simplify.

    0.375 → 375/1000 → ÷ 125 → 3/8

    Repeating decimals: a digit or group repeats forever. For these, use a little algebra.

    Fraction to Decimal Calculator

    To turn a fraction into a decimal, divide the numerator by the denominator: 3/8 = 3 ÷ 8 = 0.375. The decimal of any fraction either stops or repeats a pattern.

    You can tell which one you’ll get before dividing. Reduce the fraction to lowest terms, then factor the denominator. If its only prime factors are 2 and 5, the decimal terminates. Any other prime factor means it repeats.

    Fraction

    Denominator factors

    Decimal

    7/40

    2 × 2 × 2 × 5

    0.175 (stops)

    5/12

    2 × 2 × 3

    0.41666… (repeats)

    3/6 = 1/2

    2

    0.5 (stops)

    Reduce first. 3/6 has a factor of 3 in its denominator, yet it equals 1/2, which terminates.

    A repeating block can be up to one digit shorter than the denominator. 1/7 repeats every 6 digits, and 1/97 repeats every 96. That’s why a fraction calculator shows a rounded decimal for fractions like these, while the fraction form stays exact.

    How to Add Fractions

    You can only add parts that are the same. The rule depends on the denominators: if they match, add straight away. If not, rewrite the fractions with a common denominator first.

    Check your answer with a quick step. A sum of two positive fractions must be bigger than each one.

    Adding Fractions with the Same Denominator

    Fractions with the same denominator are called like fractions. Add the numerators and keep the denominator.

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

    The denominator stays because it is the same number of equal parts. 3/8 + 7/8 means 3 eighths plus 7 eighths, which is 10 eighths. The unit is still eighths.

    Both fractions must refer to the same whole.

    Adding Fractions with Different Denominators

    When the denominators differ, rewrite both fractions over the least common denominator (LCD), which is the least common multiple (LCM) of the denominators.

    1. Find the LCD.
    2. Rewrite each fraction with that denominator, multiplying its top and bottom by the same number.
    3. Add the numerators and simplify.

    Two shortcuts for finding the LCD:

    • If the larger denominator is a multiple of the smaller, it is the LCD. For 2/5 + 3/10, the LCD is 10.
    • If the denominators share no common factor, multiply them. For 1/3 + 2/5, the LCD is 15: 5/15 + 6/15 = 11/15.

    Multiplying the denominators always works (a/b + c/d = (ad + bc)/bd), but it isn’t always the least one. For 3/4 + 5/6 it gives 38/24, which you then have to reduce to 19/12.

    Adding Mixed Numbers

    Add the whole numbers, add the fractions, then combine. If the fraction part comes out improper, carry the extra whole.

    9 5⁄9 + 5 7⁄9 = 14 12⁄9 → 12/9 = 1 3⁄9 → 15 3⁄9 = 15 1⁄3

    With different denominators, find the LCD first:

    2 1⁄2 + 5 2⁄3 = 2 3⁄6 + 5 4⁄6 = 7 7⁄6 = 8 1⁄6

    Alternative: convert both to improper fractions, add, then convert back.

    3 7⁄8 + 4 3⁄8 = 31/8 + 35/8 = 66/8 = 8 1⁄4

    Both methods give the same answer, so choose the one that keeps your numbers smaller.

    How to Subtract Fractions

    Subtraction follows the same denominator rule as addition. Like fractions subtract straight away. Unlike fractions need a common denominator first.

    The difference is that order matters. 3/5 − 1/5 is 2/5, but 1/5 − 3/5 is −2/5. When you take a larger fraction from a smaller one, the answer is negative, and the fraction calculator shows it with a single minus sign in front.

    Subtracting Fractions with the Same Denominator

    Subtract the numerators and keep the denominator.

    a/b − c/b = (a − c)/b

    Think of it as steps back on a number line. Start at 7/8 and step back 3/8:

    7/8 − 3/8 = 4/8 = 1/2

    Always finish by simplifying. 4/8 is correct but not in simplest form.

    Subtracting Fractions with Different Denominators

    Rewrite both fractions over the LCD, then subtract the numerators.

    a/b − c/d = (ad − bc)/bd

    A negative result works the same way. 1/3 − 3/4 = 4/12 − 9/12 = −5/12. Keep a single minus sign in front of the fraction.

    Subtracting Mixed Numbers

    When the first fraction part is at least as large as the second, subtract the fractions, then the whole numbers. When it’s smaller, you borrow first.

    Borrowing, step by step

    1. Compare the fraction parts. If the top one is smaller, take 1 from its whole number.
    2. Add that 1 to the fraction as a full set of parts.
    3. Subtract the fractions, then the whole numbers.
    4. Simplify.

    The fraction calculator handles borrowing behind the scenes.

    How to Multiply Fractions

    Multiplication is the one operation where you never need a common denominator. Multiply straight across and simplify.

    The result surprises many students. Multiplying by a fraction smaller than 1 makes a number smaller. Multiplying by a fraction greater than 1 makes it bigger.

    Multiplying Fractions Rule

    (a/b) × (c/d) = (a × c)/(b × d)

    Multiply the numerators, multiply the denominators, then simplify. The same rule covers three or more fractions.

    Cancel first to keep numbers small. Any numerator can cancel with any denominator before you multiply.

    Never cancel two numerators against each other. The fraction calculator always returns the product in lowest terms.

    Multiplying Mixed Numbers

    Convert each mixed number to an improper fraction, multiply, then simplify and convert back.

    When one factor is a whole number, multiply it by each part of the mixed number and add the results:

    3 × 2 1⁄2 = (3 × 2) + (3 × 1/2) = 6 + 3/2 = 7 1⁄2

    That matches the improper method. For two mixed numbers, stick with improper fractions. A fraction calculator converts the inputs for you and gives the final product in lowest terms.

    Multiplying a Fraction by a Whole Number

    Multiply the whole number by the numerator and keep the denominator.

    n × (a/b) = (n × a)/b

    A common method is multiplying the denominator too: 3 × 2/5 → 6/15. But 6/15 reduces to 2/5, the fraction you started with, so nothing got multiplied.

    How to Divide Fractions

    Dividing by a fraction asks how many times it fits.

    You can check any division by multiplying back. 2/3 ÷ 3/4 = 8/9 is right because 3/4 × 8/9 = 2/3. The answer can get bigger because 3/4 ÷ 1/2 asks how many halves fit in three quarters. One half fits, plus half of another half, so the answer is 3/2 (1 1⁄2). Dividing by a number smaller than 1 always gives a result larger than the number you started with.

    Dividing Fractions Rule

    Multiply the first fraction by the reciprocal of the second.

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

    You can remember this as Keep, Change, Flip: keep the first fraction, change ÷ to ×, and flip the second fraction. Only the second fraction (the divisor) gets flipped.

    Case

    Example

    Fraction ÷ fraction

    2/3 ÷ 3/4 = 2/3 × 4/3 = 8/9

    Fraction ÷ whole number

    2/3 ÷ 10 = 2/3 × 1/10 = 2/30 = 1/15

    Whole number ÷ fraction

    3 ÷ 1/2 = 3/1 × 2/1 = 6

    The divisor can never be 0, because 0 has no reciprocal.

    What Is a Reciprocal?

    The reciprocal of a number is the value you multiply it by to get 1. For a fraction, swap the numerator and denominator: the reciprocal of 3/7 is 7/3. Convert a mixed number to an improper fraction before flipping it.

    A negative number keeps its sign, because the product with its reciprocal has to be positive 1.

    To check a reciprocal, multiply: 3/7 × 7/3 = 1.

    Dividing Mixed Numbers

    1. Convert both mixed numbers to improper fractions.
    2. Multiply the first by the reciprocal of the second.
    3. Simplify and convert back if needed.

    Converting Fractions to Decimals and Percentages

    Percent means per hundred, so 30% is 30/100. That’s why you multiply by 100 to turn a fraction into a percent.

    • Fraction → percent: multiply by 100. 3/4 × 100 = 75%. You can also get the decimal first (0.75), then multiply by 100.
    • Percent → fraction: divide by 100 and simplify. 2.4% = 2.4/100 = 24/1000 = 3/125. And 0.25% = 1/400.

    Repeating decimals give percents that never end, so write them two ways. 1/3 is exactly 33 1⁄3%, and about 33.3% when rounded.

    Fraction

    Decimal

    Percent

    1/2

    0.5

    50%

    1/3

    0.333…

    33 1⁄3%

    1/4

    0.25

    25%

    1/5

    0.2

    20%

    1/8

    0.125

    12.5%

    2/3

    0.666…

    66 2⁄3%

    3/4

    0.75

    75%

    Common Fraction Mistakes and How to Fix Them

    The mistakes below come from the U.S. Department of Education’s practice guide on fractions instruction (IES, NCEE 2010-4039). Each row adds a quick check you can do without a calculator.

    Mistake

    Fix

    Quick check

    Adding tops and bottoms: 1/2 + 1/3 = 2/5

    Use the LCD: 3/6 + 2/6 = 5/6

    A sum must be bigger than each part. 2/5 is smaller than 1/2, so it’s wrong

    Thinking a bigger denominator means a bigger fraction (3/8 > 3/5)

    The denominator sets the part size. More parts means smaller parts

    Eighths are smaller than fifths, so 3/8 < 3/5

    Believing multiplying always makes things bigger

    Multiplying by a fraction less than 1 shrinks the number

    12 × 3/4 = 9, which is less than 12

    Treating 3/4 as two separate numbers and placing it between 3 and 4

    3/4 is a single number between 0 and 1

    Any proper fraction is less than 1

    Thinking nothing fits between 5/7 and 6/7

    Rewrite as 10/14 and 12/14

    11/14 sits between them

    Flipping the first fraction when dividing

    Flip only the divisor (the second fraction)

    Multiply the answer by the divisor. You should get the first fraction back

    Multiplying mixed numbers part by part

    Convert to improper fractions first

    2 1⁄4 × 1 1⁄3 is 3, not 2 1⁄12

    Cancelling numbers that are added, as in (3 + 6)/6

    Cancel only factors. Add first: 9/6 = 3/2

    Work out the top before you cancel

    The same guide recommends that students learn why each procedure works, not just steps. That’s the best way to use a fraction calculator for learning: work the problem yourself, then compare each line against the tool’s steps to find exactly where your working changed.

    Additional Features of the Fraction Calculator

    The fraction calculator shows step-by-step working, answers a simplified fraction, mixed number, plus its decimal and percent. It also includes three extra tools: Decimal to Fraction, Simplify Fractions, and Mixed Fractions.

    Each feature is there for a reason:

    • Step-by-step working lets you compare each line with your own work and find exactly where a mistake happened.
    • Several answer formats (simplified fraction, mixed number, decimal, percent) cover what different teachers and tasks expect.

    Edge cases we test. A fraction calculator earns trust on the tricky inputs. The expected column shows the correct math. The result column records what this tool returned.

    Input

    Correct answer

    Tool result

    3/0

    Undefined (denominator can’t be 0)

    Error: “The denominator (bottom number) of Fraction 1 cannot be 0.”

    1/2 ÷ 0

    Undefined (0 has no reciprocal)

    Error: “You cannot divide by zero (fraction 2 equals 0).”

    −2 3⁄4 + 1/2

    −2 1⁄4

    −9/4 = −2 1⁄4 ✓

    1/3 + 1/6

    1/2

    1/2 ✓

    1071/462 simplified

    51/22

    51/22 ✓

    1/97 as a decimal

    Repeats every 96 digits

    0.010309 (rounded to 6 decimal places)

    Real-Life Examples of Fraction Calculations

    The hard part of a real word problem is usually choosing the right method. In each example below, that choice comes first.

    Multiply

    Halving a recipe

    The recipe needs 2/3 cup of flour, and you’re making half. 2/3 × 1/2 = 1/3 cup. NIST recommends weighing ingredients rather than measuring by volume.

    Divide

    Counting servings

    How many 3/4-cup servings are in 2/3 cup of yogurt? 2/3 ÷ 3/4 = 8/9, so you have just under one serving.

    Subtract

    Trimming a board

    A board is 7/8 inch thick and you plane off 1/4 inch. 7/8 − 2/8 = 5/8 inch.

    Simplify and convert

    Test scores

    24 correct out of 30 is 24/30 = 4/5 = 80%.

    Frequently Asked Questions

    A proper fraction has a numerator smaller than its denominator, so its value is less than 1 (3/5). An improper fraction has a numerator equal to or larger than its denominator, so it equals 1 or more (7/4). Any improper fraction can be written as a mixed number: 7/4 = 1 3⁄4. A proper and improper fraction calculator handles both kinds.

    The numerator can be 0, and the fraction then equals 0 (0/5 = 0). The denominator can never be 0, because a whole can’t be split into zero parts. For the same reason you can’t divide by 0: zero has no reciprocal.

    Not always. Fractions like 1/3 have decimals that repeat forever, so any screen shows a rounded value. Computers also store most decimals only approximately, which is why 0.1 + 0.1 + 0.1 can show as slightly more than 0.3. The fraction form is the exact answer.

    Yes. Write one minus sign in front of the fraction or mixed number: −3/4 or −2 3⁄4. The sign applies to the whole value, so −2 3⁄4 equals −11/4.

    Yes. Find one LCD for all the denominators, rewrite each fraction over it, then add. For 1/4 + 1/6 + 1/2, the LCD is 12: 3/12 + 2/12 + 6/12 = 11/12.

    Use it to check work, not to replace it. The U.S. Department of Education’s fractions practice guide recommends that students understand why each procedure works.