Pick an operation in the Operation dropdown. The inputs below it change to match: two fractions, one number, or two mixed numbers. Learn more about choosing an operation
In Basic Fraction Operations, type each fraction as a numerator and a denominator in separate boxes, and pick add, subtract, multiply or divide in the middle dropdown. Learn more about basic fraction operations
The four conversion modes take one value: a decimal to turn into a fraction or mixed number, a fraction to turn into a decimal, or a mixed number to turn into a decimal. Learn more about converting
The mixed-number modes take each number as whole part, space, fraction, for example 1 1/2. A plain fraction such as 3/4 also works. Learn more about mixed numbers
Click Calculate. The result appears under the form in lowest terms; a message appears instead when an input is missing or invalid. Learn more about results and error messages
The top panel on the right explains the operation you picked. Its link opens the section below that explains that operation in full. Learn more about the explanation panels
The Step-by-Step panel appears as soon as the inputs are valid and shows the working for your own numbers. It updates as you type. Learn more about the step-by-step display
The fraction calculator has two main areas: a left panel for inputs and calculations, and a right sidebar showing explanations. Start by clicking the Operation dropdown at the top of the left panel. You'll see 10 different operations to choose from, including basic fraction math, decimal conversions, and mixed number operations.
After selecting an operation, the input fields change automatically to match what you need. For Basic Fraction Operations, you'll see two fractions with numerator and denominator boxes, plus an operation selector. For Convert Float to Fraction, you get a single decimal input box. For Add Mixed Numbers, you'll see two text inputs for mixed number format.
Enter your numbers in the appropriate fields. For fractions, type the numerator in the top box and denominator in the bottom box. For mixed numbers, use the format "1 1/2" (whole number, space, fraction). For decimals, type any number like 0.75 or 2.5.
Click the blue Calculate button to see your result appear in the result section below. The right sidebar updates with static explanations for the operation type, and when you enter valid inputs, step-by-step working appears showing exactly how the calculator solved your problem. Use Reset anytime to clear everything and start fresh.
Using Basic Fraction Operations
DemoAdd, multiply and divide two fractions
Step 0 of 5
Select Basic Fraction Operations from the dropdown to add, subtract, multiply, or divide two fractions. You'll see two fraction input areas, each with a numerator box on top and denominator box on bottom. Enter your first fraction's numbers, then choose your operation: Add (+), Subtract (−), Multiply (×), or Divide (÷).
Try adding 21+31. Enter 1 and 2 for the first fraction, select Add (+), then enter 1 and 3 for the second fraction. Click Calculate to see the result 65. The step-by-step section shows how the calculator found the common denominator (2×3=6), converted both fractions, and added the numerators.
For multiplication like 32×43, you don't need common denominators. The calculator multiplies numerators together (2×3=6) and denominators together (3×4=12), giving 126, which simplifies to 21.
Division works by flipping the second fraction. When you calculate 21÷41, the calculator flips 41 to 14, then multiplies: 21×14=24=2. Watch the step-by-step display to see this reciprocal process in action.
The calculator offers four conversion modes for switching between decimal and fraction formats. Convert Float to Fraction changes decimals like 0.75 into fractions (43). Enter any decimal, click Calculate, and see both the fraction result and the step-by-step conversion showing how decimal places become the denominator.
Try converting 0.625 to a fraction. The calculator counts 3 decimal places, creates 1000625 by multiplying by 103, then simplifies by finding the greatest common divisor. The result is 85.
Convert Fraction to Decimal does the opposite. Select this mode, enter a fraction like 83, and the calculator divides 3÷8=0.375. The result appears immediately with the division shown step-by-step.
Convert Float to Mixed Number and Convert Mixed Number to Float work with mixed numbers. Enter 2.75 and get 243, or enter "1 1/2" to get 1.5. The mixed number format requires a space between the whole number and fraction: type "1 1/2" not "11/2". The calculator separates the parts and shows you each conversion step.
Four operations handle mixed numbers specifically: Add Mixed Numbers, Subtract Mixed Numbers, Multiply Mixed Numbers, and Divide Mixed Numbers. Select any of these modes to see two text input boxes asking for mixed numbers in the format "whole fraction" like "1 1/2" or "2 3/4".
When adding mixed numbers like 121+241, type "1 1/2" in the first box and "2 1/4" in the second. The calculator converts both to improper fractions (23 and 49), finds a common denominator, adds them, and converts back to mixed number form. The result 343 appears with every conversion step shown.
You can also use regular fractions in mixed number operations. Type "3/4" instead of a mixed number and the calculator treats it as 043. This works for all four mixed operations—the format accepts both "1 1/2" and "3/2" interchangeably.
For division like 321÷141, enter "3 1/2" and "1 1/4". The step-by-step shows conversion to improper fractions (27÷45), flipping the second fraction (54), multiplying, and simplifying. Watch how the calculator handles each transformation clearly.
The right sidebar contains two explanation panels. The top panel shows a static description of the current operation—what it does and when to use it. This text updates whenever you change the operation dropdown. Read this first to understand what calculation you're about to perform.
The bottom panel, labeled Step-by-Step, appears only after you enter valid inputs. This dynamic section shows exactly how the calculator solves your specific problem. For adding fractions, you'll see steps like "Find common denominator → 2 × 3 = 6" followed by "Convert fractions" with the actual numbers from your input.
Each step uses mathematical notation to show formulas. When adding 21+31, the steps display: Step 1 finds the common denominator 6, Step 2 shows 21=63 and 31=62, Step 3 adds numerators 3+2=5, and Step 4 shows the result 65.
The step-by-step updates in real-time as you type. Change any number in your input, or the operation in the middle dropdown, and watch the explanation adjust instantly: 32+43 becomes 128+129=1217, and with subtraction 128−129=−121. This feature helps you learn the process, not just get an answer. Follow along with your own paper to verify each calculation step matches the mathematical rules for that operation.
The top panel ends with a Learn more link. It jumps to the section below that explains the chosen operation, such as adding fractions.
Reading Results and Error Messages
DemoError messages and Reset
Step 0 of 4
After clicking Calculate, your result appears in the Result section between the input form and sidebar. The answer displays in large, clear text using proper fraction notation. For fraction results, you'll see the numerator over a horizontal line over the denominator. For decimal results, you get a standard number like 0.75 or 1.5.
The calculator automatically simplifies all fraction results. If you add 42+41, you won't see 43 written as 86—the calculator finds the greatest common divisor and reduces to simplest form. Mixed numbers appear as "whole number fraction" format when appropriate.
Red error messages appear above the result area when inputs are invalid; they are checked on this page before anything is sent, so a bad input never reaches the server. "Please enter a valid numerator" means you left a fraction box empty or typed non-numeric characters. "Denominator cannot be zero" prevents division by zero errors. "Please enter a valid mixed number" reminds you to use the correct format like "1 1/2" with a space.
Orange validation errors appear for mathematical impossibilities like dividing by zero. If you try 21÷10, you'll see "Cannot divide by zero" in orange. The calculator won't process the calculation until you fix the error. Simply correct your input and the error disappears when you click Calculate again.
What Are Fractions
A fraction represents part of a whole. It has two numbers: the numerator (top) shows how many parts you have, and the denominator (bottom) shows how many equal parts make the whole. In 43, you have 3 parts out of 4 total equal parts.
Think of a pizza cut into 8 slices. If you eat 3 slices, you ate 83 of the pizza. The denominator (8) is the total slices, and the numerator (3) is how many you took. Fractions let you describe quantities between whole numbers precisely.
Proper fractions have numerators smaller than denominators: 21, 43, 85. These represent values less than 1. Improper fractions have numerators equal to or greater than denominators: 45, 37, 88. These equal 1 or more.
For more detailed fraction theory and visual representations, see fractions fundamentals and fraction visualization tools.
Fraction Operations Explained
Adding and subtracting fractions requires a common denominator. You can't add 21+31 directly because the pieces are different sizes. Find a common denominator (usually by multiplying denominators: 2×3=6), convert both fractions (21=63 and 31=62), then add numerators: 63+62=65.
Multiplying fractions is simpler—multiply numerators together and denominators together. For 32×54, calculate 2×4=8 (numerator) and 3×5=15 (denominator) to get 158. No common denominator needed.
Dividing fractions uses the "flip and multiply" rule. To divide 21÷41, flip the second fraction to 14 (the reciprocal), then multiply: 21×14=24=2. This works because dividing by a fraction is the same as multiplying by its reciprocal.
Simplifying means reducing to lowest terms by dividing both numerator and denominator by their greatest common factor. The fraction 86 simplifies to 43 because both 6 and 8 divide by 2. For comprehensive fraction operation rules, see fraction arithmetic concepts.
Adding Fractions
Fractions can be added only when they count pieces of the same size, so the first job is a common denominator. Multiplying the two denominators always gives one: for 21+31 it is 2×3=6. Each fraction is then rewritten over 6 by scaling its top and bottom by the same number: 21=63 and 31=62.
With equal denominators, add the numerators and keep the denominator: 63+62=65. Finish by reducing to lowest terms.
The common mistake is adding straight across: 21+31 is not 52. The denominator says what size the pieces are; it is never added.
Subtraction follows the same path as addition. Rewrite both fractions over a common denominator, subtract the numerators, keep the denominator, and simplify.
For 43−61, the product of the denominators is 24: 2418−244=2414=127. The least common denominator, 12, gives the same answer with smaller numbers: 129−122=127.
Order matters. 61−43 is −127, a negative result, because the second fraction is larger than the first.
To divide by a fraction, multiply by its reciprocal, the fraction turned upside down. For 21÷41, flip 41 to 14 and multiply: 21×14=24=2.
The answer makes sense: four quarters make a whole, so two quarters fit into one half.
Only the second fraction is flipped. Flipping the first instead gives 12×41=21, which is wrong. Dividing by a fraction with 0 on top is undefined, because 0 has no reciprocal.
A decimal with n digits after the point is a fraction over 10n. Write the digits over that power of ten, then reduce.
For 0.625 there are 3 decimal places, so 0.625=1000625. The greatest common divisor of 625 and 1000 is 125, and dividing both by it gives 85. In the same way, 0.75=10075=43.
Count the places carefully. 0.05 is 1005=201, not 105.
A typed decimal always ends, so 0.333 becomes 1000333, not 31. Only the exact repeating decimal equals 31.
A fraction is a division: the numerator divided by the denominator. 83=3÷8=0.375 and 41=0.25.
Some fractions give a decimal that repeats forever: 31=0.333… and 112=0.1818…. A fraction in lowest terms gives an ending decimal exactly when its denominator has no prime factors other than 2 and 5.
Decimals make fractions easy to compare. 85=0.625 is larger than 53=0.6, which is hard to see from the fractions alone.
The reciprocal, or multiplicative inverse, of a number x is x1. It is the number that multiplies with x to give 1.
For a whole number, the reciprocal is 1 over it: the reciprocal of 2 is 21=0.5. For a fraction, swap top and bottom: the reciprocal of 32 is 23. For a decimal, divide 1 by it: the reciprocal of 0.25 is 4.
The check is always the product: 0.25×4=1. Zero has no reciprocal, because nothing multiplied by 0 gives 1.
Reciprocals are what make fraction division work. See reciprocals.
Mixed Numbers vs Improper Fractions
A mixed number combines a whole number with a fraction: 241 means 2 whole units plus 41 of another unit. An improper fraction has a numerator larger than its denominator: 49. These two forms represent the same value—241=49.
Convert mixed numbers to improper fractions by multiplying the whole number by the denominator and adding the numerator. For 352, calculate 3×5=15, add 2 to get 17, so 352=517.
Convert improper fractions to mixed numbers by dividing numerator by denominator. For 311, divide 11÷3=3 remainder 2. The quotient (3) is the whole number, remainder (2) is the new numerator, original denominator stays: 311=332.
Use mixed numbers for measurements and real-world quantities like "221 cups of flour" or "I ran 343 miles." Use improper fractions for calculations—they're easier to add, multiply, and divide. The calculator handles both and converts between them automatically. See fraction types and fraction conversion methods for more details.
Adding Mixed Numbers
The reliable method is to convert each mixed number to an improper fraction, add, and convert back. 121+241=23+49=46+49=415=343.
When the fractions are small, you can also add the whole parts and the fraction parts separately: (1+2)+(21+41)=343. If the fraction parts add up to more than 1, carry the extra whole into the whole part.
The calculator uses the improper-fraction method, so its steps always have the same shape.
Convert both numbers to improper fractions, subtract over a common denominator, and convert back. 341−121=413−23=413−46=47=143.
Subtracting the parts separately is where most errors happen. Here 41−21 is negative, so a whole must be borrowed first: 341=245. The improper-fraction method avoids borrowing completely.
Always convert to improper fractions first, then multiply the tops and the bottoms. 121×232=23×38=624=4.
Multiplying the parts separately gives the wrong answer: 1×2+21×32=231, not 4. Each part of the first number has to multiply each part of the second.
Cancelling before multiplying works here too: the 3s cancel, leaving 21×18=4.
Fractions Visualizer - See fractions as visual shapes and diagrams. Watch how 21+41 combines graphically, making abstract fraction operations concrete and understandable.
Percentage Calculator - Convert between fractions, decimals, and percentages. The fraction 43 equals 75%, and understanding these relationships helps with real-world applications.
GCD Calculator - Find the greatest common divisor for simplifying fractions. If you need to reduce 3624, find GCD(24,36)=12 and divide both parts by 12 to get 32.
LCM Calculator - Calculate the least common multiple for finding common denominators. To add 61+81, find LCM(6,8)=24 as your common denominator.
Ratio Calculator - Work with ratios, which are closely related to fractions. The ratio 3:4 is the same as the fraction 43.