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Β½ Fraction Calculator

Add, subtract, multiply, and divide fractions and mixed numbers

πŸ”’ 100% client-side processing

The Fraction Calculator does exact arithmetic on fractions β€” addition, subtraction, multiplication, and division β€” and shows each result reduced to lowest terms, with an optional mixed-number display and step-by-step working for plus and minus. It accepts what you actually have at hand: proper fractions like 3/4, improper ones like 7/4, mixed numbers like 1 3/4, decimals like 2.5, and plain integers. It is for checking math homework, scaling a recipe, adding fractional inch measurements, or turning a decimal into an exact fraction.

How to Use

  1. Enter both operands. Each field takes a fraction (7/4), a mixed number (1 3/4), a decimal (2.5), or an integer.
  2. Choose the operation: +, βˆ’, Γ—, or Γ·.
  3. Read the result. The answer is reduced automatically, so 6/8 is reported as 3/4.
  4. Toggle improper or mixed display depending on whether you are working in algebra or in measurements; 7/4 and 1 3/4 are the same value, and the tool shows whichever helps.
  5. Open Show Steps for addition and subtraction to see the common denominator and the converted numerators.

Worked Examples

Example 1 β€” adding unlike denominators. 1/2 + 3/4. The common denominator is 4, so 1/2 becomes 2/4, and 2/4 + 3/4 = 5/4. The steps panel shows exactly that re-expression, which is the part a student needs to check β€” the final 5/4 is easy, the conversion is where mistakes happen.

Example 2 β€” multiplying a mixed number. 1 3/4 Γ— 2/3. The mixed number becomes the improper fraction 7/4, multiplication across gives 14/12, and reduction by the greatest common divisor yields 7/6, shown as 1 1/6 in mixed display.

Example 3 β€” a decimal that hides an exact fraction. A measurement reads 0.375 inches. Entered as a decimal, it converts to 3/8 β€” the exact value a tape measure is showing. This is the case where converting to a fraction beats keeping the decimal: 3/8 can be located on a ruler immediately, while 0.375 cannot.

How the Math Works

Addition and subtraction need a common denominator. The tool takes the least common multiple of the two denominators, scales each numerator accordingly, performs the operation, and then reduces the result with the greatest common divisor. Multiplication is direct β€” numerator times numerator, denominator times denominator β€” followed by the same reduction. Division multiplies by the reciprocal of the second operand.

Decimal inputs take a different route. The continued-fractions algorithm repeatedly approximates the decimal, each step producing a better simple fraction. It stops when further refinement would need a denominator above 10,000, or when the fraction matches exactly. The result is the nearest human-plausible fraction, which is why 0.333 is treated as 1/3 and not 333/1000.

Reduction matters for more than tidiness. Working with 7/6 instead of 14/12 makes the next operation smaller and reduces the chance of arithmetic slips when a problem has several steps.

Input Formats It Accepts

  • Proper and improper fractions: 3/4, 7/4, 123/4567.
  • Mixed numbers: 1 3/4 β€” a whole number, a space, then the fraction.
  • Decimals: 2.5, 0.375, 3.14159 (converted to the closest simple fraction).
  • Integers: 2, βˆ’5 (treated as 2/1, βˆ’5/1).
  • Negative values: a leading minus sign on any of the above.

If a value is not recognized, the tool reports it rather than guessing, so a typo like 1/2/3 is flagged instead of silently misread.

Common Mistakes

  • Splitting a mixed number without realising. 1 3/4 is one value, not 1 Γ— 3/4. The space matters; entering 13/4 gives a different number entirely.
  • Rounding a decimal too early. Enter 0.333 and you get 1/3, which is more accurate than 333/1000 for the intended value β€” but if you genuinely meant the exact decimal, note that the conversion approximates.
  • Forgetting to reduce by hand when checking. Teachers usually require the lowest terms; the calculator’s output is a reliable reference.
  • Dividing by zero. It is undefined, and the tool reports an error. Test expressions with a zero denominator deliberately to see that behavior.
  • Mixing units silently. Adding 1/2 inch to 3/4 centimetre gives a mathematically correct fraction of mixed units, which is rarely what you want β€” convert to one unit first.

Features

  • Add, subtract, multiply, and divide two fractions exactly
  • Accepts fractions, mixed numbers, decimals, and integers
  • Automatic reduction to lowest terms via GCD
  • Toggle between improper fraction and mixed number display
  • Step-by-step common-denominator work for addition and subtraction
  • Copy the equation and steps, and fully client-side processing

Use Cases

  • Math homework: Verify fraction arithmetic with the working shown.
  • Cooking and baking: Scale recipes written in fractional cups and spoons.
  • Woodworking and DIY: Combine fractional inch measurements exactly.
  • Unit conversion: Turn a decimal measurement into the exact fraction a ruler shows.

Frequently Asked Questions

Can it add three fractions at once?

No β€” the calculator works on two operands at a time. For a longer expression, combine the first two, copy the result, and use it as the first operand of the next step. That mirrors how you would work it out on paper and keeps the intermediate value exact, since results are always reduced fractions rather than rounded decimals.

How does a decimal like 0.375 become 3/8?

The tool uses the continued-fractions algorithm, which searches for the closest simple fraction whose denominator is at most 10,000. For 0.375 the algorithm converges on 3/8 exactly. The same method turns 0.333 into 1/3 instead of the literal 333/1000, which is almost always what someone typing 0.333 intends.

Why is the step-by-step solution only shown for addition and subtraction?

Adding and subtracting fractions requires a visible common denominator, and that is the part most people want to check. Multiplication and division are simpler β€” multiply across, or multiply by the reciprocal β€” so the tool shows the result directly. The Show Steps panel is available for the + and βˆ’ operations.

Does it handle negative fractions?

Yes. Enter a minus sign before the numerator, as in -3/4 or -1 1/2, and the calculator treats it as a negative value. This matters for algebra homework where the sign can flip during subtraction, and it lets you confirm that, say, 1/2 βˆ’ 3/4 is βˆ’1/4 rather than 1/4.

What is the largest denominator it works with?

There is no fixed limit on fractions you type directly β€” 123/4567 is fine. The 10,000-denominator cap applies only to decimal inputs being converted into fractions, where it keeps the search fast and returns a human-scale result instead of an unwieldy exact fraction.

Why can't I divide by zero?

Division by zero is undefined in arithmetic, so the calculator reports an error rather than inventing a value. If you are testing an expression that includes a zero denominator, the correct answer is that the expression has no defined result, not a very large number.

Reviewed by the HandyTools Hub team Β· Last updated