Fraction Calculator - Add, Subtract, Multiply, and Divide Fractions

A fraction calculator adds, subtracts, multiplies, and divides rational numbers written as a/b, mixed numbers such as 1 1/2, or plain integers, then reduces the answer with a greatest common divisor so the result is in lowest terms. The default on this page is the first homework problem most people type: 1/2 + 1/3 = 5/6.

Fractions are exact. 1/3 is not 0.33, and 1/7 is not 0.14. A desk calculator that only shows decimals will round those values and then compound the rounding when you add another term. This tool keeps numerator and denominator as integers (arbitrary-size integers in the browser) until it optionally prints an IEEE decimal for convenience. The fraction is the answer; the decimal is a preview.

This free online fraction calculator runs entirely in your browser. Nothing is uploaded. You can type a mixed string with a space (1 1/2), an improper fraction (3/4 or 11/4), or an integer (5). Optional whole, numerator, and denominator fields build the same string if you prefer boxes to typing a slash. A denominator of zero is rejected. After simplifying, the sign lives on the numerator, never on the denominator, which is the usual textbook convention.

Using this mixed number calculator is straightforward:

1. Enter the first operand as mixed 1 1/2, improper 3/4, or integer 5. You can instead fill whole (optional), numerator, and denominator.
2. Choose add, subtract, multiply, or divide.
3. Enter the second operand the same way. A zero denominator is an error. Dividing by a zero fraction (0/1) is also rejected.
4. Read the improper fraction in lowest terms. If the absolute numerator is at least the denominator, a mixed number is shown as well, plus a decimal equivalent. Copy the form your assignment wants. The last inputs are saved locally for up to 30 days.

Note: numerators and denominators must be whole numbers (optionally signed). This is not a calculator for algebraic expressions with variables, and it is not a repeating-decimal recognizer. Pair a percent word problem with the percentage calculator when the question is written with % instead of a slash.

You do not have to hunt for the least common denominator by hand for the arithmetic to be valid. Any common denominator works; bd always works. After you add, divide numerator and denominator by their GCD so the printed fraction is in lowest terms. That last step is what turns 6/12 into 1/2.

Example - 1/2 + 1/3 (the default):

• ad + bc = 1×3 + 1×2 = 3 + 2 = 5
• bd = 2×3 = 6
• 5/6 is already lowest terms (GCD of 5 and 6 is 1)
• 1/2 + 1/3 = 5/6, decimal 0.833333…

Example - 2/4 + 1/6, which is not yet simplified going in:

• This calculator first reduces 2/4 to 1/2
• 1/2 + 1/6 = (6 + 2) / 12 = 8/12 = 2/3
• If you skip reducing inputs, 2/4 + 1/6 = (12 + 4)/24 = 16/24 = 2/3 - same answer. Reducing early just keeps the integers smaller.

Example - adding a mixed number, 1 1/2 + 2 1/4:

• 1 1/2 = 3/2, 2 1/4 = 9/4
• 3/2 + 9/4 = 6/4 + 9/4 = 15/4
• |15| ≥ 4, so mixed form is 3 3/4

Subtracting is the same skeleton with a minus: a/b − c/d = (ad − bc) / (bd). 1/2 − 1/3 = (3 − 2)/6 = 1/6. If the second fraction is larger, the numerator goes negative and stays there: 1/3 − 1/2 = −1/6. This page never moves the minus onto the denominator.

The most common mix-up in middle school is treating multiplication like addition: adding numerators and adding denominators, or finding a common denominator when you did not need one. 1/2 × 1/3 = 1/6, not 2/5 and not 5/6. 5/6 is the sum, which is why this FAQ and the operation picker exist as separate modes. If a word problem says “half of a third of a cup,” that is multiplication. If it says “half a cup plus a third of a cup,” that is addition.

Division is multiply by the reciprocal: a/b ÷ c/d = (a/b) × (d/c) = ad / bc, provided c ≠ 0. 1/2 ÷ 1/3 = 3/2, which is also the mixed number 1 1/2. Dividing by a whole number n is dividing by n/1: 3/4 ÷ 2 = 3/8. Dividing by zero - whether you typed 0, 0/1, or 0/5 - is rejected.

Example - 3/4 × 8/9:

• Numerators 3×8 = 24, denominators 4×9 = 36
• 24/36, GCD 12, so 2/3
• Cross-canceling before multiplying (3 and 9 share 3; 4 and 8 share 4) is the same GCD work done earlier. This calculator multiplies then reduces; the value matches.

Cross-canceling is a homework speed trick, not a different operation. If your teacher wants to see cancel marks on the page, write those steps in the notebook. The number you copy from this tool should match the reduced product.

A mixed number is a whole part plus a proper fraction: 1 1/2 means 1 + 1/2. An improper fraction has |numerator| ≥ denominator: 3/2 is the same value. An integer is a fraction with denominator 1. This calculator converts mixed input to improper form, does the operation, simplifies, then shows mixed again when the absolute numerator is at least the denominator. 5/6 stays 5/6 with no mixed line, because 5 < 6.

The optional whole field is exactly that mixed whole part. If you fill whole 1, numerator 1, denominator 2, the combined string becomes 1 1/2. If you leave whole empty and type 3 and 4, you get 3/4. If you fill only whole 5, you get the integer 5. Do not put the mixed whole into the numerator as well - that would double-count (typing whole 1 and numerator 3/2 is not a valid parse).

A fraction a/b is in lowest terms when the greatest common divisor of |a| and b is 1. Euclidean GCD repeatedly replaces (a, b) with (b, a mod b) until the remainder is 0; the last non-zero remainder is the GCD. Then divide both parts by that GCD. 18/24 has GCD 6, so 3/4. Negative 18/24 becomes −3/4 - sign on the numerator.

If you need the GCD or the full factor list without doing a fraction operation, use the common factor calculator. That page is for GCD, LCM, and listing factors of whole numbers. This page uses GCD only as a reduction step after an arithmetic operation.

Zero simplifies to 0/1. A result that is a whole number is printed without a slash (6/2 becomes 3). Mixed form of an integer is the integer itself; there is no leftover numerator.

The decimal is numerator ÷ denominator in IEEE-754 floating-point, shown to about 12 significant digits. 1/2 = 0.5 exactly in binary. 1/3 = 0.333333333333 in the preview, which is rounded; the exact value remains 1/3. 1/7 is a repeating 142857 cycle; the decimal line will not write a vinculum over the repeat. If a teacher wants the repeating form, write it from the fraction, not from this float.

Extremely large numerators or denominators can overflow what JavaScript Number can represent. In that case the decimal line says so and you should trust the integer fraction only. For chained four-function decimal arithmetic without fractions, the basic calculator is sequential two-register math, not a fraction engine.

Adding denominators: 1/2 + 1/3 is not 2/5. 2/5 is smaller than either common-denominator result and shows up when someone adds tops and bottoms. Multiplying when the word problem said “and” or “plus.” Forgetting to take a reciprocal on division: 1/2 ÷ 1/3 is 3/2, not 1/6 (that 1/6 is the product). Leaving 6/8 unreduced when the rubric requires lowest terms. Writing 1.5 + 1/3 as if the 1.5 were still exact - type 3/2 instead of 1.5 on this page.

A minus on the denominator is legal input (3/-4) and is rewritten as −3/4. Two minuses cancel: −3/-4 = 3/4. A mixed number without a space, 11/2, is eleven halves, not one and one-half. You need the space: 1 1/2. That parse rule is strict on purpose so 11/2 stays 11/2.

This tool does not solve equations, factor polynomials, or simplify algebraic fractions with x in them. It does not convert repeating decimals back into fractions. It does not apply a teacher’s mixed-number-only rule if the result is proper - 5/6 will not be forced into a mixed display.

Teachers often insist on the least common denominator (LCD) so the numbers stay small. The LCD of 8 and 12 is 24, so 3/8 + 5/12 becomes 9/24 + 10/24 = 19/24. This calculator instead multiplies denominators: 3/8 + 5/12 = (36 + 40) / 96 = 76/96, then GCD 4 reduces it to the same 19/24. The LCD path and the bd path are the same rational number. If a rubric awards points for writing 24 as the LCD, write that step in the notebook; copy 19/24 from here as the value check.

Comparing two fractions without adding them is the same cross-multiply: a/b vs c/d compares ad vs bc (with b,d positive). 3/8 vs 5/12 is 36 vs 40, so 3/8 is smaller. Subtracting and looking at the sign of the numerator is another check: 3/8 − 5/12 = −1/24, negative, so the first is smaller. Equality is when the simplified forms match, not when the decimals look close: 1/2 and 500/1000 are equal; 0.333 and 1/3 are not.

Unlike denominators after an operation are not a problem once you have used a common denominator. Leaving 3/8 + 5/12 as “3/8 + 5/12” is an expression, not a single fraction. Homework that says “write as a single fraction in lowest terms” wants 19/24, which is what this page prints.

A batter calls for 3/4 cup flour, 1/3 cup sugar, 2 eggs (integers), and 1 1/2 teaspoons vanilla. You want two-thirds of the batch: multiply each amount by 2/3.

Flour: (3/4)×(2/3) = 6/12 = 1/2. Sugar: (1/3)×(2/3) = 2/9 cup - not a standard measuring cup mark; 2/9 is about 0.222 cups, a little under 1/4. Eggs: 2 × 2/3 = 4/3 = 1 1/3 eggs, which is why bakers weigh eggs or beat two and weigh two-thirds of the mass. Vanilla: 3/2 × 2/3 = 1 teaspoon exactly. Multiplication scaled every line; addition would have been the wrong operation if you were combining two full recipes (that would be ×2, or add the recipe to itself).

Negative mixed numbers show up in finance more than in kitchens: −1 1/2 cups is not a recipe, but −3/2 as a change in inventory is. Type -1 1/2; the sign applies to the whole mixed number, then stays on the numerator after simplify. Subtracting a larger fraction from a smaller one is how you get a negative without typing a minus on the first operand: 1/4 − 1/2 = −1/4.