Mathematics · Updated 2026

Fraction Calculator

Add, subtract, multiply and divide fractions instantly. Results are automatically simplified to lowest terms with step-by-step explanations. Works with negative fractions and shows mixed number form.

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Fraction Arithmetic Rules

To add or subtract fractions, rewrite them over the least common denominator, combine the numerators, then simplify: 1/2 + 3/4 = 2/4 + 3/4 = 5/4, or 1 1/4. To multiply, multiply straight across. To divide, flip the second fraction and multiply. The calculator above handles all four operations, reduces each answer to lowest terms and shows it as a decimal and mixed number.

Fractions represent parts of a whole. Every fraction has a numerator (top number) and denominator (bottom number). The four arithmetic operations each follow specific rules that ensure results are mathematically correct and expressed in lowest terms.

Adding Fractions

Find the LCD (Least Common Denominator), convert both fractions, add the numerators. Example: 1/2 + 1/3. LCD = 6. 3/6 + 2/6 = 5/6. Same-denominator fractions: just add numerators and keep denominator.

Subtracting Fractions

Same as addition: find LCD, convert, subtract numerators. Example: 3/4 − 1/3. LCD = 12. 9/12 − 4/12 = 5/12. Order matters: first fraction minus second.

Multiplying Fractions

Multiply numerators together, multiply denominators together. Example: 2/3 × 3/4 = 6/12 = 1/2. Can cross-simplify before multiplying to keep numbers smaller.

Dividing Fractions

Keep-Change-Flip: keep first fraction, change ÷ to ×, flip the second. Example: 5/6 ÷ 2/3 = 5/6 × 3/2 = 15/12 = 5/4. Dividing by a fraction = multiplying by its reciprocal.

Four Worked Examples

Addition: 5/6 + 3/8

The least common denominator of 6 and 8 is 24. Scale each fraction up: 5/6 = 20/24 and 3/8 = 9/24. Add the numerators: 20/24 + 9/24 = 29/24, which is 1 5/24 as a mixed number. 29 and 24 share no factor, so it is already in lowest terms.

Subtraction: 2/5 − 7/10

10 is already a multiple of 5, so the common denominator is 10. 2/5 = 4/10, and 4/10 − 7/10 = −3/10. When the second fraction is bigger, the answer is negative. That is correct, not an error.

Multiplication: 4/9 × 15/16

Multiplying straight across gives 60/144, which reduces to 5/12. Cancelling first is quicker: 4 and 16 share a 4 (leaving 1 and 4), and 15 and 9 share a 3 (leaving 5 and 3). That leaves 1/3 × 5/4 = 5/12, with no big numbers to simplify.

Division: 3/4 ÷ 9/10

Keep the first fraction, change the sign to multiplication and flip the second: 3/4 × 10/9 = 30/36. The greatest common factor of 30 and 36 is 6, so the answer is 5/6.

Common Fractions as Decimals and Percents

Digits in brackets repeat forever, so 0.(3) means 0.333... Percents are rounded to two decimal places.

FractionDecimalPercent
1/20.550%
1/30.(3)33.33%
2/30.(6)66.67%
1/40.2525%
3/40.7575%
1/50.220%
1/60.1(6)16.67%
5/60.8(3)83.33%
1/70.(142857)14.29%
1/80.12512.5%
3/80.37537.5%
5/80.62562.5%
7/80.87587.5%
1/90.(1)11.11%
1/120.08(3)8.33%
1/160.06256.25%

A fraction in lowest terms gives a terminating decimal only when its denominator has no prime factors other than 2 and 5. That is why eighths and sixteenths end, while thirds, sixths and sevenths repeat. To go the other way, use the decimal to fraction calculator.

Mistakes That Cost Points

  • Adding the denominators. 1/2 + 1/3 is not 2/5. A quick check shows why: 2/5 is 0.4, which is less than 1/2 on its own. The right answer is 5/6.
  • Flipping the wrong fraction. In a division only the second fraction (the divisor) is flipped. 3/4 ÷ 9/10 becomes 3/4 × 10/9, never 4/3 × 9/10.
  • Losing the sign. −3/4, (−3)/4 and 3/(−4) are the same number. Two negatives cancel: (−3)/(−4) = 3/4. The calculator always moves the sign to the numerator.
  • Zero in the wrong place. 0/5 is simply 0, but 5/0 has no value at all. Dividing by a fraction whose numerator is 0 is dividing by zero, so it is also undefined.
  • Multiplying mixed numbers part by part. 2 1/2 × 2 1/2 is not 4 1/4. Convert first: 5/2 × 5/2 = 25/4 = 6 1/4. The mixed number calculator does this conversion for you.
  • Stopping before lowest terms. 30/36 is correct but unfinished. Divide top and bottom by their greatest common factor (6 here) to get 5/6. The GCF calculator finds that number for large fractions.
Method and sources. Standard fraction arithmetic as taught in the Common Core State Standards for Mathematics (grade 5 and 6 fraction standards): addition and subtraction over the least common denominator (the LCM of the denominators), multiplication across, division by the reciprocal, and reduction by the greatest common divisor using the Euclidean algorithm. Every example and table value above was computed with the same integer arithmetic the calculator uses. The calculator works with whole numbers up to about 9 quadrillion in size, the range JavaScript can hold exactly.
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Fraction Rules Explained

Find the LCD (Least Common Denominator), convert both fractions to use it, then add the numerators. Example: 1/2 + 1/3. LCD = 6. Convert: 3/6 + 2/6 = 5/6. Steps: multiply 1 × 3 and 2 × 3 to get 3/6, multiply 1 × 2 and 3 × 2 to get 2/6, then add: (3+2)/6 = 5/6. The LCD is the smallest number both denominators divide into evenly.

Multiply the numerators together and the denominators together, then simplify. Example: 2/3 × 3/4 = (2×3)/(3×4) = 6/12 = 1/2. You can also cross-simplify before multiplying: divide 2 and 4 by 2 (getting 1 and 2), divide 3 and 3 by 3 (getting 1 and 1), leaving 1/1 × 1/2 = 1/2. Cross-simplification avoids large intermediate numbers.

Keep-Change-Flip (KCF): keep the first fraction, change division to multiplication, flip (invert) the second fraction. Example: 5/6 ÷ 2/3 = 5/6 × 3/2 = 15/12 = 5/4 = 1 and 1/4. The rule works because dividing by a fraction is mathematically identical to multiplying by its reciprocal. KCF works for all fractions including negative ones and improper fractions.

Find the GCF (Greatest Common Factor) of the numerator and denominator, then divide both by it. Example: 12/18. GCF(12,18) = 6. 12/6 = 2, 18/6 = 3. Simplified: 2/3. A fraction is fully simplified when GCF(numerator, denominator) = 1. All results from this calculator are automatically simplified to lowest terms.

Multiply the whole number by the denominator, add the numerator, keep the same denominator. Example: 2 and 3/4 = (2×4 + 3)/4 = 11/4. To reverse (improper to mixed): divide numerator by denominator. 11 ÷ 4 = 2 remainder 3, so 11/4 = 2 and 3/4. Mixed numbers like 2 and 3/4 can be entered by converting to improper fractions first.

The LCD is the Least Common Multiple (LCM) of the denominators. It is the smallest number that both denominators divide into evenly. Example: LCD(4, 6). LCM(4,6) = 12. To add 1/4 + 1/6: convert to 3/12 + 2/12 = 5/12. Using the LCD (rather than just multiplying denominators) keeps numbers smaller and reduces simplification needed at the end.

Yes: it is much simpler. When denominators are the same, just add (or subtract) the numerators and keep the denominator. Example: 3/8 + 2/8 = 5/8. Example: 7/10 − 3/10 = 4/10 = 2/5. No LCD calculation needed. This is why converting fractions to a common denominator is the key step in adding fractions with different denominators.

An improper fraction has a numerator equal to or greater than the denominator. Examples: 7/4, 11/3, 5/5. Improper fractions represent values equal to or greater than 1. They are perfectly valid mathematically and are often easier to work with in calculations. Convert to mixed number: 7/4 = 1 and 3/4. Convert back: 1 and 3/4 = (1×4+3)/4 = 7/4.

The result will be negative. Use the same process: find LCD, convert, subtract. Example: 1/4 − 3/4 = (1−3)/4 = −2/4 = −1/2. Or 1/3 − 1/2. LCD = 6. 2/6 − 3/6 = −1/6. Negative fractions follow the same rules as positive ones. A negative numerator indicates the result is negative.

Fractions with different denominators represent parts of different-sized wholes. You cannot directly add 1/2 and 1/3 without converting, just as you cannot add 50 cents and about 33 cents (roughly 1/3 of a dollar) by adding 1+1=2. The common denominator converts both to the same "unit size." 1/2 = 3/6 and 1/3 = 2/6: now both count sixths, so 3 sixths + 2 sixths = 5 sixths = 5/6.

No. A fraction means division, and division by zero is undefined, so 5/0 has no value. A zero on top is fine: 0/5 = 0. For the same reason you cannot divide by a fraction that equals zero, such as 0/7. The calculator shows a message instead of an answer in both cases.

Use one common denominator for all three. For 1/2 + 1/3 + 1/4 the least common denominator is 12, so the sum is 6/12 + 4/12 + 3/12 = 13/12, or 1 1/12. With this calculator, add the first two, then add the third fraction to that result.

Divide the numerator by the denominator, then multiply by 100 for a percent. 3/8 = 3 ÷ 8 = 0.375 = 37.5%. 1/3 gives 0.333..., a repeating decimal, which is about 33.33%. Every answer from this calculator also shows the decimal value.
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