Fraction Calculator

How to Use the Fraction Calculator

This fraction calculator adds, subtracts, multiplies and divides fractions, mixed numbers, whole numbers and decimals, and gives the answer as a simplified fraction, a mixed number, a decimal and a percentage. Every answer comes with step-by-step working, so you can see how the fractions were combined and not only what the result is.

Use the other tabs when you need them. The Simplify tab reduces a fraction to lowest terms and turns improper fractions into mixed numbers, the Decimal ↔ Fraction tab converts in both directions (including repeating decimals), and the Compare tab shows which of two fractions is larger. All the arithmetic is exact, with no rounding until the decimal and percentage are displayed.

The Rules for Fraction Arithmetic

Worked Examples

Adding with different denominators: 3/4 + 2/3. The LCM of 4 and 3 is 12, so 3/4 = 9/12 and 2/3 = 8/12. Adding gives 17/12. The GCD of 17 and 12 is 1, so it's already in lowest terms. As a mixed number that's 1 5/12, as a decimal 1.41(6) (1.41666…) and as a percentage 141.6666667%.

Multiplying mixed numbers: 1 1/2 × 2 2/3. Convert to improper fractions, 3/2 and 8/3, then multiply across to get 24/6. The GCD is 6, so it simplifies to 4, a whole number.

Dividing fractions: 5/6 ÷ 2/9. Invert the second fraction to 9/2 and multiply: 5 × 9 = 45 and 6 × 2 = 12, giving 45/12. The GCD is 3, so the answer is 15/4, which is 3 3/4 or 3.75.

Decimal to fraction: 0.375. Three decimal places means writing 375 over 1,000. The GCD is 125, so 0.375 = 3/8, which is 37.5%.

Fraction to decimal: 2/7. Long division never ends: the remainders cycle, so the digits repeat. The decimal is 0.(285714), which is 0.285714285714…, or 0.2857142857 rounded to 10 significant figures.

Terminating and Repeating Decimals

Once a fraction is in lowest terms, its decimal ends only if the denominator's prime factors are just 2 and 5. That's why 3/8 (8 = 2 × 2 × 2) is exactly 0.375, but 2/7 and 1/3 repeat forever. A repeating decimal is written with brackets around the repeating block: 1/6 is 0.1(6) and 1/7 is 0.(142857). Rounding a repeating decimal such as 0.333333 and converting it back gives 333333/1000000 rather than 1/3, which is what the Approximate option and its maximum denominator are for: it finds the closest simple fraction.

Frequently Asked Questions

How do I use this fraction calculator?

Type each fraction in its own box, such as 3/4, a mixed number like 1 1/2, a whole number or a decimal, then choose add, subtract, multiply or divide. The answer appears straight away as a simplified fraction, a mixed number, a decimal and a percentage, and the Show working panel lays out each step. The other tabs simplify a fraction, convert between decimals and fractions, and compare two fractions.

How do I add fractions with different denominators?

First find a common denominator, usually the lowest common multiple (LCM) of the two denominators. Rewrite each fraction over that denominator by multiplying its top and bottom by the same number, then add the numerators and keep the denominator. For 1/4 + 1/6 the LCM of 4 and 6 is 12, so the sum is 3/12 + 2/12 = 5/12. Subtracting works the same way.

Can this adding fractions calculator add mixed numbers?

Yes. Enter mixed numbers with a space between the whole part and the fraction, like 1 1/2 or 2 2/3, and it converts them to improper fractions first. You can also mix formats, such as a mixed number plus a decimal, or a whole number minus a fraction. Negative mixed numbers like -2 3/8 are read as minus two and three-eighths.

How do I multiply and divide fractions?

To multiply, multiply the numerators together and the denominators together, then simplify. To divide, invert the second fraction (swap its top and bottom) and multiply. So 5/6 ÷ 2/9 becomes 5/6 × 9/2 = 45/12, which simplifies to 15/4. Dividing by zero, such as ÷ 0 or ÷ 0/5, has no answer, and the calculator will tell you so.

How do I simplify a fraction?

Divide the numerator and the denominator by their greatest common divisor (GCD), the biggest whole number that goes into both. For 18/24 the GCD is 6, so 18/24 simplifies to 3/4. If the GCD is 1, the fraction is already in lowest terms. The Simplify tab shows the Euclidean algorithm used to find the GCD, line by line.

How do I change an improper fraction to a mixed number?

Divide the numerator by the denominator: the whole-number part of the answer is the whole part of the mixed number, and the remainder goes over the original denominator. For example, 17/5 is 3 remainder 2, so it is 3 2/5. To go the other way, multiply the whole part by the denominator, add the numerator, and keep the denominator. The Simplify tab shows both forms for anything you enter.

How do I convert a fraction to a decimal?

Divide the numerator by the denominator. Some fractions end, like 3/8 = 0.375, and others repeat forever, like 2/7 = 0.285714285714… The calculator writes repeating decimals with brackets around the repeating digits, so 2/7 is 0.(285714) and 1/6 is 0.1(6), and it also shows the digits written out and rounded to 10 significant figures.

How do I convert a decimal to a fraction?

Write the digits over a power of 10 that matches the number of decimal places, then simplify: 0.375 is 375/1000, which simplifies to 3/8. For a rounded decimal such as 0.333333, pick the Approximate option and a maximum denominator, and the calculator finds the closest simple fraction, 1/3 when the limit is 1,000. You can also type a repeating decimal using brackets, like 0.1(6).

Which fraction is bigger, and how do I compare fractions?

Put both fractions over a common denominator and compare the numerators: the bigger numerator wins. For 3/4 and 2/3 the common denominator is 12, giving 9/12 and 8/12, so 3/4 is larger by 1/12. The Compare tab does this for any two fractions, mixed numbers or decimals and shows the difference.