Fraction Calculator

Type two fractions, mixed numbers, whole numbers or decimals and choose add, subtract, multiply or divide. The answer appears in lowest terms, as a mixed number, a decimal and a percent, with each step written out: the common denominator, the rewritten fractions, the sum and the simplifying. The calculator also simplifies a single fraction and turns decimals into fractions and back, repeating decimals included. All the arithmetic is exact.

How it works

Fraction Calculator is a web page that does its work on your own device. Everything you type or choose is worked out by your browser and never sent to a server, so nothing is stored and there is nothing to delete. There is no account, no sign-up and no limit on how often you use it.

Straight to one job

Mixed Number Calculator · Simplify Fractions Calculator · Decimal to Fraction Calculator

Adding and subtracting fractions

Fractions can only be added when they share a denominator, the number on the bottom. To add 1/2 and 1/3, find the smallest number both 2 and 3 divide into, 6, and rewrite each fraction over it: 1/2 = 3/6 and 1/3 = 2/6. Then add the tops: 3/6 + 2/6 = 5/6. Subtracting works the same way. Mixed numbers such as 2 1/3 are turned into improper fractions first: 2 × 3 + 1 = 7, so 2 1/3 is 7/3.

Multiplying and dividing fractions

To multiply, multiply the tops together and the bottoms together: 2/3 × 3/4 = 6/12, which simplifies to 1/2. No common denominator is needed. To divide, flip the second fraction and multiply: 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2. Halving a recipe is multiplying by 1/2; asking how many quarter-cup scoops fill one and a half cups is 1 1/2 ÷ 1/4 = 6.

Simplifying

A fraction is in lowest terms when the top and bottom have no common factor except 1. Divide both by their greatest common factor: for 18/24 that is 6, giving 3/4. The calculator finds it by the method Euclid described, which works for numbers of any size, and it does every sum with whole numbers, so an answer such as 1/3 stays exact instead of becoming 0.3333.

Decimals and fractions

A decimal that stops is a fraction over 10, 100, 1,000 and so on: 0.375 = 375/1000 = 3/8. A decimal that repeats for ever is a fraction too: type the repeating digits in brackets, so 0.(6) for 0.666…, and the calculator returns 2/3. Going the other way, it divides and marks any digits that repeat.

What it does

• Add, subtract, multiply and divide
• Fractions, mixed numbers, whole numbers and decimals
• Answers in lowest terms, as a mixed number, decimal and percent
• Every step written out
• Simplify any fraction
• Decimal to fraction and back, repeating decimals included
• Exact whole-number arithmetic, no rounding

Questions

How do you add fractions with different denominators?

Find the least common multiple of the denominators, rewrite each fraction over it, then add the numerators. For 1/2 + 1/3, the common denominator is 6, so 3/6 + 2/6 = 5/6.

How do you multiply fractions?

Multiply the numerators together and the denominators together, then simplify. 2/3 × 3/4 = 6/12 = 1/2.

How do you divide fractions?

Flip the second fraction and multiply. 1/2 ÷ 1/4 = 1/2 × 4/1 = 2.

How do I type a mixed number?

Put a space between the whole number and the fraction: 2 1/3. A hyphen, 2-1/3, works too.

How do you simplify a fraction?

Divide the top and bottom by their greatest common factor. For 18/24 it is 6, so 18/24 = 3/4.

How do I turn a decimal into a fraction?

Write it over 10, 100 or 1,000 according to the number of decimal places, then simplify: 0.375 = 375/1000 = 3/8. Choose Decimal ⇄ fraction and type the decimal.

How do I enter a repeating decimal?

Put the digits that repeat in brackets: 0.(3) for 0.333… or 0.1(6) for 0.1666…. The calculator turns it into the exact fraction, 1/3 or 1/6.

Is anything sent anywhere?

No. The sums run in your browser and nothing you type is sent to us or stored.

More

Privacy policy · Support · Changelog