Fraction calculator with steps

A fraction calculator that shows its working

This fraction calculator adds, subtracts, multiplies and divides two fractions, including mixed numbers and negative numbers. You get the answer in simplest form, as a mixed number and as a decimal. Below it, every step is laid out the way a teacher would write it: common denominator, multiplying, flipping for division, cancelling down. Pupils can check homework line by line.

All the arithmetic uses exact whole numbers, so there are no rounding errors, even with fifteen-digit values.

How to use it

1. Pick a tab: "Operations", "Simplify", "Decimal → fraction", "Compare" or "Expression".
2. In "Operations", type the numerator above the line and the denominator below it, then choose +, −, × or ÷. The "Whole" box is for mixed numbers such as 2 1/3.
3. The result updates as you type, with the "Working out" underneath. "Copy result" copies everything as plain text.
4. The "Examples" buttons fill in the boxes for you. Your last entry is kept on your device.

Key words

In 3/4, the top number is the numerator: how many parts you have. The bottom number is the denominator: how many equal parts the whole is cut into. A denominator can never be 0.

Simplify fractions

To simplify fractions, divide the top and the bottom by the same number. The quickest way is to divide by their greatest common divisor (GCD), also called the highest common factor. The "Simplify" tab finds it with the Euclidean algorithm. For 84/126: 126 = 1 × 84 + 42, then 84 = 2 × 42 + 0. The GCD is 42, so 84/126 = 2/3, which is in lowest terms.

Adding and subtracting fractions

When the denominators match, add the numerators and keep the denominator: 1/4 + 2/4 = 3/4. When they differ, rewrite both fractions over a common denominator first. As an adding fractions calculator, the tool uses the lowest common multiple (LCM). For 3/4 − 5/6, the LCM of 4 and 6 is 12: 3/4 = 9/12 and 5/6 = 10/12, so 9/12 − 10/12 = −1/12.

It works for workshop measurements too: 3/8 in + 5/16 in = 6/16 + 5/16 = 11/16 in.

Multiplying and dividing

To multiply, multiply the numerators together and the denominators together: 2/3 × 9/4 = 18/12 = 3/2.

To divide, multiply by the reciprocal of the second fraction, which means turning it upside down: 5/6 ÷ 10/9 = 5/6 × 9/10 = 45/60 = 3/4.

Mixed numbers

A mixed number combines a whole number and a fraction, like 1 1/2. To calculate, turn it into an improper fraction: 2 1/3 = (2 × 3 + 1)/3 = 7/3. So 2 1/3 + 1 3/4 = 7/3 + 7/4 = 28/12 + 21/12 = 49/12 = 4 1/12.

Fractions and decimals

To turn a fraction into a decimal, divide the top by the bottom: 3/2 = 1.5. Sometimes the division never ends and a group of digits repeats. The calculator spots this recurring part and puts it in brackets: 1/3 = 0.(3) and 1/7 = 0.(142857).

For decimal to fraction, use the "Decimal → fraction" tab. 0.125 = 125/1000 = 1/8. For a recurring decimal, put the repeating digits in brackets: 0.(3) gives 1/3 and 0.1(6) gives 1/6. The method shown is: 100x = 16.(6) and 10x = 1.(6), so 90x = 15 and x = 15/90 = 1/6.

Tips

• To compare fractions, give them the same denominator: 3/4 = 9/12 is smaller than 5/6 = 10/12. The "Compare" tab does this for you.
• In "Expression", multiplication comes before addition (BIDMAS): 1/2 + 1/3 × 3/4 = 1/2 + 1/4 = 3/4.

Frequently asked questions

How do I enter a negative mixed number?

Type the minus sign in the "Whole" box: −2 with 1 over 3 gives −2 1/3, which is −7/3.

Why is the answer sometimes an improper fraction?

A fraction greater than 1, such as 3/2, is called improper. The calculator shows it in that form, then as a mixed number (1 1/2) and as a decimal (1.5).

What do the brackets in 0.(3) mean?

They mark the digits that repeat forever: 0.(3) means 0.3333… In textbooks the same digits are often written with a dot or a bar above them.

Are results with very large numbers exact?

Yes. The calculator works with exact whole numbers and never rounds: 123456789/987654321 is divided by 9 to give 13717421/109739369.