How to Add, Subtract, Multiply and Divide Fractions (Step by Step)

The short answer

• Add or subtract: rewrite both fractions over a common denominator, then add or subtract the numerators. 3/4 + 2/5 = 15/20 + 8/20 = 23/20.
• Multiply: multiply the tops and multiply the bottoms. 2/3 × 9/10 = 18/30 = 3/5.
• Divide: flip the second fraction and multiply. 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8.
• Always simplify by dividing the top and bottom by their greatest common divisor (GCD).

The Fraction Calculator does all four operations and shows each step, so you can check your working.

Adding fractions with different denominators

You can only add fractions directly when the bottoms (denominators) match. So the first job is to find a common denominator. The smallest one is the lowest common denominator (LCD), which is the least common multiple of the two denominators.

Example: 3/4 + 2/5

Find the LCD of 4 and 5. They share no factors, so the LCD is 4 × 5 = 20.

Convert each fraction: 3/4 = (3 × 5)/(4 × 5) = 15/20. 2/5 = (2 × 4)/(5 × 4) = 8/20.

Add the numerators: 15 + 8 = 23. Keep the denominator: 23/20.

Simplify: GCD(23, 20) = 1, so it is already in lowest terms.

As a mixed number: 23/20 = 1 3/20. As a decimal: 1.15.

A quick way to find the LCD

LCD = (d1 × d2) ÷ GCD(d1, d2). For 6 and 4: GCD is 2, so LCD = 24 ÷ 2 = 12. Multiplying the denominators (24) also works, but you get bigger numbers and more simplifying at the end.

Subtracting fractions

Same method as adding, but subtract the numerators.

Example: 5/6 − 1/4

LCD of 6 and 4 = 12.

5/6 = 10/12 and 1/4 = 3/12.

10 − 3 = 7, so the answer is 7/12.

If the second fraction is bigger, the answer is negative: 1/4 − 5/6 = 3/12 − 10/12 = −7/12.

Multiplying fractions

No common denominator needed.

Example: 2/3 × 9/10

Multiply numerators: 2 × 9 = 18.

Multiply denominators: 3 × 10 = 30.

Result: 18/30.

Simplify: GCD(18, 30) = 6, so 18/30 = 3/5.

Shortcut: cancel before multiplying. The 3 and the 9 share a factor of 3, and the 2 and the 10 share a factor of 2: 2/3 × 9/10 becomes 1/1 × 3/5 = 3/5. Smaller numbers, same answer.

Dividing fractions

Dividing by a fraction is the same as multiplying by its reciprocal (the fraction turned upside down). A common memory aid is "keep, change, flip": keep the first fraction, change ÷ to ×, flip the second.

Example: 3/4 ÷ 2/5

Flip 2/5 to get 5/2.

Multiply: 3/4 × 5/2 = 15/8.

GCD(15, 8) = 1, so 15/8 is final. As a mixed number: 1 7/8.

You cannot divide by zero, so dividing by a fraction with 0 on top (like 0/5) has no answer.

Mixed numbers

A mixed number such as 1 1/2 must be turned into an improper fraction before calculating:

• Multiply the whole number by the denominator and add the numerator: 1 × 2 + 1 = 3, so 1 1/2 = 3/2.
• 2 3/4 = (2 × 4 + 3)/4 = 11/4.

Example: 1 1/2 + 1 1/4

Convert: 3/2 + 5/4.

LCD of 2 and 4 is 4: 6/4 + 5/4 = 11/4.

Convert back: 11 ÷ 4 = 2 remainder 3, so 2 3/4.

The Fraction Calculator takes a numerator and a denominator for each fraction, so enter mixed numbers as improper fractions (3 and 2 for 1 1/2).

Using the Fraction Calculator

Open the Fraction Calculator.

Enter the first fraction's numerator and denominator.

Pick the operation: +, −, × or ÷.

Enter the second fraction.

Click Calculate.

You get the simplified result as a fraction, its decimal value to four places, and a step-by-step solution: the LCD used for adding or subtracting, the converted fractions, the multiplication, and the GCD used to simplify. For 3/4 + 2/5 it shows the LCD of 20, the conversions to 15/20 and 8/20, and the result 23/20.

The calculator works with whole-number numerators and denominators. If a denominator is 0, or you try to divide by a fraction whose numerator is 0, nothing is calculated because the result is undefined. Results are shown as improper fractions, so convert to a mixed number yourself if needed (divide the top by the bottom, keep the remainder over the denominator).

Quick reference

Operation	Rule	Example	Answer
Add	Common denominator, add tops	3/4 + 2/5	23/20
Subtract	Common denominator, subtract tops	5/6 − 1/4	7/12
Multiply	Tops × tops, bottoms × bottoms	2/3 × 9/10	3/5
Divide	Flip the second, then multiply	3/4 ÷ 2/5	15/8

Common mistakes

• Adding the denominators. 1/2 + 1/3 is not 2/5. It is 3/6 + 2/6 = 5/6.
• Flipping the wrong fraction when dividing. Only the second fraction (the divisor) is flipped.
• Forgetting to simplify. 18/30 and 3/5 are equal, but most answer keys expect lowest terms.
• Converting mixed numbers wrongly. 2 3/4 is 11/4, not 6/4 or 5/4.
• Losing the negative sign. Keep the sign on the numerator throughout.

For converting a fraction to a percentage, divide and multiply by 100 (3/5 = 0.6 = 60%), or use the Percentage Calculator. For powers and roots of fractions, the Scientific Calculator helps.