How to Do Fractions, Step by Step (With Examples)

A fraction has a numerator on top and a denominator on the bottom — for example, in 3/4 the 3 is the numerator and the 4 is the denominator. Here's how to handle every common operation, one step at a time.

Want your own fractions worked out with steps? Open the Fraction Calculator →

Simplifying a fraction

Divide the top and bottom by their greatest common factor (GCF) — the biggest number that goes into both.

Simplify 8/12.
The GCF of 8 and 12 is 4.
Divide both by 4: 8 ÷ 4 = 2 and 12 ÷ 4 = 3.

8/12 = 2/3

Adding and subtracting fractions

You can only add or subtract fractions that share a denominator. Rewrite them over a common denominator first, then add or subtract the numerators.

Add 1/2 + 1/3.
The least common denominator of 2 and 3 is 6.
Rewrite: 1/2 = 3/6 and 1/3 = 2/6.
Add the numerators: 3 + 2 = 5, over 6.

1/2 + 1/3 = 5/6

Subtraction works exactly the same way — just subtract the numerators instead of adding.

Multiplying fractions

This is the easiest one: multiply straight across — numerators together, denominators together — then simplify.

Multiply 2/3 × 3/4.
Numerators: 2 × 3 = 6. Denominators: 3 × 4 = 12.
That gives 6/12, which simplifies to 1/2.

2/3 × 3/4 = 1/2

Dividing fractions

Use keep, change, flip: keep the first fraction, change ÷ to ×, and flip the second fraction to its reciprocal.

Divide 1/2 ÷ 1/4.
Flip the second fraction: 1/4 → 4/1.
Multiply: 1/2 × 4/1 = 4/2 = 2.

1/2 ÷ 1/4 = 2

Improper fractions and mixed numbers

An improper fraction has a numerator larger than its denominator, like 7/3. To write it as a mixed number, divide: 7 ÷ 3 = 2 remainder 1, so 7/3 = 2 1/3. This builds directly on division.

Comparing fractions

To compare two fractions, give them the same denominator (or cross-multiply) and compare the numerators. For 1/2 and 3/4, rewrite 1/2 as 2/4 — since 2/4 is less than 3/4, 1/2 < 3/4.

Frequently asked questions

How do you add fractions with different denominators?

Rewrite both over a common denominator, add the numerators, keep the denominator, then simplify.

How do you divide fractions?

Keep, change, flip: keep the first fraction, change ÷ to ×, flip the second, then multiply.

Where can I practice with steps shown?

Use the free Fraction Calculator to add, subtract, multiply, divide, simplify or compare fractions with the working shown.

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