How to Add, Subtract, and Multiply Fractions

February 17, 2026 |

math fractions

Each fraction operation follows a specific rule. Here are all four operations with step-by-step examples.

Adding fractions

Rule: You can only add fractions that have the same denominator. If they do not, find a common denominator first, then add the numerators.

Same denominator example: 2/7 + 3/7

The denominators match, so add the numerators: (2 + 3) / 7 = 5/7

Different denominator example: 1/4 + 2/3

Step 1: Find the least common denominator (LCD). The LCD of 4 and 3 is 12.

Step 2: Convert each fraction.

1/4 = 3/12 (multiply top and bottom by 3)
2/3 = 8/12 (multiply top and bottom by 4)

Step 3: Add the numerators. 3/12 + 8/12 = 11/12

Subtracting fractions

Rule: Same as addition. Get a common denominator, then subtract the numerators.

Example: 5/6 - 1/4

Step 1: LCD of 6 and 4 is 12.

Step 2: Convert each fraction.

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

Step 3: Subtract the numerators. 10/12 - 3/12 = 7/12

The result is 7/12.

Example with simplifying: 7/8 - 3/8

The denominators match: (7 - 3) / 8 = 4/8. This simplifies to 1/2 (divide both by 4).

Multiplying fractions

Rule: Multiply the numerators together. Multiply the denominators together. No common denominator needed.

Example: 2/3 x 4/5

Numerators: 2 x 4 = 8

Denominators: 3 x 5 = 15

Result: 8/15

Example with simplifying: 3/4 x 2/9

Numerators: 3 x 2 = 6

Denominators: 4 x 9 = 36

Result: 6/36. The GCD of 6 and 36 is 6, so divide both by 6: 1/6

Shortcut: You can simplify before multiplying. In 3/4 x 2/9, the 3 in the numerator and the 9 in the denominator share a factor of 3. Cancel first: 1/4 x 2/3 = 2/12 = 1/6. Same answer, smaller numbers to work with.

Dividing fractions

Rule: Flip the second fraction (take its reciprocal), then multiply.

Example: 3/5 divided by 2/7

Step 1: Flip the second fraction. 2/7 becomes 7/2.

Step 2: Multiply. 3/5 x 7/2

Numerators: 3 x 7 = 21

Denominators: 5 x 2 = 10

Result: 21/10, which equals 2 1/10 as a mixed number.

Example: 4/9 divided by 2/3

Flip: 2/3 becomes 3/2. Multiply: 4/9 x 3/2 = 12/18. Simplify by dividing both by 6: 2/3

How to find the least common denominator

The LCD is the smallest number that both denominators divide into evenly.

Method 1: List multiples.

Multiples of 4: 4, 8, 12, 16, 20…
Multiples of 6: 6, 12, 18, 24…
First common multiple: 12

Method 2: Use the formula. LCD = (a x b) / GCD(a, b). For 4 and 6: GCD is 2, so LCD = (4 x 6) / 2 = 12.

For small denominators, listing multiples is fast. For larger numbers, the formula is more reliable.

How to simplify a fraction

Divide both the numerator and denominator by their greatest common divisor (GCD).

Example: Simplify 18/24.

Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. GCD = 6.

18 / 6 = 3. 24 / 6 = 4.

Simplified: 3/4

A fraction is fully simplified when the numerator and denominator share no common factor other than 1.

Key takeaways

Adding and subtracting require a common denominator; then operate on the numerators only
Multiplying goes straight across: numerator x numerator, denominator x denominator
Dividing means flip the second fraction and multiply
Always check if the result can be simplified by dividing both parts by their GCD
You can cancel common factors before multiplying to keep the numbers smaller

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