How to Add and Subtract Fractions

You can't add fractions the way you add whole numbers. ½ + ⅓ is not ⅖ — the denominators must match first. Here's how to do it correctly.

Same denominator (easy case)

When denominators are the same, add or subtract the numerators and keep the denominator.

Example: ⅖ + ⅕

Answer: ⅗

Example: ⅞ − ⅜

We simplified ⁴⁄₈ to ½ by dividing numerator and denominator by 4.

Different denominators

When denominators differ, you need a common denominator before adding or subtracting.

Step 1: Find a common denominator

The easiest is usually the least common multiple (LCM) of the denominators. For 4 and 6, the LCM is 12.

Step 2: Convert each fraction

Multiply numerator and denominator so each fraction has the common denominator.

Example: ¼ + ⅙

Common denominator: 12

Answer: ⁵⁄₁₂

Another example: ⅔ − ¼

Common denominator: 12

Answer: ⁵⁄₁₂

Mixed numbers

For mixed numbers like 2⅓ + 1½, convert to improper fractions first, then add.

Common mistakes

Adding denominators: The most frequent error is adding both top and bottom. 1/2 + 1/3 is NOT 2/5. You must find a common denominator first.

Forgetting to simplify: Always check if your answer can be reduced. 4/8 should be written as 1/2.

Wrong LCM: You can always use the product of both denominators (e.g., 3 × 4 = 12), but the LCM gives smaller numbers and less simplifying.

More examples

Example: 3/5 + 1/4

Answer: 17/20

Example: 5/6 − 1/3

Answer: 1/2

Example: 1 3/4 + 2 1/3

Answer: 4 1/12

Quick tips

• Same denominator → add/subtract numerators only
• Different denominators → find common denominator, convert, then add/subtract
• Always simplify your final answer when possible

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