Adding and subtracting fractions with the same denominator

Reminder: what is a fraction?

A fraction a/b represents a parts out of b equal parts. The number at the top (a) is called the numerator, and the number at the bottom (b) is called the denominator. For example, 3/4 means 3 parts out of a total of 4 equal parts.

The rule when the denominator is the same

When two fractions have the same denominator, we simply add (or subtract) the numerators, and keep the denominator the same:

• a/c + b/c = (a+b)/c
• a/c - b/c = (a-b)/c

Examples

• 3/7 + 2/7 = (3+2)/7 = 5/7
• 5/9 - 2/9 = (5-2)/9 = 3/9, which simplifies to 1/3

Common pitfall

Never add the denominators together! 1/4 + 1/4 is NOT equal to 2/8. The correct calculation is 1/4 + 1/4 = 2/4 = 1/2. The denominator remains the same; only the numerators are added together.

Summary table

Operation	Rule	Example
Addition	(a+b)/c	2/5 + 1/5 = 3/5
Subtraction	(a-b)/c	4/5 - 1/5 = 3/5

Always remember to check whether the result can be simplified, such as 3/9, which becomes 1/3.