Add Fractions with a Common Denominator
Pre-algebra students in OpenStax Prealgebra 2E learn the fundamental rule for adding fractions with a common denominator: a/c + b/c = (a+b)/c. When denominators are equal, simply add the numerators and keep the same denominator. For example, 3/11 + 5/11 = 8/11. With variables, x/4 + 3/4 = (x+3)/4 and cannot be simplified further because x and 3 are unlike terms. This property extends to algebraic fractions, making it one of the most widely used fraction rules across all levels of mathematics.
Key Concepts
Property If $a$, $b$, and $c$ are numbers where $c \neq 0$, then.
$$\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}$$.
To add fractions with a common denominator, add the numerators and place the sum over the common denominator.
Common Questions
How do you add fractions with a common denominator?
Add the numerators together and keep the same denominator. Do not add the denominators.
What is 3/11 + 5/11?
Add the numerators: 3 + 5 = 8. The answer is 8/11.
What is x/4 + 3/4?
Add the numerators: (x + 3)/4. Since x and 3 are unlike terms, this cannot be simplified further.
Why do the denominators stay the same when adding?
The denominator tells you the size of each piece. Adding pieces of the same size gives more pieces of that same size, so the denominator does not change.
What must you do if denominators are different before adding?
Find a common denominator by converting one or both fractions to equivalent fractions with the same denominator, then add.