Adding With Common Denominators
Add and subtract fractions with common denominators by combining numerators directly. Build Grade 9 rational expression skills from this foundational rule.
Key Concepts
Property If the denominators are the same, add or subtract the numerators and keep the common denominator. For example, $ \frac{A}{C} + \frac{B}{C} = \frac{A+B}{C} $. Explanation Think of it like adding pizza slices! If the slices are the same size (common denominator), you just count up how many you have (the numerators). The slice size doesn't change, so the denominator stays the same. Simple! Examples $ \frac{4x^2}{25x} + \frac{6x^2}{25x} = \frac{10x^2}{25x} = \frac{2x}{5} $ $ \frac{d^2}{d 9} + \frac{3d}{d 9} = \frac{d^2+3d}{d 9} = \frac{d(d+3)}{d 9} $.
Common Questions
How do you add fractions with common denominators?
When denominators are equal, add the numerators and keep the same denominator: A/C + B/C = (A+B)/C. For example, 3/7 + 2/7 = 5/7.
Can you simplify after adding fractions with common denominators?
Yes. After combining numerators, check if the result can be reduced by dividing numerator and denominator by their GCF.
Does this rule apply to subtracting fractions too?
Yes. A/C - B/C = (A-B)/C. Subtract the second numerator from the first, keeping the shared denominator unchanged, then simplify.