Adding Fractions With Common Denominators
Adding fractions with common denominators follows a direct rule: add the numerators and keep the denominator unchanged. In Grade 6 Saxon Math Course 1, a/c + b/c = (a+b)/c. For example, 3/8 + 2/8 = 5/8. The denominator labels what kind of pieces you have — eighths, fifths, thirds — and it stays the same because you are counting more pieces of the same size. After adding, always check if the resulting fraction can be simplified or converted to a mixed number.
Key Concepts
Property When adding fractions that have the same denominator, we add the numerators. The denominator does not change. This rule can be written as $ \frac{a}{c} + \frac{b}{c} = \frac{a+b}{c} $.
Examples $ \frac{1}{4} + \frac{1}{4} = \frac{2}{4} $ $ \frac{3}{8} + \frac{2}{8} = \frac{5}{8} $ $ \frac{1}{8} + \frac{1}{8} + \frac{1}{8} = \frac{3}{8} $.
Explanation Imagine you have a pizza cut into 8 giant slices. The denominator '8' is your slice size. If you have 3 slices and your friend gives you 2 more, you now have 5 slices! You simply added the number of slices (the numerators) together. The size of the slices (the denominator) stayed the same. Easy peasy!
Common Questions
How do you add fractions with the same denominator?
Add the numerators, keep the denominator: a/c + b/c = (a+b)/c. Example: 3/8 + 2/8 = 5/8.
Why does the denominator stay the same when adding?
The denominator names the size of the pieces. Adding more of the same-sized pieces does not change what size they are.
Add 5/12 + 7/12.
5/12 + 7/12 = 12/12 = 1.
Add 2/5 + 4/5.
2/5 + 4/5 = 6/5 = 1⅕.
Do you need to simplify after adding fractions with common denominators?
Always check. If numerator and denominator share a common factor, simplify. For example, 4/6 should be reduced to 2/3.