If a student works with same denominators when adding fractions, what is true about the fractions?

When adding fractions that have the same denominators, it is indeed true that the fractions can be added easily without adjustments. This is because having a common denominator means that the fractions represent parts of the same whole, allowing for straightforward addition of the numerators while keeping the denominator unchanged.

For example, if you have the fractions ( \frac{2}{5} ) and ( \frac{1}{5} ), both are divided into 5 equal parts. To add them, you simply add the numerators: ( 2 + 1 = 3), and retain the common denominator of 5, resulting in ( \frac{3}{5} ). This process highlights the simplicity and efficiency when working with fractions that share the same denominator.

In contrast, other statements about the nature of the fractions do not hold true. Fractions can have the same denominators and still represent the same or different values. They can also be proper fractions, improper fractions, or mixed numbers; the key point is that they share a denominator, which allows for easy addition. Hence, being able to combine fractions with a common denominator without additional steps is a fundamental principle in fraction addition.