Which of the following is true when adding or subtracting fractions with the same denominator?

Which of the following is true when adding or subtracting fractions with the same denominator?

• A. Keep the denomiator the same and adjust the numerators
• B. Add the denominators together and keep the numerators
• C. Subtract the denominators from each numerator
• D. Convert them to mixed numbers first

Answer: (A)

When adding or subtracting fractions that share the same denominator, it is essential to maintain the common denominator while adjusting the numerators accordingly. For instance, consider the fractions 2/5 and 3/5. Since they have the same denominator of 5, when adding them, you would simply add the numerators (2 + 3), resulting in 5/5, which simplifies to 1. Similarly, for subtraction, say you had 3/5 and you wanted to subtract 2/5. You would subtract the numerators (3 - 2), giving you 1/5, while the denominator remains 5. This principle allows for straightforward operations without complicating the fractions. The other options suggest altering the denominators or converting the fractions into mixed numbers, which are unnecessary steps when working with fractions that share the same denominator. This reason underscores why the first option is the correct approach to adding or subtracting fractions effectively.

When adding or subtracting fractions that share the same denominator, it is essential to maintain the common denominator while adjusting the numerators accordingly.

For instance, consider the fractions 2/5 and 3/5. Since they have the same denominator of 5, when adding them, you would simply add the numerators (2 + 3), resulting in 5/5, which simplifies to 1. Similarly, for subtraction, say you had 3/5 and you wanted to subtract 2/5. You would subtract the numerators (3 - 2), giving you 1/5, while the denominator remains 5.

This principle allows for straightforward operations without complicating the fractions. The other options suggest altering the denominators or converting the fractions into mixed numbers, which are unnecessary steps when working with fractions that share the same denominator. This reason underscores why the first option is the correct approach to adding or subtracting fractions effectively.