Before adding or subtracting fractions, what must they have in common?

To add or subtract fractions, it is essential for the fractions to have a common denominator. The denominator is the lower part of a fraction, indicating into how many equal parts the whole is divided. When the denominators are the same, the fractions can be easily combined by keeping the denominator constant and simply adding or subtracting the numerators. This ensures that both fractions are represented with respect to the same whole before any operation is performed.

For instance, consider the fractions 1/4 and 1/2. To add these fractions directly, they must first be converted to a common denominator, which in this case is 4. This results in 1/4 remaining as it is, while 1/2 becomes 2/4. Only then can you add the two fractions together, resulting in a total of 3/4.

When fractions have different denominators, adding them directly without adjusting to a common denominator would yield incorrect results, as it would not accurately represent the proportional values of the fractions in relation to the whole. Therefore, having a common denominator is crucial in fraction addition and subtraction.