To add the fractions 1/4 and 1/3, what common denominator is required?

To add the fractions 1/4 and 1/3, it's essential to find a common denominator. The common denominator must be a multiple of both denominators (4 and 3) so that the fractions can be combined easily.

First, let's identify the denominators: 4 from the first fraction and 3 from the second fraction. To find the least common multiple (LCM) of these two numbers, we consider the multiples of each:

• The multiples of 4 are: 4, 8, 12, 16, …

• The multiples of 3 are: 3, 6, 9, 12, 15, …

The smallest multiple they have in common is 12. Thus, 12 serves as the least common denominator for both fractions.

To convert each fraction to have this common denominator, you would do the following:

• Convert 1/4 to an equivalent fraction with a denominator of 12:

(1 × 3) / (4 × 3) = 3/12.

• Convert 1/3 to an equivalent fraction with a denominator of 12:

(1 × 4) / (3 × 4) =