Perform the indicated operation, and write each answer in lowest terms. 2x/5 + x/4

Key Concepts

Finding a Common Denominator

To add fractions, it is essential to find a common denominator, which is a shared multiple of the denominators involved. In this case, the denominators are 5 and 4. The least common denominator (LCD) is 20, as it is the smallest number that both denominators can divide into without leaving a remainder.

Adding Fractions

Once a common denominator is established, fractions can be added by converting each fraction to an equivalent fraction with the common denominator. This involves multiplying the numerator and denominator of each fraction by the necessary factors to achieve the common denominator, allowing for straightforward addition of the numerators while keeping the denominator consistent.

Simplifying Fractions

After performing the addition, the resulting fraction may need to be simplified to its lowest terms. This involves dividing both the numerator and the denominator by their greatest common divisor (GCD). Simplifying ensures that the fraction is expressed in the simplest form, making it easier to understand and use in further calculations.