Question

Find the sum. $$\frac{2}{5}+\frac{1}{4}$$

Short answer

The sum of the fractions \(\frac{2}{5}\) and \(\frac{1}{4}\) is \(\frac{13}{20}\).

Step-by-step solution

Finding the LCD

The denominators here are 5 and 4. To find the least common denominator (LCD), find the least common multiple (LCM) of the two denominators. The LCM of 5 and 4 is 20.

Convert the Fractions

With the LCD identified as 20, convert each of the fractions to have 20 as the denominator. This is done by multiplying the numerator and the denominator by the same value such that the denominator becomes 20. \[\frac{2}{5} = \frac{2 \times 4}{5 \times 4} = \frac{8}{20}\] and \[\frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}\]

Add the Fractions

Now that both fractions have the same denominators, we can add the numerators: \[\frac{8}{20} + \frac{5}{20} = \frac{8 + 5}{20}= \frac{13}{20}\]