Adding and Subtracting Fractions

To add two fractions, follow these general steps:

1. Find a common denominator: The denominators (bottom numbers) must be the same. If they are different, find the least common denominator (LCD), which is the smallest number both denominators can divide into evenly.

2. Adjust the numerators: Once you’ve found the common denominator, adjust the numerators (top numbers) by multiplying them by the factor used to adjust their denominators.

3. Add the numerators: Add the two adjusted numerators together while keeping the common denominator.

4. Simplify the fraction: If possible, simplify the resulting fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).

Example: $\frac{1}{4} + \frac{2}{5}$

Let’s apply the steps to the example $\frac{1}{4} + \frac{2}{5}$:

1. Find a common denominator:

   • The denominators are 4 and 5.
   • The least common denominator (LCD) is 20 because it’s the smallest number that both 4 and 5 can divide into.

2. Adjust the numerators:

   • For $\frac{1}{4}$, multiply both the numerator and denominator by 5 to get $\frac{1 \times 5}{4 \times 5} = \frac{5}{20}$.
   • For $\frac{2}{5}$, multiply both the numerator and denominator by 4 to get $\frac{2 \times 4}{5 \times 4} = \frac{8}{20}$.

3. Add the numerators:

   • Now add the numerators: $\frac{5}{20} + \frac{8}{20} = \frac{5 + 8}{20} = \frac{13}{20}$.

4. Simplify the fraction:

   • In this case, $\frac{13}{20}$ is already in its simplest form because 13 and 20 have no common factors other than 1.

Final Answer:

$\frac{1}{4} + \frac{2}{5} = \frac{13}{20}$.