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When adding fractions, the key is to make sure the parts we are adding are the same size. The size of these parts is determined by the denominator. The denominator is the bottom number of a fraction, and it tells us into how many equal parts the whole is divided. Common denominator means that the denominators of the fractions must be the same before you can directly add or subtract the numerators. In the problem \(\frac{2}{5} + \frac{1}{5}\), both fractions already have the common denominator of 5. This makes the addition straightforward. If the denominators weren't the same, you would need to find a common denominator, which often involves finding the least common multiple (LCM) of the two denominators.

The numerator is the top number in a fraction and indicates how many parts we have. In the given problem \(\frac{2}{5} + \frac{1}{5}\), we first check the numerators. For the fraction \(\frac{2}{5}\), the numerator is 2, and for \(\frac{1}{5}\), it is 1. When the denominators are the same, adding fractions is a matter of adding these numerators. So, we add 2 and 1, which equals 3. This means we now have 3 parts of our fraction.

Adding fractions follows a simple process when the denominators are the same. Here are the steps in this example:

• Step 1: Ensure the denominators are the same. For \(\frac{2}{5} + \frac{1}{5}\), the denominator is 5 for both fractions.
• Step 2: Add the numerators. This gives us \(2+1 = 3\).
• Step 3: Place the sum of the numerators over the common denominator. The result is \(\frac{3}{5}\).

If the denominators were different, additional steps would be required to find a common denominator. In such situations, rewrite each fraction with the new common denominator before performing the addition.