Solve the Fraction Addition: 2/6 + 5/12 Step-by-Step

To solve this problem, we'll follow these steps:

• Step 1: Identify the least common denominator (LCD) for the given fractions.
• Step 2: Convert each fraction to an equivalent fraction with this common denominator.
• Step 3: Add the numerators, keeping the denominator unchanged.
• Step 4: Simplify the resultant fraction if possible.

Now, let's work through each step:

Step 1: Identify the least common denominator (LCD).
The denominators are 6 and 12. The smallest number that both 6 and 12 divide evenly into is 12. Therefore, the LCD is 12.

Step 2: Convert the fractions to have the LCD as their denominator.
$\frac{2}{6}$ needs to be converted to a fraction with a denominator of 12. We multiply both the numerator and denominator by 2:

$\frac{2 \times 2}{6 \times 2} = \frac{4}{12}$.

The second fraction, $\frac{5}{12}$, already has the denominator of 12, so it remains $\frac{5}{12}$.

Step 3: Add the two fractions:
$\frac{4}{12} + \frac{5}{12} = \frac{4 + 5}{12} = \frac{9}{12}$.

Step 4: Simplify the fraction.
The fraction $\frac{9}{12}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3:

$\frac{9 \div 3}{12 \div 3} = \frac{3}{4}$.

Therefore, after fully simplifying, the sum of the fractions is $\frac{3}{4}$.