Solve Fraction Addition: 5/6 + 2/3 Step by Step

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

• Step 1: Identify a common denominator for the fractions.
• Step 2: Convert the fractions to equivalent fractions with the common denominator.
• Step 3: Add the fractions by summing the numerators.
• Step 4: Simplify the resulting fraction if necessary.

Now, let's work through each step:

Step 1: Identify a common denominator.
The denominators of the fractions are 6 and 3.
The least common multiple (LCM) of 6 and 3 is 6.

Step 2: Convert each fraction to equivalent fractions with a common denominator.
$\frac{5}{6}$ is already expressed with the denominator 6.
To convert $\frac{2}{3}$ to a fraction with the denominator 6, we multiply both the numerator and the denominator by 2:
$\frac{2}{3} \times \frac{2}{2} = \frac{4}{6}$.

Step 3: Add the fractions.
Now that both fractions have the same denominator, we can add them:
$\frac{5}{6} + \frac{4}{6} = \frac{9}{6}$.

Step 4: Simplify the resulting fraction.
The fraction $\frac{9}{6}$ can be simplified by dividing the numerator and the denominator by their greatest common divisor, which is 3:
$\frac{9}{6} = \frac{9 \div 3}{6 \div 3} = \frac{3}{2}$.

Therefore, the solution to the problem is $\frac{3}{2}$.