Solve Fraction Addition: 1/2 + 2/7 Step-by-Step

Solve the following exercise:

$\frac{1}{2}+\frac{2}{7}=\text{?}$

To solve the given problem of adding two fractions $\frac{1}{2}$ and $\frac{2}{7}$, follow these steps:

• Step 1: Determine the common denominator.

The denominators of the fractions are $2$ and $7$. Multiply these two numbers to find the common denominator: $2 \times 7 = 14$.

• Step 2: Adjust each fraction to have the common denominator.

Convert $\frac{1}{2}$ to an equivalent fraction with a denominator of $14$:
$\frac{1}{2} = \frac{1 \times 7}{2 \times 7} = \frac{7}{14}$

Convert $\frac{2}{7}$ to an equivalent fraction with a denominator of $14$:
$\frac{2}{7} = \frac{2 \times 2}{7 \times 2} = \frac{4}{14}$

• Step 3: Add the adjusted fractions.

Now that both fractions have a common denominator, add them:
$\frac{7}{14} + \frac{4}{14} = \frac{7 + 4}{14} = \frac{11}{14}$

We have successfully added the fractions and obtained the result.

Therefore, the solution to the problem is $\frac{11}{14}$.