Solve the Fraction Equation: Finding the Missing Addend in 1/2 + ? = 2/5

To solve the problem $\frac{1}{2} + x = \frac{2}{5}$, we need to find $x$. We will achieve this by following these steps:

• Calculate a common denominator for the fractions $\frac{1}{2}$ and $\frac{2}{5}$.
• Subtract $\frac{1}{2}$ from $\frac{2}{5}$ once both fractions have equivalent denominators.
• Determine the simplified result for $x$.

Here's the solution:

Step 1: The denominators for $\frac{1}{2}$ and $\frac{2}{5}$ are 2 and 5. The least common denominator is 10.

Step 2: Convert each fraction to have the denominator of 10.

Convert $\frac{1}{2}$ to $\frac{5}{10}$ because $\frac{1 \cdot 5}{2 \cdot 5} = \frac{5}{10}$.

Convert $\frac{2}{5}$ to $\frac{4}{10}$ because $\frac{2 \cdot 2}{5 \cdot 2} = \frac{4}{10}$.

Step 3: Subtract the converted $\frac{1}{2}$ from $\frac{2}{5}$.

This gives us $\frac{4}{10} - \frac{5}{10} = -\frac{1}{10}$.

Therefore, the value of $x$ that satisfies the equation is $-\frac{1}{10}$.