Solve: 2/7 + 1/2 - 7/14 Fraction Operation Challenge

Solve the following exercise:

$\frac{2}{7}+\frac{1}{2}-\frac{7}{14}=\text{?}$

To solve the expression $\frac{2}{7} + \frac{1}{2} - \frac{7}{14}$, we need to add and subtract fractions, which requires a common denominator.

• Step 1: Identify the denominators and find the least common denominator (LCD):
  • The denominators are 7, 2, and 14.
  • The LCM of 7, 2, and 14 is 14.
• Step 2: Convert each fraction to have the denominator 14:
  • $\frac{2}{7} = \frac{2 \times 2}{7 \times 2} = \frac{4}{14}$
  • $\frac{1}{2} = \frac{1 \times 7}{2 \times 7} = \frac{7}{14}$
  • $\frac{7}{14}$ is already in the form with denominator 14.
• Step 3: Perform the operations using the common denominator:
  • Add the first two fractions: $\frac{4}{14} + \frac{7}{14} = \frac{11}{14}$
  • Subtract the third fraction: $\frac{11}{14} - \frac{7}{14} = \frac{4}{14}$
• Step 4: Simplify the result if necessary:
  • $\frac{4}{14}$ is already simplified to its simplest form.

Therefore, the solution to the expression $\frac{2}{7} + \frac{1}{2} - \frac{7}{14}$ is $\frac{4}{14}$, which matches choice 3.