Solve: Adding Mixed Numbers 6⅖ + 1³/₁₄ + 2³/₇ + 1¹/₁₄

To solve this problem, we'll proceed with these steps:

• Step 1: Convert each mixed number to an improper fraction.
• Step 2: Calculate the least common denominator of the fractions.
• Step 3: Express each fraction with this common denominator.
• Step 4: Add the fractions together.
• Step 5: Simplify the result and convert back to a mixed number if necessary.

Let's begin the solution:

Step 1: Convert the mixed numbers to improper fractions:

• $6\frac{2}{7} = \frac{6 \times 7 + 2}{7} = \frac{44}{7}$
• $1\frac{3}{14} = \frac{1 \times 14 + 3}{14} = \frac{17}{14}$
• $2\frac{3}{7} = \frac{2 \times 7 + 3}{7} = \frac{17}{7}$
• $1\frac{1}{14} = \frac{1 \times 14 + 1}{14} = \frac{15}{14}$

Step 2: Determine the least common denominator (LCD). Here, the denominators are 7 and 14. The LCD of 7 and 14 is 14.

Step 3: Express each fraction with the common denominator of 14:

• $\frac{44}{7} = \frac{44 \times 2}{14} = \frac{88}{14}$
• $\frac{17}{14} = \frac{17}{14}$ (already with the denominator 14)
• $\frac{17}{7} = \frac{17 \times 2}{14} = \frac{34}{14}$
• $\frac{15}{14} = \frac{15}{14}$ (already with the denominator 14)

Step 4: Add the fractions together:

$\frac{88}{14} + \frac{17}{14} + \frac{34}{14} + \frac{15}{14} = \frac{154}{14}$

Step 5: Simplify the result:

$\frac{154}{14} = \frac{11 \times 14}{14} = 11$

Thus, the solution to the problem is $11$.